diff --git a/docs/.buildinfo b/docs/.buildinfo new file mode 100644 index 0000000..79e3920 --- /dev/null +++ b/docs/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 460f45d6faf9867abf533d23c6816ee9 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/.nojekyll b/docs/.nojekyll new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/docs/.nojekyll @@ -0,0 +1 @@ + diff --git a/docs/.nojekyll copy b/docs/.nojekyll copy new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/docs/.nojekyll copy @@ -0,0 +1 @@ + diff --git a/docs/2phase.html b/docs/2phase.html new file mode 100644 index 0000000..6df4792 --- /dev/null +++ b/docs/2phase.html @@ -0,0 +1,125 @@ + + + + + + + 2phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

2phase

+
+

Contents:

+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/2phase.rst b/docs/2phase.rst new file mode 100644 index 0000000..d0d402f --- /dev/null +++ b/docs/2phase.rst @@ -0,0 +1,11 @@ +2phase +============== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + twophase/lbm_solver_3d_2phase_sparse + twophase/lbm_solver_3d_2phase + + diff --git a/docs/Convert_stl_to_binary.html b/docs/Convert_stl_to_binary.html new file mode 100644 index 0000000..9a97016 --- /dev/null +++ b/docs/Convert_stl_to_binary.html @@ -0,0 +1,126 @@ + + + + + + + Convert_stl_to_binary — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Convert_stl_to_binary

+

This file reads the stl file and output to vtk file

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Grey_Scale.html b/docs/Grey_Scale.html new file mode 100644 index 0000000..5485831 --- /dev/null +++ b/docs/Grey_Scale.html @@ -0,0 +1,125 @@ + + + + + + + Grey_Scale — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Grey_Scale

+
+

Contents:

+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Grey_Scale.rst b/docs/Grey_Scale.rst new file mode 100644 index 0000000..ef21d69 --- /dev/null +++ b/docs/Grey_Scale.rst @@ -0,0 +1,10 @@ +Grey\_Scale +=================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Grey_scale/flow_domain_geo_generation + Grey_scale/lbm_solver_3d_Macro_Sukop + diff --git a/docs/Grey_scale/flow_domain_geo_generation.html b/docs/Grey_scale/flow_domain_geo_generation.html new file mode 100644 index 0000000..ea8bf17 --- /dev/null +++ b/docs/Grey_scale/flow_domain_geo_generation.html @@ -0,0 +1,149 @@ + + + + + + + flow_domain_geo_generation — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation

+

This file output geometry data

+
#import numpy and math packahe
+import numpy as np
+import math
+
+
+# INPUT STL FILE NAME
+output_name = 'geo.dat'
+
+# POINT SEARCHING RESOLUTION IN X direction, Y,Z direction will be calculate by the code
+# the bigger value ~ more points will be found inside STL
+dnx, dny, dnz = 60, 60, 60
+
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+#create np matrix with dnx*dny*dnz zero
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#out_dat[1,:,:] = 1
+
+#=========================================================
+#reshape out_dat with column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+#save the file with the transfer of out_dat based on integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Grey_scale/flow_domain_geo_generation.rst b/docs/Grey_scale/flow_domain_geo_generation.rst new file mode 100644 index 0000000..bf4c4a7 --- /dev/null +++ b/docs/Grey_scale/flow_domain_geo_generation.rst @@ -0,0 +1,34 @@ +flow_domain_geo_generation +================================= + +This file output geometry data + +.. code-block:: python + + #import numpy and math packahe + import numpy as np + import math + + + # INPUT STL FILE NAME + output_name = 'geo.dat' + + # POINT SEARCHING RESOLUTION IN X direction, Y,Z direction will be calculate by the code + # the bigger value ~ more points will be found inside STL + dnx, dny, dnz = 60, 60, 60 + + + #========================================================== + # DO NOT CHANGE BELOW + #========================================================== + #create np matrix with dnx*dny*dnz zero + out_dat = np.zeros((dnx,dny,dnz)) + + #=======Can define some geometry here to out_dat========= + #out_dat[1,:,:] = 1 + + #========================================================= + #reshape out_dat with column major + out_dat = out_dat.reshape(out_dat.size, order = 'F') + #save the file with the transfer of out_dat based on integer type + np.savetxt(output_name,out_dat.T,fmt='%d') \ No newline at end of file diff --git a/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.html b/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.html new file mode 100644 index 0000000..5668cf1 --- /dev/null +++ b/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.html @@ -0,0 +1,185 @@ + + + + + + + lbm_solver_3d_Macro_Sukop — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_Macro_Sukop

+

This solver is almost similar to lbm_solver_3d expect several difference as follows:

+
    +

  1. Some parameter is different

    2. +
+
#grid resolution
+nx,ny,nz = 60,50,5
+#external force
+fx,fy,fz = 1.0e-6,0.0,0.0
+#viscosity
+niu = 0.1
+#import geometry
+geo_name = './BC.dat'
+#maximum timestep
+max_timestep = 5000
+#output frequency
+output_fre = 100
+#vtk file output frequency
+vtk_fre = 500
+
+
+
    +

  1. There are two array for solid flag data.

    2. +
+
ns_np = init_geo(geo_name)
+solid_np = ns_np.astype(int)
+#solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+ns.from_numpy(ns_np)
+
+
+
    +

  1. The streaming function is different

    2. +
+
@ti.kernel
+def streaming0():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            for s in ti.static(range(19)):
+                ip = periodic_index(i+e[s])
+                #if it is fluid f2=f otherwise apply bounce-back f2[i,s]=f[ip,LR[s]]
+                f2[i,s] = f[i,s] + ns[i]*(f[ip,LR[s]] - f[i,s])
+
+
+@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            #if it is fluid apply streaming
+            for s in ti.static(range(19)):
+                ip = periodic_index(i+e[s])
+                F[ip,s] = f2[i,s]
+
+                #if (solid[ip]==0):
+                #    F[ip,s] = f[i,s]
+                #else:
+                #    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+#not used
+@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in ti.static(range(19)):
+            f[i,s] = F[i,s]
+
+
+

streaming3() calculates the macroscopic variable

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.rst b/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.rst new file mode 100644 index 0000000..26eb0cc --- /dev/null +++ b/docs/Grey_scale/lbm_solver_3d_Macro_Sukop.rst @@ -0,0 +1,70 @@ +lbm_solver_3d_Macro_Sukop +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. Some parameter is different + +.. code-block:: python + + #grid resolution + nx,ny,nz = 60,50,5 + #external force + fx,fy,fz = 1.0e-6,0.0,0.0 + #viscosity + niu = 0.1 + #import geometry + geo_name = './BC.dat' + #maximum timestep + max_timestep = 5000 + #output frequency + output_fre = 100 + #vtk file output frequency + vtk_fre = 500 + +2. There are two array for solid flag data. + +.. code-block:: python + + ns_np = init_geo(geo_name) + solid_np = ns_np.astype(int) + #solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + ns.from_numpy(ns_np) + +3. The streaming function is different + +.. code-block:: python + + @ti.kernel + def streaming0(): + for i in ti.grouped(rho): + if (solid[i] == 0): + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + #if it is fluid f2=f otherwise apply bounce-back f2[i,s]=f[ip,LR[s]] + f2[i,s] = f[i,s] + ns[i]*(f[ip,LR[s]] - f[i,s]) + + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + if (solid[i] == 0): + #if it is fluid apply streaming + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + F[ip,s] = f2[i,s] + + #if (solid[ip]==0): + # F[ip,s] = f[i,s] + #else: + # F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + #not used + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in ti.static(range(19)): + f[i,s] = F[i,s] + +``streaming3()`` calculates the macroscopic variable \ No newline at end of file diff --git a/docs/LBM_3D_SinglePhase_Solver.html b/docs/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..2a694db --- /dev/null +++ b/docs/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,660 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 0000000..d4bb2cb --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = . +BUILDDIR = _build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/docs/Phase_change.html b/docs/Phase_change.html new file mode 100644 index 0000000..3d736f6 --- /dev/null +++ b/docs/Phase_change.html @@ -0,0 +1,135 @@ + + + + + + + Phase_change — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Phase_change.rst b/docs/Phase_change.rst new file mode 100644 index 0000000..485b770 --- /dev/null +++ b/docs/Phase_change.rst @@ -0,0 +1,15 @@ +Phase\_change +===================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + phasechange/example_cavity_melting + phasechange/example_phase_change + phasechange/LBM_3D_SinglePhase_Solute_Solver + phasechange/LBM_3D_SinglePhase_Solver + phasechange/read_img_solute_psi_generation_2D + phasechange/solute_psi_generation_2D + phasechange/test1 + diff --git a/docs/Single_phase.LBM_3D_SinglePhase_Solver.html b/docs/Single_phase.LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..3ff0dd7 --- /dev/null +++ b/docs/Single_phase.LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,644 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase.example_cavity.html b/docs/Single_phase.example_cavity.html new file mode 100644 index 0000000..7668e20 --- /dev/null +++ b/docs/Single_phase.example_cavity.html @@ -0,0 +1,119 @@ + + + + + + + Single_phase_example — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase_example

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase.html b/docs/Single_phase.html new file mode 100644 index 0000000..21fdb62 --- /dev/null +++ b/docs/Single_phase.html @@ -0,0 +1,137 @@ + + + + + + + Single_phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase.lbm_solver_3d.html b/docs/Single_phase.lbm_solver_3d.html new file mode 100644 index 0000000..b6c4821 --- /dev/null +++ b/docs/Single_phase.lbm_solver_3d.html @@ -0,0 +1,425 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

this

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

``

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

this

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        if (solid[i,j,k] == 0):
+            m_temp = multiply_M(i,j,k)
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

this

+
@ti.func
+def periodic_index(i):
+    iout = i
+    if i[0]<0:     iout[0] = nx-1
+    if i[0]>nx-1:  iout[0] = 0
+    if i[1]<0:     iout[1] = ny-1
+    if i[1]>ny-1:  iout[1] = 0
+    if i[2]<0:     iout[2] = nz-1
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

this

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            for s in range(19):
+                ip = periodic_index(i+e[s])
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

this

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

this

+
@ti.kernel
+def Boundary_condition():
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

this

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

this

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase.rst b/docs/Single_phase.rst new file mode 100644 index 0000000..d66928e --- /dev/null +++ b/docs/Single_phase.rst @@ -0,0 +1,20 @@ +Single\_phase +===================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Single_phase/LBM_3D_SinglePhase_Solver + Single_phase/lbm_solver_3d + Single_phase/lbm_solver_3d_cavity + Single_phase/lbm_solver_3d_sparse + Single_phase/flow_domain_geo_generation_2D + Single_phase/example_cavity + Single_phase/example_porous_medium + Single_phase/Convert_stl_to_binary + + + + + diff --git a/docs/Single_phase/Convert_stl_to_binary.html b/docs/Single_phase/Convert_stl_to_binary.html new file mode 100644 index 0000000..a9d5677 --- /dev/null +++ b/docs/Single_phase/Convert_stl_to_binary.html @@ -0,0 +1,126 @@ + + + + + + + Convert_stl_to_binary — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Convert_stl_to_binary

+

This file reads the stl file and output to vtk file

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/Convert_stl_to_binary.rst b/docs/Single_phase/Convert_stl_to_binary.rst new file mode 100644 index 0000000..edf04e6 --- /dev/null +++ b/docs/Single_phase/Convert_stl_to_binary.rst @@ -0,0 +1,4 @@ +Convert_stl_to_binary +================================= + +This file reads the stl file and output to vtk file \ No newline at end of file diff --git a/docs/Single_phase/LBM_3D_SinglePhase_Solver.html b/docs/Single_phase/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..37c70ec --- /dev/null +++ b/docs/Single_phase/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,667 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/LBM_3D_SinglePhase_Solver.rst b/docs/Single_phase/LBM_3D_SinglePhase_Solver.rst new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/Single_phase/LBM_3D_SinglePhase_Solver.rst @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.x + + + + + + example_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_cavity

+

This file use the LBM_3D_SinglePhase_Solver to simulate the cavity flow

+
#import certain packages
+import time
+import taichi as ti
+
+ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#set 50*50*50 cavity based on LB3D_Solver_Single_Phase solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=50,ny=50,nz=50, sparse_storage=False)
+
+#import geometry data
+lb3d.init_geo('./geo_cavity.dat')
+#set the x-right velocity
+lb3d.set_bc_vel_x1([0.0,0.0,0.1])
+#initialize
+lb3d.init_simulation()
+
+#simulation step
+for iter in range(2000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #get the maximum velocity
+        max_v = lb3d.get_max_v()
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the number of time steps, maxiumum force and the force scale=0
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, max_v,  0.0))
+        #every 1000 time steps export the vtk file
+        if (iter%1000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/example_cavity.rst b/docs/Single_phase/example_cavity.rst new file mode 100644 index 0000000..d3b2b17 --- /dev/null +++ b/docs/Single_phase/example_cavity.rst @@ -0,0 +1,52 @@ +example_cavity +================================= + +This file use the LBM_3D_SinglePhase_Solver to simulate the cavity flow + +.. code-block:: python + + #import certain packages + import time + import taichi as ti + + ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False) + import LBM_3D_SinglePhase_Solver as lb3dsp + #set the time + time_init = time.time() + time_now = time.time() + time_pre = time.time() + + #set 50*50*50 cavity based on LB3D_Solver_Single_Phase solver + lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=50,ny=50,nz=50, sparse_storage=False) + + #import geometry data + lb3d.init_geo('./geo_cavity.dat') + #set the x-right velocity + lb3d.set_bc_vel_x1([0.0,0.0,0.1]) + #initialize + lb3d.init_simulation() + + #simulation step + for iter in range(2000+1): + lb3d.step() + + if (iter%500==0): + + #calculate the time + time_pre = time_now + time_now = time.time() + diff_time = int(time_now-time_pre) + elap_time = int(time_now-time_init) + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + #get the maximum velocity + max_v = lb3d.get_max_v() + #print the time + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + #print the number of time steps, maxiumum force and the force scale=0 + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, max_v, 0.0)) + #every 1000 time steps export the vtk file + if (iter%1000==0): + lb3d.export_VTK(iter) \ No newline at end of file diff --git a/docs/Single_phase/example_porous_medium.html b/docs/Single_phase/example_porous_medium.html new file mode 100644 index 0000000..2d11834 --- /dev/null +++ b/docs/Single_phase/example_porous_medium.html @@ -0,0 +1,170 @@ + + + + + + + example_porous_medium — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_porous_medium

+

This file simulate the porous medium based on the LBM_3D_SinglePhase_Solver

+
#import time and taichi package
+import time
+import taichi as ti
+#taichi intialization
+ti.init(arch=ti.cpu)
+#import the LBM_3D_SinglePhase_Solver
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#create the 131*131*131 gird LBM_3D_SinglePhase_Solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=131,ny=131,nz=131)
+#import the porous medium geometry
+lb3d.init_geo('./img_ftb131.txt')
+#set x-left and x-right density
+lb3d.set_bc_rho_x1(0.99)
+lb3d.set_bc_rho_x0(1.0)
+#initialize the simulation
+lb3d.init_simulation()
+#simulation loop
+for iter in range(50000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the time step, max force=10, force_scale=10
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+        #export VTK every 2000 time step
+        if (iter%2000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/example_porous_medium.rst b/docs/Single_phase/example_porous_medium.rst new file mode 100644 index 0000000..fb47072 --- /dev/null +++ b/docs/Single_phase/example_porous_medium.rst @@ -0,0 +1,49 @@ +example_porous_medium +================================= + +This file simulate the porous medium based on the LBM_3D_SinglePhase_Solver + +.. code-block:: python + + #import time and taichi package + import time + import taichi as ti + #taichi intialization + ti.init(arch=ti.cpu) + #import the LBM_3D_SinglePhase_Solver + import LBM_3D_SinglePhase_Solver as lb3dsp + #set the time + time_init = time.time() + time_now = time.time() + time_pre = time.time() + + #create the 131*131*131 gird LBM_3D_SinglePhase_Solver + lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=131,ny=131,nz=131) + #import the porous medium geometry + lb3d.init_geo('./img_ftb131.txt') + #set x-left and x-right density + lb3d.set_bc_rho_x1(0.99) + lb3d.set_bc_rho_x0(1.0) + #initialize the simulation + lb3d.init_simulation() + #simulation loop + for iter in range(50000+1): + lb3d.step() + + if (iter%500==0): + #calculate the time + time_pre = time_now + time_now = time.time() + diff_time = int(time_now-time_pre) + elap_time = int(time_now-time_init) + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + #print the time + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + #print the time step, max force=10, force_scale=10 + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + #export VTK every 2000 time step + if (iter%2000==0): + lb3d.export_VTK(iter) \ No newline at end of file diff --git a/docs/Single_phase/flow_domain_geo_generation_2D.html b/docs/Single_phase/flow_domain_geo_generation_2D.html new file mode 100644 index 0000000..5ed62c6 --- /dev/null +++ b/docs/Single_phase/flow_domain_geo_generation_2D.html @@ -0,0 +1,163 @@ + + + + + + + flow_domain_geo_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation_2D

+

This file generate geometry file for solver to read

+
#import certain module
+import numpy as np
+import math
+
+
+#define the input file name
+# INPUT STL FILE NAME
+output_name = 'geo_cavity.dat'
+
+#define the grid resolution
+dnx, dny, dnz = 50, 50, 50
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+
+#define an matrix dnx*dny*dnz with zero values
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#define the boundary to be solid
+out_dat[0,:,:] = 1
+#cout_dat[:,:,0] = 1
+out_dat[:,0,:] = 1
+out_dat[:,-1,:] = 1
+out_dat[:,:,0] = 1
+out_dat[:,:,-1] = 1
+
+#=========================================================
+#reshape the data to be column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+
+
+#output the transfer of out_dat to the file with integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/flow_domain_geo_generation_2D.rst b/docs/Single_phase/flow_domain_geo_generation_2D.rst new file mode 100644 index 0000000..d12b8e1 --- /dev/null +++ b/docs/Single_phase/flow_domain_geo_generation_2D.rst @@ -0,0 +1,42 @@ +flow_domain_geo_generation_2D +================================= + +This file generate geometry file for solver to read + +.. code-block:: python + + #import certain module + import numpy as np + import math + + + #define the input file name + # INPUT STL FILE NAME + output_name = 'geo_cavity.dat' + + #define the grid resolution + dnx, dny, dnz = 50, 50, 50 + + #========================================================== + # DO NOT CHANGE BELOW + #========================================================== + + #define an matrix dnx*dny*dnz with zero values + out_dat = np.zeros((dnx,dny,dnz)) + + #=======Can define some geometry here to out_dat========= + #define the boundary to be solid + out_dat[0,:,:] = 1 + #cout_dat[:,:,0] = 1 + out_dat[:,0,:] = 1 + out_dat[:,-1,:] = 1 + out_dat[:,:,0] = 1 + out_dat[:,:,-1] = 1 + + #========================================================= + #reshape the data to be column major + out_dat = out_dat.reshape(out_dat.size, order = 'F') + + + #output the transfer of out_dat to the file with integer type + np.savetxt(output_name,out_dat.T,fmt='%d') \ No newline at end of file diff --git a/docs/Single_phase/lbm_solver_3d.html b/docs/Single_phase/lbm_solver_3d.html new file mode 100644 index 0000000..9007848 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d.html @@ -0,0 +1,536 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s Force scheme

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+    #calculate Guo's force here
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) calculate equilibrium density distribution function in momentum space

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

collison() define the prcoess of collision

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is fluid
+        if (solid[i,j,k] == 0):
+            #calculate m
+            m_temp = multiply_M(i,j,k)
+            #calculate meq
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                #calculate -s*(m-meq)
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #add Guo's force
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    #f=-M^-1*S(m-meq)
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

periodic_index(i) set the bounary index with periodic bounary condition

+
@ti.func
+def periodic_index(i):
+    #inner index
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = nx-1
+    #x-right
+    if i[0]>nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = ny-1
+    #y-right
+    if i[1]>ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = nz-1
+    #z-right
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming process of denisty distibution function

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        #if it is fluid
+        if (solid[i] == 0):
+            for s in range(19):
+                #the neighbour index
+                ip = periodic_index(i+e[s])
+                #if neighbour index is fluid just streaming
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                #if neighbour index is solid just bounce back
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

streaming2() a simple streaming process without consideration of solid and boundary

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

Boudary_condition() define the bounary condition of fixed pressure and fixed velocity

+
@ti.kernel
+def Boundary_condition():
+    #pressure-boundary condtion x-left
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #if boundary is fluid but the neighbour is solid
+                #equilibrium density distribution function is calculated based on the neighbour velocity
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                #if boundary is fluid and the neighbour is also fluid
+                #equilibrium density distribution function is calculated based on the boundary velocity
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    #velocity-boundary conditon x-left
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #calculate density distribution fucntion based on equilibrium part and non-equilibrium part
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    #pressure boundary condition x-right similar to x-left
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    #velocity booundary condition x-right similar to x-left
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

streaming3() calculate the macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        #if it is fluid calculate density and velocity based on density distribution function
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+        # if it is solid set denisty equals one and velocity equals zero
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

At the end of the file do the actual simulation and export the data

+
#define some time varible
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+#import the solid flag data
+#solid_np = init_geo('./BC.dat')
+solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+
+# do the initialization
+static_init()
+init()
+
+# do the actual simulation
+for iter in range(50000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    # calculate every 1000 time step
+    if (iter%1000==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        #calculate the time difference between now and previous time step
+        diff_time = int(time_now-time_pre)
+        #calculate the time difference between now and the initial time
+        elap_time = int(time_now-time_init)
+        #divmod function return the quotient and the remainder
+        #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2]))
+                            }
+            )
+# ti.sync()
+# ti.profiler.print_kernel_profiler_info()
+#print the profiler information of every kernel and task of taichi in this file
+ti.profiler.print_scoped_profiler_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/lbm_solver_3d.rst b/docs/Single_phase/lbm_solver_3d.rst new file mode 100644 index 0000000..c8df414 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d.rst @@ -0,0 +1,443 @@ +Single\_phase.lbm\_solver\_3d +================================= +This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first. + +.. code-block:: python + + #import some package + import taichi as ti + import numpy as np + from pyevtk.hl import gridToVTK + import time + #initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation + ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False) + #enable projection + enable_projection = True + #nx,ny,nz = 100,50,5 + #define 131x131x131 and zero external force + nx,ny,nz = 131,131,131 + fx,fy,fz = 0.0e-6,0.0,0.0 + #viscosity=0.1 + niu = 0.1 + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + + #define old density distribution funciton nx*ny*nz*19 + f = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #define new density distribution function nx*ny*nz*19 + F = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #define density nx*ny*nz + rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity nx*ny*nz + v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + #define lattice speed 3*19 + e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagonal 19 dimension vector + S_dig = ti.field(ti.f32,shape=(19)) + #define another lattice speed 3*19 + e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter 19 dimesnion vector + w = ti.field(ti.f32, shape=(19)) + #define solid flag nx*ny*nz + solid = ti.field(ti.i32,shape=(nx,ny,nz)) + #define vector for streaming 19 dimensional vector + LR = ti.field(ti.i32,shape=(19)) + #define external force with a 3 dimensional vector + ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define velocity in x,y,z direction with 3 dimensional vector + bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=()) + bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=()) + bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=()) + bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=()) + bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=()) + bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=()) + #define transforming matrix 19*19 + M = ti.field(ti.f32, shape=(19,19)) + #define inverse of transforming matrix + inv_M = ti.field(ti.f32, shape=(19,19)) + #define single relaxation parameter + tau_f=3.0*niu+0.5 + #define single relaxation frequency + s_v=1.0/tau_f + #define other parameter in the s diagonal + s_other=8.0*(2.0-s_v)/(8.0-s_v) + #define s matrix but not used + S_np = np.zeros((19,19)) + S_np[0,0]=0; S_np[1,1]=s_v; S_np[2,2]=s_v; S_np[3,3]=0; S_np[4,4]=s_other; S_np[5,5]=0; + S_np[6,6]=s_other; S_np[7,7]=0; S_np[8,8]=s_other; S_np[9,9]=s_v; S_np[10,10]=s_v; S_np[11,11]=s_v; + S_np[12,12]=s_v; S_np[13,13]=s_v; S_np[14,14]=s_v; S_np[15,15]=s_v; S_np[16,16]=s_other; S_np[17,17]=s_other; + S_np[18,18]=s_other + #define numpy array version of s diagonal. + S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other]) + #define numpy version of transforming matrix + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define inverse of transforming matrix using inv function in linalg package + inv_M_np = np.linalg.inv(M_np) + #define index for streaming + LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]) + #assign numpy version to M.np to M + M.from_numpy(M_np) + #assign numpy version of inverser matrix inv_M_np to inv_M + inv_M.from_numpy(inv_M_np) + #assign numpy versio of LR array to LR + LR.from_numpy(LR_np) + #assign fx,fy,fz to vector external force + ext_f[None] = ti.Vector([fx,fy,fz]) + #assign numpy version of S diagnal S_dig_np to S_dig + S_dig.from_numpy(S_dig_np) + #make inv_M,M,LR,S_dig not modified + ti.static(inv_M) + ti.static(M) + ti.static(LR) + ti.static(S_dig) + + #create mesh nx*ny*nz + x = np.linspace(0, nx, nx) + y = np.linspace(0, ny, ny) + z = np.linspace(0, nz, nz) + #numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing + X, Y, Z = np.meshgrid(x, y, z, indexing='ij') + +``feq(k,rho_local,u)`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + # taichi funciton + @ti.func + def feq(k,rho_local, u): + eu = e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, w[k]) + return feqout + +``init()`` initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function + +.. code-block:: python + + @ti.kernel + def init(): + for i,j,k in rho: + rho[i,j,k] = 1.0 + v[i,j,k] = ti.Vector([0,0,0]) + for s in range(19): + f[i,j,k,s] = feq(s,1.0,v[i,j,k]) + F[i,j,k,s] = feq(s,1.0,v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` load geometry file + +.. code-block:: python + + def init_geo(filename): + #load data + in_dat = np.loadtxt(filename) + #reshape it with column major + in_dat = np.reshape(in_dat, (nx,ny,nz),order='F') + return in_dat + +``static_init()`` initialize lattixe speed weight parameter and boundary velocity + +.. code-block:: python + + @ti.kernel + def static_init(): + if ti.static(enable_projection): # No runtime overhead + #initialize lattice speed + e[0] = ti.Vector([0,0,0]) + e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1]) + e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0]) + e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1]) + e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1]) + #initialize lattice speed + e_f[0] = ti.Vector([0,0,0]) + e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1]) + e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0]) + e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1]) + e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1]) + #intialize weight parameter + w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0; + w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0; + w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0; + #intialize boundary velocity + bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl]) + bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr]) + bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl]) + bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr]) + bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl]) + bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr]) + +``multiply_M`` calculate denisty distribution function in momentum space M*f=m + +.. code-block:: python + + @ti.func + def multiply_M(i,j,k): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + for index in range(19): + for s in range(19): + #calculte m=M*f here + out[index] += M[index,s]*F[i,j,k,s] + #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s]) + return out + +``GuoF(i,j,k,s,u)`` calculate Guo's Force scheme + +.. code-block:: python + + @ti.func + def GuoF(i,j,k,s,u): + out=0.0 + for l in range(19): + #calculate Guo's force here + out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l] + + return out + +``meq_vec(rho_local,u)`` calculate equilibrium density distribution function in momentum space + +.. code-block:: python + + @ti.func + def meq_vec(rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``collison()`` define the prcoess of collision + +.. code-block:: python + + @ti.kernel + def colission(): + for i,j,k in rho: + #if it is fluid + if (solid[i,j,k] == 0): + #calculate m + m_temp = multiply_M(i,j,k) + #calculate meq + meq = meq_vec(rho[i,j,k],v[i,j,k]) + for s in range(19): + #calculate -s*(m-meq) + m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s]) + #add Guo's force + m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k]) + + for s in range(19): + f[i,j,k,s] = 0 + for l in range(19): + #f=-M^-1*S(m-meq) + f[i,j,k,s] += inv_M[s,l]*m_temp[l] + +``periodic_index(i)`` set the bounary index with periodic bounary condition + +.. code-block:: python + + @ti.func + def periodic_index(i): + #inner index + iout = i + #x-left + if i[0]<0: iout[0] = nx-1 + #x-right + if i[0]>nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = ny-1 + #y-right + if i[1]>ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = nz-1 + #z-right + if i[2]>nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming process of denisty distibution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + #if it is fluid + if (solid[i] == 0): + for s in range(19): + #the neighbour index + ip = periodic_index(i+e[s]) + #if neighbour index is fluid just streaming + if (solid[ip]==0): + F[ip,s] = f[i,s] + #if neighbour index is solid just bounce back + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +``streaming2()`` a simple streaming process without consideration of solid and boundary + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +``Boudary_condition()`` define the bounary condition of fixed pressure and fixed velocity + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + #pressure-boundary condtion x-left + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #if boundary is fluid but the neighbour is solid + #equilibrium density distribution function is calculated based on the neighbour velocity + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + #if boundary is fluid and the neighbour is also fluid + #equilibrium density distribution function is calculated based on the boundary velocity + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + #velocity-boundary conditon x-left + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #calculate density distribution fucntion based on equilibrium part and non-equilibrium part + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + #pressure boundary condition x-right similar to x-left + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + #velocity booundary condition x-right similar to x-left + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + + +``streaming3()`` calculate the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + #if it is fluid calculate density and velocity based on density distribution function + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + # if it is solid set denisty equals one and velocity equals zero + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +At the end of the file do the actual simulation and export the data + +.. code-block:: python + + #define some time varible + time_init = time.time() + time_now = time.time() + time_pre = time.time() + dt_count = 0 + + #import the solid flag data + #solid_np = init_geo('./BC.dat') + solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + + # do the initialization + static_init() + init() + + # do the actual simulation + for iter in range(50000+1): + colission() + streaming1() + Boundary_condition() + #streaming2() + streaming3() + # calculate every 1000 time step + if (iter%1000==0): + + time_pre = time_now + time_now = time.time() + #calculate the time difference between now and previous time step + diff_time = int(time_now-time_pre) + #calculate the time difference between now and the initial time + elap_time = int(time_now-time_init) + #divmod function return the quotient and the remainder + #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + + #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable + if (iter%10000==0): + gridToVTK( + "./structured"+str(iter), + x, + y, + z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()), + "rho": np.ascontiguousarray(rho.to_numpy()), + "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2])) + } + ) + # ti.sync() + # ti.profiler.print_kernel_profiler_info() + #print the profiler information of every kernel and task of taichi in this file + ti.profiler.print_scoped_profiler_info() diff --git a/docs/Single_phase/lbm_solver_3d_cavity.html b/docs/Single_phase/lbm_solver_3d_cavity.html new file mode 100644 index 0000000..f851f46 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d_cavity.html @@ -0,0 +1,155 @@ + + + + + + + lbm_solver_3d_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_cavity

+

This solver is almost similar to lbm_solver_3d expect several difference as follows:

+
    +

  1. The Grid resolution in this solver is 50x50x50

    2. +

  2. The viscosity in this solver is 0.16667

    3. +

  3. The boundary condition in this solver is velocity solver on x-right as follows

    4. +
+

boundary condition of this solver

+
#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+
+

x-right is implementated with velocity boundary condition

+

4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary.

+
if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left))
+
+
+
    +

  1. Finally, the definition of the varible is slightly different from lbm_solver_3d

    2. +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/lbm_solver_3d_cavity.rst b/docs/Single_phase/lbm_solver_3d_cavity.rst new file mode 100644 index 0000000..08d16d9 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d_cavity.rst @@ -0,0 +1,37 @@ +lbm_solver_3d_cavity +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. The Grid resolution in this solver is 50x50x50 +2. The viscosity in this solver is 0.16667 +3. The boundary condition in this solver is velocity solver on x-right as follows + +boundary condition of this solver + +.. code-block:: python + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + +x-right is implementated with velocity boundary condition + +4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary. + +.. code-block:: python + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left)) + + +5. Finally, the definition of the varible is slightly different from lbm_solver_3d \ No newline at end of file diff --git a/docs/Single_phase/lbm_solver_3d_sparse.html b/docs/Single_phase/lbm_solver_3d_sparse.html new file mode 100644 index 0000000..9064c37 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d_sparse.html @@ -0,0 +1,143 @@ + + + + + + + lbm_solver_3d_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_sparse

+

This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible:

+
f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse.

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/Single_phase/lbm_solver_3d_sparse.rst b/docs/Single_phase/lbm_solver_3d_sparse.rst new file mode 100644 index 0000000..d76a344 --- /dev/null +++ b/docs/Single_phase/lbm_solver_3d_sparse.rst @@ -0,0 +1,24 @@ +lbm_solver_3d_sparse +================================= + + +This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible: + +.. code-block:: python + + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse. \ No newline at end of file diff --git a/docs/_build/doctrees/2phase.doctree b/docs/_build/doctrees/2phase.doctree new file mode 100644 index 0000000..895738d Binary files /dev/null and b/docs/_build/doctrees/2phase.doctree differ diff --git a/docs/_build/doctrees/Convert_stl_to_binary.doctree b/docs/_build/doctrees/Convert_stl_to_binary.doctree new file mode 100644 index 0000000..790d79f Binary files /dev/null and b/docs/_build/doctrees/Convert_stl_to_binary.doctree differ diff --git a/docs/_build/doctrees/Grey_Scale.doctree b/docs/_build/doctrees/Grey_Scale.doctree new file mode 100644 index 0000000..253d554 Binary files /dev/null and b/docs/_build/doctrees/Grey_Scale.doctree differ diff --git a/docs/_build/doctrees/Grey_scale/flow_domain_geo_generation.doctree 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When it is not found, a full rebuild will be done. +config: 460f45d6faf9867abf533d23c6816ee9 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/_build/html/.nojekyll b/docs/_build/html/.nojekyll new file mode 100644 index 0000000..8b13789 --- /dev/null +++ b/docs/_build/html/.nojekyll @@ -0,0 +1 @@ + diff --git a/docs/_build/html/2phase.html b/docs/_build/html/2phase.html new file mode 100644 index 0000000..6df4792 --- /dev/null +++ b/docs/_build/html/2phase.html @@ -0,0 +1,125 @@ + + + + + + + 2phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

2phase

+
+

Contents:

+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Convert_stl_to_binary.html b/docs/_build/html/Convert_stl_to_binary.html new file mode 100644 index 0000000..9a97016 --- /dev/null +++ b/docs/_build/html/Convert_stl_to_binary.html @@ -0,0 +1,126 @@ + + + + + + + Convert_stl_to_binary — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Convert_stl_to_binary

+

This file reads the stl file and output to vtk file

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Grey_Scale.html b/docs/_build/html/Grey_Scale.html new file mode 100644 index 0000000..5485831 --- /dev/null +++ b/docs/_build/html/Grey_Scale.html @@ -0,0 +1,125 @@ + + + + + + + Grey_Scale — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Grey_Scale

+
+

Contents:

+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Grey_scale/flow_domain_geo_generation.html b/docs/_build/html/Grey_scale/flow_domain_geo_generation.html new file mode 100644 index 0000000..ea8bf17 --- /dev/null +++ b/docs/_build/html/Grey_scale/flow_domain_geo_generation.html @@ -0,0 +1,149 @@ + + + + + + + flow_domain_geo_generation — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation

+

This file output geometry data

+
#import numpy and math packahe
+import numpy as np
+import math
+
+
+# INPUT STL FILE NAME
+output_name = 'geo.dat'
+
+# POINT SEARCHING RESOLUTION IN X direction, Y,Z direction will be calculate by the code
+# the bigger value ~ more points will be found inside STL
+dnx, dny, dnz = 60, 60, 60
+
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+#create np matrix with dnx*dny*dnz zero
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#out_dat[1,:,:] = 1
+
+#=========================================================
+#reshape out_dat with column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+#save the file with the transfer of out_dat based on integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Grey_scale/lbm_solver_3d_Macro_Sukop.html b/docs/_build/html/Grey_scale/lbm_solver_3d_Macro_Sukop.html new file mode 100644 index 0000000..5668cf1 --- /dev/null +++ b/docs/_build/html/Grey_scale/lbm_solver_3d_Macro_Sukop.html @@ -0,0 +1,185 @@ + + + + + + + lbm_solver_3d_Macro_Sukop — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_Macro_Sukop

+

This solver is almost similar to lbm_solver_3d expect several difference as follows:

+
    +

  1. Some parameter is different

    2. +
+
#grid resolution
+nx,ny,nz = 60,50,5
+#external force
+fx,fy,fz = 1.0e-6,0.0,0.0
+#viscosity
+niu = 0.1
+#import geometry
+geo_name = './BC.dat'
+#maximum timestep
+max_timestep = 5000
+#output frequency
+output_fre = 100
+#vtk file output frequency
+vtk_fre = 500
+
+
+
    +

  1. There are two array for solid flag data.

    2. +
+
ns_np = init_geo(geo_name)
+solid_np = ns_np.astype(int)
+#solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+ns.from_numpy(ns_np)
+
+
+
    +

  1. The streaming function is different

    2. +
+
@ti.kernel
+def streaming0():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            for s in ti.static(range(19)):
+                ip = periodic_index(i+e[s])
+                #if it is fluid f2=f otherwise apply bounce-back f2[i,s]=f[ip,LR[s]]
+                f2[i,s] = f[i,s] + ns[i]*(f[ip,LR[s]] - f[i,s])
+
+
+@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            #if it is fluid apply streaming
+            for s in ti.static(range(19)):
+                ip = periodic_index(i+e[s])
+                F[ip,s] = f2[i,s]
+
+                #if (solid[ip]==0):
+                #    F[ip,s] = f[i,s]
+                #else:
+                #    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+#not used
+@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in ti.static(range(19)):
+            f[i,s] = F[i,s]
+
+
+

streaming3() calculates the macroscopic variable

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/LBM_3D_SinglePhase_Solver.html b/docs/_build/html/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..2a694db --- /dev/null +++ b/docs/_build/html/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,660 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Phase_change.html b/docs/_build/html/Phase_change.html new file mode 100644 index 0000000..3d736f6 --- /dev/null +++ b/docs/_build/html/Phase_change.html @@ -0,0 +1,135 @@ + + + + + + + Phase_change — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase.LBM_3D_SinglePhase_Solver.html b/docs/_build/html/Single_phase.LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..3ff0dd7 --- /dev/null +++ b/docs/_build/html/Single_phase.LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,644 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase.example_cavity.html b/docs/_build/html/Single_phase.example_cavity.html new file mode 100644 index 0000000..7668e20 --- /dev/null +++ b/docs/_build/html/Single_phase.example_cavity.html @@ -0,0 +1,119 @@ + + + + + + + Single_phase_example — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase_example

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase.html b/docs/_build/html/Single_phase.html new file mode 100644 index 0000000..21fdb62 --- /dev/null +++ b/docs/_build/html/Single_phase.html @@ -0,0 +1,137 @@ + + + + + + + Single_phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase.lbm_solver_3d.html b/docs/_build/html/Single_phase.lbm_solver_3d.html new file mode 100644 index 0000000..b6c4821 --- /dev/null +++ b/docs/_build/html/Single_phase.lbm_solver_3d.html @@ -0,0 +1,425 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

this

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

``

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

this

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        if (solid[i,j,k] == 0):
+            m_temp = multiply_M(i,j,k)
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

this

+
@ti.func
+def periodic_index(i):
+    iout = i
+    if i[0]<0:     iout[0] = nx-1
+    if i[0]>nx-1:  iout[0] = 0
+    if i[1]<0:     iout[1] = ny-1
+    if i[1]>ny-1:  iout[1] = 0
+    if i[2]<0:     iout[2] = nz-1
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

this

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        if (solid[i] == 0):
+            for s in range(19):
+                ip = periodic_index(i+e[s])
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

this

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

this

+
@ti.kernel
+def Boundary_condition():
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

this

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

this

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/Convert_stl_to_binary.html b/docs/_build/html/Single_phase/Convert_stl_to_binary.html new file mode 100644 index 0000000..a9d5677 --- /dev/null +++ b/docs/_build/html/Single_phase/Convert_stl_to_binary.html @@ -0,0 +1,126 @@ + + + + + + + Convert_stl_to_binary — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Convert_stl_to_binary

+

This file reads the stl file and output to vtk file

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/LBM_3D_SinglePhase_Solver.html b/docs/_build/html/Single_phase/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..37c70ec --- /dev/null +++ b/docs/_build/html/Single_phase/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,667 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/example_cavity.html b/docs/_build/html/Single_phase/example_cavity.html new file mode 100644 index 0000000..9d41d02 --- /dev/null +++ b/docs/_build/html/Single_phase/example_cavity.html @@ -0,0 +1,173 @@ + + + + + + + example_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_cavity

+

This file use the LBM_3D_SinglePhase_Solver to simulate the cavity flow

+
#import certain packages
+import time
+import taichi as ti
+
+ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#set 50*50*50 cavity based on LB3D_Solver_Single_Phase solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=50,ny=50,nz=50, sparse_storage=False)
+
+#import geometry data
+lb3d.init_geo('./geo_cavity.dat')
+#set the x-right velocity
+lb3d.set_bc_vel_x1([0.0,0.0,0.1])
+#initialize
+lb3d.init_simulation()
+
+#simulation step
+for iter in range(2000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #get the maximum velocity
+        max_v = lb3d.get_max_v()
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the number of time steps, maxiumum force and the force scale=0
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, max_v,  0.0))
+        #every 1000 time steps export the vtk file
+        if (iter%1000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/example_porous_medium.html b/docs/_build/html/Single_phase/example_porous_medium.html new file mode 100644 index 0000000..2d11834 --- /dev/null +++ b/docs/_build/html/Single_phase/example_porous_medium.html @@ -0,0 +1,170 @@ + + + + + + + example_porous_medium — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_porous_medium

+

This file simulate the porous medium based on the LBM_3D_SinglePhase_Solver

+
#import time and taichi package
+import time
+import taichi as ti
+#taichi intialization
+ti.init(arch=ti.cpu)
+#import the LBM_3D_SinglePhase_Solver
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#create the 131*131*131 gird LBM_3D_SinglePhase_Solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=131,ny=131,nz=131)
+#import the porous medium geometry
+lb3d.init_geo('./img_ftb131.txt')
+#set x-left and x-right density
+lb3d.set_bc_rho_x1(0.99)
+lb3d.set_bc_rho_x0(1.0)
+#initialize the simulation
+lb3d.init_simulation()
+#simulation loop
+for iter in range(50000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the time step, max force=10, force_scale=10
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+        #export VTK every 2000 time step
+        if (iter%2000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/flow_domain_geo_generation_2D.html b/docs/_build/html/Single_phase/flow_domain_geo_generation_2D.html new file mode 100644 index 0000000..5ed62c6 --- /dev/null +++ b/docs/_build/html/Single_phase/flow_domain_geo_generation_2D.html @@ -0,0 +1,163 @@ + + + + + + + flow_domain_geo_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation_2D

+

This file generate geometry file for solver to read

+
#import certain module
+import numpy as np
+import math
+
+
+#define the input file name
+# INPUT STL FILE NAME
+output_name = 'geo_cavity.dat'
+
+#define the grid resolution
+dnx, dny, dnz = 50, 50, 50
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+
+#define an matrix dnx*dny*dnz with zero values
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#define the boundary to be solid
+out_dat[0,:,:] = 1
+#cout_dat[:,:,0] = 1
+out_dat[:,0,:] = 1
+out_dat[:,-1,:] = 1
+out_dat[:,:,0] = 1
+out_dat[:,:,-1] = 1
+
+#=========================================================
+#reshape the data to be column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+
+
+#output the transfer of out_dat to the file with integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/lbm_solver_3d.html b/docs/_build/html/Single_phase/lbm_solver_3d.html new file mode 100644 index 0000000..9007848 --- /dev/null +++ b/docs/_build/html/Single_phase/lbm_solver_3d.html @@ -0,0 +1,536 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s Force scheme

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+    #calculate Guo's force here
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) calculate equilibrium density distribution function in momentum space

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

collison() define the prcoess of collision

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is fluid
+        if (solid[i,j,k] == 0):
+            #calculate m
+            m_temp = multiply_M(i,j,k)
+            #calculate meq
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                #calculate -s*(m-meq)
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #add Guo's force
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    #f=-M^-1*S(m-meq)
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

periodic_index(i) set the bounary index with periodic bounary condition

+
@ti.func
+def periodic_index(i):
+    #inner index
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = nx-1
+    #x-right
+    if i[0]>nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = ny-1
+    #y-right
+    if i[1]>ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = nz-1
+    #z-right
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming process of denisty distibution function

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        #if it is fluid
+        if (solid[i] == 0):
+            for s in range(19):
+                #the neighbour index
+                ip = periodic_index(i+e[s])
+                #if neighbour index is fluid just streaming
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                #if neighbour index is solid just bounce back
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

streaming2() a simple streaming process without consideration of solid and boundary

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

Boudary_condition() define the bounary condition of fixed pressure and fixed velocity

+
@ti.kernel
+def Boundary_condition():
+    #pressure-boundary condtion x-left
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #if boundary is fluid but the neighbour is solid
+                #equilibrium density distribution function is calculated based on the neighbour velocity
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                #if boundary is fluid and the neighbour is also fluid
+                #equilibrium density distribution function is calculated based on the boundary velocity
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    #velocity-boundary conditon x-left
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #calculate density distribution fucntion based on equilibrium part and non-equilibrium part
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    #pressure boundary condition x-right similar to x-left
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    #velocity booundary condition x-right similar to x-left
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

streaming3() calculate the macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        #if it is fluid calculate density and velocity based on density distribution function
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+        # if it is solid set denisty equals one and velocity equals zero
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

At the end of the file do the actual simulation and export the data

+
#define some time varible
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+#import the solid flag data
+#solid_np = init_geo('./BC.dat')
+solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+
+# do the initialization
+static_init()
+init()
+
+# do the actual simulation
+for iter in range(50000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    # calculate every 1000 time step
+    if (iter%1000==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        #calculate the time difference between now and previous time step
+        diff_time = int(time_now-time_pre)
+        #calculate the time difference between now and the initial time
+        elap_time = int(time_now-time_init)
+        #divmod function return the quotient and the remainder
+        #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2]))
+                            }
+            )
+# ti.sync()
+# ti.profiler.print_kernel_profiler_info()
+#print the profiler information of every kernel and task of taichi in this file
+ti.profiler.print_scoped_profiler_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/lbm_solver_3d_cavity.html b/docs/_build/html/Single_phase/lbm_solver_3d_cavity.html new file mode 100644 index 0000000..f851f46 --- /dev/null +++ b/docs/_build/html/Single_phase/lbm_solver_3d_cavity.html @@ -0,0 +1,155 @@ + + + + + + + lbm_solver_3d_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_cavity

+

This solver is almost similar to lbm_solver_3d expect several difference as follows:

+
    +

  1. The Grid resolution in this solver is 50x50x50

    2. +

  2. The viscosity in this solver is 0.16667

    3. +

  3. The boundary condition in this solver is velocity solver on x-right as follows

    4. +
+

boundary condition of this solver

+
#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+
+

x-right is implementated with velocity boundary condition

+

4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary.

+
if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left))
+
+
+
    +

  1. Finally, the definition of the varible is slightly different from lbm_solver_3d

    2. +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/Single_phase/lbm_solver_3d_sparse.html b/docs/_build/html/Single_phase/lbm_solver_3d_sparse.html new file mode 100644 index 0000000..9064c37 --- /dev/null +++ b/docs/_build/html/Single_phase/lbm_solver_3d_sparse.html @@ -0,0 +1,143 @@ + + + + + + + lbm_solver_3d_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_sparse

+

This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible:

+
f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse.

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_sources/2phase.rst.txt b/docs/_build/html/_sources/2phase.rst.txt new file mode 100644 index 0000000..d0d402f --- /dev/null +++ b/docs/_build/html/_sources/2phase.rst.txt @@ -0,0 +1,11 @@ +2phase +============== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + twophase/lbm_solver_3d_2phase_sparse + twophase/lbm_solver_3d_2phase + + diff --git a/docs/_build/html/_sources/Convert_stl_to_binary.rst.txt b/docs/_build/html/_sources/Convert_stl_to_binary.rst.txt new file mode 100644 index 0000000..edf04e6 --- /dev/null +++ b/docs/_build/html/_sources/Convert_stl_to_binary.rst.txt @@ -0,0 +1,4 @@ +Convert_stl_to_binary +================================= + +This file reads the stl file and output to vtk file \ No newline at end of file diff --git a/docs/_build/html/_sources/Grey_Scale.rst.txt b/docs/_build/html/_sources/Grey_Scale.rst.txt new file mode 100644 index 0000000..ef21d69 --- /dev/null +++ b/docs/_build/html/_sources/Grey_Scale.rst.txt @@ -0,0 +1,10 @@ +Grey\_Scale +=================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Grey_scale/flow_domain_geo_generation + Grey_scale/lbm_solver_3d_Macro_Sukop + diff --git a/docs/_build/html/_sources/Grey_scale/flow_domain_geo_generation.rst.txt b/docs/_build/html/_sources/Grey_scale/flow_domain_geo_generation.rst.txt new file mode 100644 index 0000000..bf4c4a7 --- /dev/null +++ b/docs/_build/html/_sources/Grey_scale/flow_domain_geo_generation.rst.txt @@ -0,0 +1,34 @@ +flow_domain_geo_generation +================================= + +This file output geometry data + +.. code-block:: python + + #import numpy and math packahe + import numpy as np + import math + + + # INPUT STL FILE NAME + output_name = 'geo.dat' + + # POINT SEARCHING RESOLUTION IN X direction, Y,Z direction will be calculate by the code + # the bigger value ~ more points will be found inside STL + dnx, dny, dnz = 60, 60, 60 + + + #========================================================== + # DO NOT CHANGE BELOW + #========================================================== + #create np matrix with dnx*dny*dnz zero + out_dat = np.zeros((dnx,dny,dnz)) + + #=======Can define some geometry here to out_dat========= + #out_dat[1,:,:] = 1 + + #========================================================= + #reshape out_dat with column major + out_dat = out_dat.reshape(out_dat.size, order = 'F') + #save the file with the transfer of out_dat based on integer type + np.savetxt(output_name,out_dat.T,fmt='%d') \ No newline at end of file diff --git a/docs/_build/html/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt b/docs/_build/html/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt new file mode 100644 index 0000000..26eb0cc --- /dev/null +++ b/docs/_build/html/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt @@ -0,0 +1,70 @@ +lbm_solver_3d_Macro_Sukop +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. Some parameter is different + +.. code-block:: python + + #grid resolution + nx,ny,nz = 60,50,5 + #external force + fx,fy,fz = 1.0e-6,0.0,0.0 + #viscosity + niu = 0.1 + #import geometry + geo_name = './BC.dat' + #maximum timestep + max_timestep = 5000 + #output frequency + output_fre = 100 + #vtk file output frequency + vtk_fre = 500 + +2. There are two array for solid flag data. + +.. code-block:: python + + ns_np = init_geo(geo_name) + solid_np = ns_np.astype(int) + #solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + ns.from_numpy(ns_np) + +3. The streaming function is different + +.. code-block:: python + + @ti.kernel + def streaming0(): + for i in ti.grouped(rho): + if (solid[i] == 0): + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + #if it is fluid f2=f otherwise apply bounce-back f2[i,s]=f[ip,LR[s]] + f2[i,s] = f[i,s] + ns[i]*(f[ip,LR[s]] - f[i,s]) + + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + if (solid[i] == 0): + #if it is fluid apply streaming + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + F[ip,s] = f2[i,s] + + #if (solid[ip]==0): + # F[ip,s] = f[i,s] + #else: + # F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + #not used + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in ti.static(range(19)): + f[i,s] = F[i,s] + +``streaming3()`` calculates the macroscopic variable \ No newline at end of file diff --git a/docs/_build/html/_sources/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_build/html/_sources/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_build/html/_sources/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.x0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + if i[1]<0: iout[1] = ny-1 + if i[1]>ny-1: iout[1] = 0 + if i[2]<0: iout[2] = nz-1 + if i[2]>nz-1: iout[2] = 0 + + return iout + +this + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + if (solid[i] == 0): + for s in range(19): + ip = periodic_index(i+e[s]) + if (solid[ip]==0): + F[ip,s] = f[i,s] + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +this + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +this + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + +this + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +this \ No newline at end of file diff --git a/docs/_build/html/_sources/Single_phase.rst.txt b/docs/_build/html/_sources/Single_phase.rst.txt new file mode 100644 index 0000000..d66928e --- /dev/null +++ b/docs/_build/html/_sources/Single_phase.rst.txt @@ -0,0 +1,20 @@ +Single\_phase +===================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Single_phase/LBM_3D_SinglePhase_Solver + Single_phase/lbm_solver_3d + Single_phase/lbm_solver_3d_cavity + Single_phase/lbm_solver_3d_sparse + Single_phase/flow_domain_geo_generation_2D + Single_phase/example_cavity + Single_phase/example_porous_medium + Single_phase/Convert_stl_to_binary + + + + + diff --git a/docs/_build/html/_sources/Single_phase/Convert_stl_to_binary.rst.txt b/docs/_build/html/_sources/Single_phase/Convert_stl_to_binary.rst.txt new file mode 100644 index 0000000..edf04e6 --- /dev/null +++ b/docs/_build/html/_sources/Single_phase/Convert_stl_to_binary.rst.txt @@ -0,0 +1,4 @@ +Convert_stl_to_binary +================================= + +This file reads the stl file and output to vtk file \ No newline at end of file diff --git a/docs/_build/html/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_build/html/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_build/html/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = ny-1 + #y-right + if i[1]>ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = nz-1 + #z-right + if i[2]>nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming process of denisty distibution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + #if it is fluid + if (solid[i] == 0): + for s in range(19): + #the neighbour index + ip = periodic_index(i+e[s]) + #if neighbour index is fluid just streaming + if (solid[ip]==0): + F[ip,s] = f[i,s] + #if neighbour index is solid just bounce back + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +``streaming2()`` a simple streaming process without consideration of solid and boundary + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +``Boudary_condition()`` define the bounary condition of fixed pressure and fixed velocity + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + #pressure-boundary condtion x-left + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #if boundary is fluid but the neighbour is solid + #equilibrium density distribution function is calculated based on the neighbour velocity + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + #if boundary is fluid and the neighbour is also fluid + #equilibrium density distribution function is calculated based on the boundary velocity + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + #velocity-boundary conditon x-left + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #calculate density distribution fucntion based on equilibrium part and non-equilibrium part + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + #pressure boundary condition x-right similar to x-left + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + #velocity booundary condition x-right similar to x-left + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + + +``streaming3()`` calculate the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + #if it is fluid calculate density and velocity based on density distribution function + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + # if it is solid set denisty equals one and velocity equals zero + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +At the end of the file do the actual simulation and export the data + +.. code-block:: python + + #define some time varible + time_init = time.time() + time_now = time.time() + time_pre = time.time() + dt_count = 0 + + #import the solid flag data + #solid_np = init_geo('./BC.dat') + solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + + # do the initialization + static_init() + init() + + # do the actual simulation + for iter in range(50000+1): + colission() + streaming1() + Boundary_condition() + #streaming2() + streaming3() + # calculate every 1000 time step + if (iter%1000==0): + + time_pre = time_now + time_now = time.time() + #calculate the time difference between now and previous time step + diff_time = int(time_now-time_pre) + #calculate the time difference between now and the initial time + elap_time = int(time_now-time_init) + #divmod function return the quotient and the remainder + #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + + #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable + if (iter%10000==0): + gridToVTK( + "./structured"+str(iter), + x, + y, + z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()), + "rho": np.ascontiguousarray(rho.to_numpy()), + "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2])) + } + ) + # ti.sync() + # ti.profiler.print_kernel_profiler_info() + #print the profiler information of every kernel and task of taichi in this file + ti.profiler.print_scoped_profiler_info() diff --git a/docs/_build/html/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt b/docs/_build/html/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt new file mode 100644 index 0000000..08d16d9 --- /dev/null +++ b/docs/_build/html/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt @@ -0,0 +1,37 @@ +lbm_solver_3d_cavity +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. The Grid resolution in this solver is 50x50x50 +2. The viscosity in this solver is 0.16667 +3. The boundary condition in this solver is velocity solver on x-right as follows + +boundary condition of this solver + +.. code-block:: python + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + +x-right is implementated with velocity boundary condition + +4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary. + +.. code-block:: python + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left)) + + +5. Finally, the definition of the varible is slightly different from lbm_solver_3d \ No newline at end of file diff --git a/docs/_build/html/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt b/docs/_build/html/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt new file mode 100644 index 0000000..d76a344 --- /dev/null +++ b/docs/_build/html/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt @@ -0,0 +1,24 @@ +lbm_solver_3d_sparse +================================= + + +This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible: + +.. code-block:: python + + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse. \ No newline at end of file diff --git a/docs/_build/html/_sources/aaa.rst.txt b/docs/_build/html/_sources/aaa.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_build/html/_sources/aaa.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = ny-1 + #y-right + if i[1]>ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = nz-1 + #z-right + if i[2]>nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming process of denisty distibution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + #if it is fluid + if (solid[i] == 0): + for s in range(19): + #the neighbour index + ip = periodic_index(i+e[s]) + #if neighbour index is fluid just streaming + if (solid[ip]==0): + F[ip,s] = f[i,s] + #if neighbour index is solid just bounce back + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +``streaming2()`` a simple streaming process without consideration of solid and boundary + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +``Boudary_condition()`` define the bounary condition of fixed pressure and fixed velocity + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + #pressure-boundary condtion x-left + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #if boundary is fluid but the neighbour is solid + #equilibrium density distribution function is calculated based on the neighbour velocity + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + #if boundary is fluid and the neighbour is also fluid + #equilibrium density distribution function is calculated based on the boundary velocity + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + #velocity-boundary conditon x-left + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #calculate density distribution fucntion based on equilibrium part and non-equilibrium part + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + #pressure boundary condition x-right similar to x-left + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + #velocity booundary condition x-right similar to x-left + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + + +``streaming3()`` calculate the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + #if it is fluid calculate density and velocity based on density distribution function + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + # if it is solid set denisty equals one and velocity equals zero + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +At the end of the file do the actual simulation and export the data + +.. code-block:: python + + #define some time varible + time_init = time.time() + time_now = time.time() + time_pre = time.time() + dt_count = 0 + + #import the solid flag data + #solid_np = init_geo('./BC.dat') + solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + + # do the initialization + static_init() + init() + + # do the actual simulation + for iter in range(50000+1): + colission() + streaming1() + Boundary_condition() + #streaming2() + streaming3() + # calculate every 1000 time step + if (iter%1000==0): + + time_pre = time_now + time_now = time.time() + #calculate the time difference between now and previous time step + diff_time = int(time_now-time_pre) + #calculate the time difference between now and the initial time + elap_time = int(time_now-time_init) + #divmod function return the quotient and the remainder + #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + + #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable + if (iter%10000==0): + gridToVTK( + "./structured"+str(iter), + x, + y, + z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()), + "rho": np.ascontiguousarray(rho.to_numpy()), + "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2])) + } + ) + # ti.sync() + # ti.profiler.print_kernel_profiler_info() + #print the profiler information of every kernel and task of taichi in this file + ti.profiler.print_scoped_profiler_info() diff --git a/docs/_build/html/_sources/lbm_solver_3d_cavity.rst.txt b/docs/_build/html/_sources/lbm_solver_3d_cavity.rst.txt new file mode 100644 index 0000000..a1861dc --- /dev/null +++ b/docs/_build/html/_sources/lbm_solver_3d_cavity.rst.txt @@ -0,0 +1,38 @@ +lbm_solver_3d_cavity +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: +.. number:: lbm_solver_3d_cavity + +1. The Grid resolution in this solver is 50x50x50 +2. The viscosity in this solver is 0.16667 +3. The boundary condition in this solver is velocity solver on x-right as follows + +boundary condition of this solver + +.. code-block:: python + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + +x-right is implementated with velocity boundary condition + +4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary. + +.. code-block:: python + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left)) + + +5. Finally, the definition of the varible is slightly different from lbm_solver_3d \ No newline at end of file diff --git a/docs/_build/html/_sources/lbm_solver_3d_sparse.rst.txt b/docs/_build/html/_sources/lbm_solver_3d_sparse.rst.txt new file mode 100644 index 0000000..d76a344 --- /dev/null +++ b/docs/_build/html/_sources/lbm_solver_3d_sparse.rst.txt @@ -0,0 +1,24 @@ +lbm_solver_3d_sparse +================================= + + +This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible: + +.. code-block:: python + + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse. \ No newline at end of file diff --git a/docs/_build/html/_sources/modules.rst.txt b/docs/_build/html/_sources/modules.rst.txt new file mode 100644 index 0000000..b9bfd06 --- /dev/null +++ b/docs/_build/html/_sources/modules.rst.txt @@ -0,0 +1,10 @@ +taichi_LBM3D +============ + +.. toctree:: + :maxdepth: 4 + + Single_phase + Grey_Scale + 2phase + Phase_change diff --git a/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt b/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt new file mode 100644 index 0000000..04dbf54 --- /dev/null +++ b/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt @@ -0,0 +1,619 @@ +LBM_3D_SinglePhase_Solute_Solver +====================================== + +This file is the solver for solute transportation + +First import the certain package and define the class of ``LB3D_Solver_Single_Phase_Solute`` which inheritant from +``LB3D_Solver_Single_Phase_Solute`` + +.. code-block:: python + + from sympy import inverse_mellin_transform + import taichi as ti + import numpy as np + from pyevtk.hl import gridToVTK + import time + + #ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False) + import LBM_3D_SinglePhase_Solver as lb3d + + @ti.data_oriented + class LB3D_Solver_Single_Phase_Solute(lb3d.LB3D_Solver_Single_Phase): + def __init__(self, nx, ny, nz): + super(LB3D_Solver_Single_Phase_Solute, self).__init__(nx, ny, nz, sparse_storage = False) + #define solute boundary condition + self.solute_bc_x_left, self.solute_bcxl = 0, 0.0 + self.solute_bc_x_right, self.solute_bcxr = 0, 0.0 + self.solute_bc_y_left, self.solute_bcyl = 0, 0.0 + self.solute_bc_y_right, self.solute_bcyr = 0, 0.0 + self.solute_bc_z_left, self.solute_bczl = 0, 0.0 + self.solute_bc_z_right, self.solute_bczr = 0, 0.0 + + #define parameters for bouyancy force + self.buoyancy_parameter = 20.0 #Buoyancy Parameter (0= no buoyancy) + self.ref_T = 20.0 #reference_psi F=/rho*g+Bouyancy*(/psi-reference_psi)*g) + #define gravity + self.gravity = 5e-7 + + #define concentration distribution function + self.fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define another concentration distribution function + self.Fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define external force + self.forcexyz = ti.Vector.field(3,ti.f32,shape=(nx,ny,nz)) + #define entropy + self.rho_H = ti.field(ti.f32, shape=(nx,ny,nz)) + #define temperature + self.rho_T = ti.field(ti.f32, shape=(nx,ny,nz)) + #define liquid volumn fraction + self.rho_fl = ti.field(ti.f32, shape=(nx,ny,nz)) + + #define specific heat of liquid + self.Cp_l= 1.0 + #define specific heat of solid + self.Cp_s = 1.0 + #define latent heat + self.Lt = 1.0 + #define solid temperature + self.T_s = -10.0 + #define liquid temperature + self.T_l = -10.0 + #define viscosity of solid + self.niu_s = 0.002 + #define viscosity of liquid + self.niu_l = 0.002 + + #define energy of solid + self.H_s = None + #define energy of liquid + self.H_l = None + + #define rock thermal diffusivity + self.niu_solid = 0.001 + #define specific heat of rock + self.Cp_solid = 1.0 + +An then it sets these parameters with functions + +.. code-block:: python + + #set gravity + def set_gravity(self, gravity): + self.gravity = gravity + #set buoyancy force parameter + def set_buoyancy_parameter(self, buoyancy_param): + self.buoyancy_parameter = buoyancy_param + #set reference temperature + def set_ref_T(self, ref_t): + self.ref_T = ref_t + #set specific heat of solid + def set_specific_heat_solid(self, cps): + self.Cp_s = cps + #set specfic heat of liquid + def set_specific_heat_liquid(self, cpl): + self.Cp_l = cpl + #set specfic heat of rock + def set_specific_heat_rock(self, cprock): + self.Cp_solid = cprock + #set latent heat + def set_latent_heat(self, ltheat): + self.Lt = ltheat + #set solidus temperature + def set_solidus_temperature(self, ts): + self.T_s = ts + #set liquidus temperature + def set_liquidus_temperature(self, tl): + self.T_l = tl + #set solid thermal diffusivity + def set_solid_thermal_diffusivity(self, nius): + self.niu_s = nius + #set liquid thermal diffusivity + def set_liquid_thermal_diffusivity(self, niul): + self.niu_l = niul + #set rock thermal diffusivity + def set_rock_thermal_diffusivity(self, niurock): + self.niu_solid = niurock + #set adiabatic boundary on x-left + def set_bc_adiabatic_x_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_left = 2 + #set adiabatic boundary on x-right + def set_bc_adiabatic_x_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_right = 2 + #set adiabatic boundary on y-left + def set_bc_adiabatic_y_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_left = 2 + #set adiabatic boundary on y-right + def set_bc_adiabatic_y_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_right = 2 + #set adiabatic boundary on z-left + def set_bc_adiabatic_z_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_left = 2 + #set adiabatic boundary on z-right + def set_bc_adiabatic_z_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_right = 2 + #set constant temperature on x-left + def set_bc_constant_temperature_x_left(self,xl): + self.solute_bc_x_left = 1 + self.solute_bcxl = xl + #set constant temperature on x-right + def set_bc_constant_temperature_x_right(self,xr): + self.solute_bc_x_right = 1 + self.solute_bcxr = xr + #set constant temperature on y-left + def set_bc_constant_temperature_y_left(self,yl): + self.solute_bc_y_left = 1 + self.solute_bcyl = yl + #set constant temperature on y-right + def set_bc_constant_temperature_y_right(self,yr): + self.solute_bc_y_right = 1 + self.solute_bcyr = yr + #set constant temperature on z-left + def set_bc_constant_temperature_z_left(self,zl): + self.solute_bc_z_left = 1 + self.solute_bczl = zl + #set constant temperature on z-right + def set_bc_constant_temperature_z_right(self,zr): + self.solute_bc_y_right = 1 + self.solute_bczr = zr + + # update energy of solid and liquid + def update_H_sl(self): + #energy of solid + self.H_s = self.Cp_s*self.T_s + #energy of liquid + self.H_l = self.H_s+self.Lt + print('H_s',self.H_s) + print('H_l',self.H_l) + +Then it initialize some variable or function + +.. code-block:: python + + #intialize the energy + @ti.kernel + def init_H(self): + for I in ti.grouped(self.rho_T): + #calculate the energy, convert_T_H() define later + self.rho_H[I] = self.convert_T_H(self.rho_T[I]) + + #intialize the density distribiution function for solute concentration + @ti.kernel + def init_fg(self): + for I in ti.grouped(self.fg): + #calculate the overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + #intialize the density distribiution function for solute concentration equals equilibrium density distribiution function for solute concentration + for s in ti.static(range(19)): + self.fg[I][s] = self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]) + self.Fg[I][s] = self.fg[I][s] + + #intialize the volumn fraction of liquid + @ti.kernel + def init_fl(self): + for I in ti.grouped(self.rho_T): + #convert_T_fl define later + self.rho_fl[I] = self.convert_T_fl(self.rho_T[I]) + +``g_feq(self, k,local_T,local_H, Cp, u)`` calculate the equilibrium density distribiution function for thermal energy + +.. code-block:: python + + @ti.func + def g_feq(self, k,local_T,local_H, Cp, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + feqout = 0.0 + #calculating the zero-velocity equilibrium thermal distribution function + if (k==0): + feqout = local_H-Cp*local_T+self.w[k]*Cp*local_T*(1-1.5*uv) + else: + #calculating other directions equilibrium thermal distribution function + feqout = self.w[k]*Cp*local_T*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, self.w[k], feqout, Cp, local_T) + return feqout + +``cal_local_force(i, j, k)`` calculates buoyancy force + +.. code-block:: python + + #density is the function of temperture delat(rho)=-rho*beta*delta(T) + @ti.func + def cal_local_force(self, i, j, k): + f = ti.Vector([self.fx, self.fy, self.fz]) + f[1] += self.gravity*self.buoyancy_parameter*(self.rho_T[i,j,k]-self.ref_T) + #f= delta(rho)*delta(v)*g + f *= self.rho_fl[i,j,k] + return f + +``collision_g()`` defines the the collision of thermal distribution function + +.. code-block:: python + + @ti.kernel + def colission_g(self): + for I in ti.grouped(self.rho_T): + #overall relaxation time + tau_s = 3*(self.niu_s*(1.0-self.rho_fl[I])+self.niu_l*self.rho_fl[I])+0.5 + #overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + + #ROCK overall relaxation time and specific heat + if (self.solid[I] >0): + tau_s = 3.0*self.niu_solid+0.5 + Cp = self.Cp_solid + + #f=f-1/tau*(f-feq) + for s in ti.static(range(19)): + tmp_fg = -1.0/tau_s*(self.fg[I][s]-self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + #print(self.fg[I][s],tmp_fg,I,s,self.rho_H[I],self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + self.fg[I][s] += tmp_fg + +``collision()`` defines the the collision of density distribution function + +.. code-block:: python + + @ti.kernel + def colission(self): + for i,j,k in self.rho: + #if (self.solid[i,j,k] == 0): + m_temp = self.M[None]@self.F[i,j,k] + meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k]) + m_temp -= self.S_dig[None]*(m_temp-meq) + f = self.cal_local_force(i,j,k) + if (ti.static(self.force_flag==1)): + for s in ti.static(range(19)): + # m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s]) + #f = self.cal_local_force() + f_guo=0.0 + for l in ti.static(range(19)): + f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l] + #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force) + m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo + + self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + #calculate the denisty distribution function in momentum space here + self.f[i,j,k] += self.inv_M[None]@m_temp + #calculate the fluid density distribution function here + for s in ti.static(range(19)): + self.f[i,j,k][s] = self.f[i,j,k][s]*(self.rho_fl[i,j,k]) + self.w[s]*(1.0-self.rho_fl[i,j,k]) + +``streaming1()`` and ``streaming1_g()`` defines the fluid denisty distribiution function and +thermal density distribiution function + +.. code-block:: python + + @ti.kernel + def streaming1(self): + for i in ti.grouped(self.rho): + #if (self.solid[i] == 0): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.F[ip][s] = self.f[i][s] + + @ti.kernel + def streaming1_g(self): + for i in ti.grouped(self.rho_T): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.Fg[ip][s] = self.fg[i][s] + +this + +.. code-block:: python + + @ti.kernel + def BC_concentration(self): + #constant temperature boundary condition + if ti.static(self.solute_bc_x_left==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[0,j,k]*self.Cp_l + (1-self.rho_fl[0,j,k])*self.Cp_s + #the boundary's thermal distribution function equals the equilibrium thermal distribution function on the boundary + for s in ti.static(range(19)): + self.fg[0,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[0,j,k]) + self.Fg[0,j,k][s] = self.fg[0,j,k][s] + #adiabatic boundary condition + elif ti.static(self.solute_bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + #there is no thermal transfer between the boundaty and neighbouring cell + self.fg[0,j,k][s] = self.fg[1,j,k][s] + self.Fg[0,j,k][s] = self.fg[1,j,k][s] + + #x-right + if ti.static(self.solute_bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[self.nx-1,j,k]*self.Cp_l + (1-self.rho_fl[self.nx-1,j,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[self.nx-1,j,k]) + self.Fg[self.nx-1,j,k][s]= self.fg[self.nx-1,j,k][s] + elif ti.static(self.solute_bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + self.Fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + + #y-left + if ti.static(self.solute_bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,0,k]*self.Cp_l + (1-self.rho_fl[i,0,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,0,k]) + self.Fg[i,0,k][s] = self.fg[i,0,k][s] + elif ti.static(self.solute_bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.fg[i,1,k][s] + self.Fg[i,0,k][s] = self.fg[i,1,k][s] + + #y-right + if ti.static(self.solute_bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,self.ny-1,k]*self.Cp_l + (1-self.rho_fl[i,self.ny-1,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,self.ny-1,k]) + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-1,k][s] + elif ti.static(self.solute_bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + + #z-left + if ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,0]*self.Cp_l + (1-self.rho_fl[i,j,0])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,0]) + self.Fg[i,j,0][s] = self.fg[i,j,0][s] + elif ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.fg[i,j,1][s] + self.Fg[i,j,0][s] = self.fg[i,j,1][s] + + #z-right + if ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,self.nz-1]*self.Cp_l + (1-self.rho_fl[i,j,self.nz-1])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,self.nz-1]) + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-1][s] + elif ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + +``convert_H_T()`` calculate the temperature + +.. code-block:: python + + @ti.func + def convert_H_T(self,local_H): + new_T=0.0 + #if local enthalpy is less than solid enthalpy + #T= enthalpy/specific heat + if (local_Hself.H_l): + new_T = self.T_l+(local_H-self.H_l)/self.Cp_l + #if if temperature is greater than solid temperature + #T= Tsolid+(enthalpy-solid enthalpy)/(enthalpy of liquid-enthalpy of solid)*(temperature of liquid- temperature of solid) + elif (self.T_l>self.T_s): + new_T = self.T_s+(local_H-self.H_s)/(self.H_l-self.H_s)*(self.T_l-self.T_s) + else: + #else T= temperature of solid + new_T = self.T_s + + return new_T + +``convert_H_fl()`` calculate the volumn fraction of liquid + +.. code-block:: python + + @ti.func + def convert_H_fl(self,local_H): + new_fl=0.0 + #if enthalpy is less than solid enthalpy + #it is zero + if (local_Hself.H_l): + new_fl = 1.0 + #else + #it equals to (enthaply- soid enthaply)/(enthaply of liquid- enthalpy of solid) + else: + new_fl = (local_H-self.H_s)/(self.H_l-self.H_s) + + return new_fl + +``convert_T_H()`` calculate the enthaply from temperature + +.. code-block:: python + + @ti.func + def convert_T_H(self,local_T): + new_H = 0.0 + # calculate enthaply for three different conditions + if (local_T<=self.T_s): + new_H = self.Cp_s*local_T + elif (local_T>self.T_l): + new_H = (local_T-self.T_l)*self.Cp_l+self.H_l + else: + fluid_frc = (local_T-self.T_s)/(self.T_l-self.T_s) + new_H = self.H_s*(1-fluid_frc) + self.H_l*fluid_frc + return new_H + +``convert_T_fl()`` calculate volumn fraction from temperature + +.. code-block:: python + + @ti.func + def convert_T_fl(self,local_T): + new_fl = 0.0 + # calculate volumn fraction for three different conditions + if (local_T<=self.T_s): + new_fl = 0.0 + elif (local_T>=self.T_l): + new_fl = 1.0 + elif (self.T_l>self.T_s): + new_fl = (local_T-self.T_s)/(self.T_l-self.T_s) + else: + new_fl = 1.0 + + return new_fl + +``streaming3()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + self.forcexyz[i] = self.cal_local_force(i.x, i.y, i.z) + #print(i.x, i.y, i.z) + if ((self.solid[i]==0) or (self.rho_fl[i]>0.0)): + self.rho[i] = 0 + self.v[i] = ti.Vector([0,0,0]) + self.f[i] = self.F[i] + for s in ti.static(range(19)): + self.f[i][s] = self.f[i][s]*self.rho_fl[i]+self.w[s]*(1.0-self.rho_fl[i]) + #density for fluid + self.rho[i] += self.f[i].sum() + + for s in ti.static(range(19)): + self.v[i] += self.e_f[s]*self.f[i][s] + + f = self.cal_local_force(i.x, i.y, i.z) + #velocity for fluid + self.v[i] /= self.rho[i] + self.v[i] += (f/2)/self.rho[i] + + else: + #density and velocity for solid + self.rho[i] = 1.0 + self.v[i] = ti.Vector([0,0,0]) + +``streaming3()`` calculate enthalpy + +.. code-block:: python + + @ti.kernel + def streaming3_g(self): + for i in ti.grouped(self.rho_T): + self.rho_H[i] = 0.0 + #enthalpy here + self.rho_H[i] = self.Fg[i].sum() + #for s in ti.static(range(19)): + # self.rho_H[i] += self.Fg[i][s] + self.fg[i] = self.Fg[i] + +``update_T_fl()`` calculate volumn fraction and temperature + +.. code-block:: python + + @ti.kernel + def update_T_fl(self): + for I in ti.grouped(self.rho_T): + self.rho_T[I] = self.convert_H_T(self.rho_H[I]) + self.rho_fl[I] = self.convert_H_fl(self.rho_H[I]) + if (self.solid[I]>0): + self.rho_fl[I] = 0.0 + +``init_solute_simulation()`` initialize the solute simulation + +.. code-block:: python + + def init_solute_simulation(self): + + self.init_simulation() + self.update_H_sl() + #ethalpy + self.init_H() + #volumn fraction + self.init_fl() + #thermal distribution function + self.init_fg() + +``init_concentration(filename)`` import concentration data from file + +.. code-block:: python + + def init_concentration(self,filename): + in_dat = np.loadtxt(filename) + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + self.rho_T.from_numpy(in_dat) + +this + +.. code-block:: python + + def step(self): + self.colission() + self.colission_g() + + self.streaming1() + self.streaming1_g() + + self.Boundary_condition() + self.BC_concentration() + + self.streaming3_g() + self.streaming3() + self.streaming3_g() + + self.update_T_fl() + +this + +.. code-block:: python + + def export_VTK(self, n): + gridToVTK( + "./LB_SingelPhase_"+str(n), + self.x, + self.y, + self.z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()), + "rho": np.ascontiguousarray(self.rho.to_numpy()), + "Solid_Liquid": np.ascontiguousarray(self.rho_fl.to_numpy()), + "Tempreture": np.ascontiguousarray(self.rho_T.to_numpy()), + "Entropy": np.ascontiguousarray(self.rho_H.to_numpy()), + "velocity": ( np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])), + "Force": ( np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])) + } + ) + +this \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..4a6528d --- /dev/null +++ b/docs/_build/html/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,4 @@ +LBM_3D_SinglePhase_Solver +=========================== + +This file is the same as LBM_3D_SinglePhase_Solver in Single_phase folder \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/example_cavity_melting.rst.txt b/docs/_build/html/_sources/phasechange/example_cavity_melting.rst.txt new file mode 100644 index 0000000..eb279eb --- /dev/null +++ b/docs/_build/html/_sources/phasechange/example_cavity_melting.rst.txt @@ -0,0 +1,2 @@ +example_cavity_melting +============================= \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/example_phase_change.rst.txt b/docs/_build/html/_sources/phasechange/example_phase_change.rst.txt new file mode 100644 index 0000000..7e2842c --- /dev/null +++ b/docs/_build/html/_sources/phasechange/example_phase_change.rst.txt @@ -0,0 +1,2 @@ +example_phase_change +==================== \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt b/docs/_build/html/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt new file mode 100644 index 0000000..6ab6dde --- /dev/null +++ b/docs/_build/html/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt @@ -0,0 +1,2 @@ +read_img_solute_psi_generation_2D +================================== \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/solute_psi_generation_2D.rst.txt b/docs/_build/html/_sources/phasechange/solute_psi_generation_2D.rst.txt new file mode 100644 index 0000000..c8c1119 --- /dev/null +++ b/docs/_build/html/_sources/phasechange/solute_psi_generation_2D.rst.txt @@ -0,0 +1,2 @@ +solute_psi_generation_2D +============================ \ No newline at end of file diff --git a/docs/_build/html/_sources/phasechange/test1.rst.txt b/docs/_build/html/_sources/phasechange/test1.rst.txt new file mode 100644 index 0000000..0b1d2a0 --- /dev/null +++ b/docs/_build/html/_sources/phasechange/test1.rst.txt @@ -0,0 +1,2 @@ +test1 +=================== \ No newline at end of file diff --git a/docs/_build/html/_sources/twophase/lbm_solver_3d_2phase.rst.txt b/docs/_build/html/_sources/twophase/lbm_solver_3d_2phase.rst.txt new file mode 100644 index 0000000..1c42671 --- /dev/null +++ b/docs/_build/html/_sources/twophase/lbm_solver_3d_2phase.rst.txt @@ -0,0 +1,734 @@ +lbm_solver_3d_2phase +======================================== + +This solver is the multiphase model based on color gradient model +Firstly, it defines some parameters + +.. code-block:: python + + # NOTE: THIS CODE NEED taichi_glsl, so please use taichi version <=0.8.5 + #import taichi, numpy, pyevtk and time package + import taichi as ti + import numpy as np + #import taichi_glsl as ts + from pyevtk.hl import gridToVTK + import time + #from taichi_glsl import scalar + + #from taichi_glsl.scalar import isinf, isnan + #from taichi_glsl.vector import vecFill + #intialize taichi + ti.init(arch=ti.cpu) + #ti.init(arch=ti.gpu, dynamic_index=True,offline_cache=True) + + #enable projection + enable_projection = True + # 131*131*131 + nx,ny,nz = 131,131,131 + #nx,ny,nz = 131,131,131 + #external force in x,y,z direction + fx,fy,fz = 5.0e-5,-2e-5,0.0 + #niu = 0.1 + #liquid viscosity + niu_l = 0.1 #psi>0 + #gas viscosity + niu_g = 0.1 #psi<0 + #psi in color gradient calculation + psi_solid = 0.7 + #surface tension + CapA = 0.005 + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 0, 0.995, 0.0, 0.0, 0.0 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + + bc_psi_x_left, psi_x_left = 1, -1.0 # boundary condition for phase-field: 0 = periodic, + bc_psi_x_right, psi_x_right = 0, 1.0 # 1 = constant value on the boundary, value = -1.0 phase1 or 1.0 = phase 2 + bc_psi_y_left, psi_y_left = 0, 1.0 + bc_psi_y_right, psi_y_right = 0, 1.0 + bc_psi_z_left, psi_z_left = 0, 1.0 + bc_psi_z_right, psi_z_right = 0, 1.0 + + # Non Sparse memory allocation + #density distribution function nx*ny*nz*19 + f = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density distribution function nx*ny*nz*19 + F = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density nx*ny*nz + rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #velocity nx*ny*nz vector + v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + #psi nx*ny*nz + psi = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rho_r = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rho_b = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rhor = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rhob = ti.field(ti.f32, shape=(nx,ny,nz)) + #lattice speed 19 dimensional vector + e = ti.Vector.field(3,ti.i32, shape=(19)) + #S_dig = ti.field(ti.f32,shape=(19)) + #lattice speed 19 dimensional vector + e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #weight parameter 19 dimensional vector + w = ti.field(ti.f32, shape=(19)) + #solid flag nx*ny*nz + solid = ti.field(ti.i32,shape=(nx,ny,nz)) + #streaming vector 19 dimensional vector + LR = ti.field(ti.i32,shape=(19)) + + #external force 3 dimensional vector + ext_f = ti.Vector.field(3,ti.f32,shape=()) + # x-left velocity 3 dimensional vector + bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=()) + # x-right velocity 3 dimensional vector + bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=()) + # y-left velocity 3 dimensional vector + bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=()) + # y-right velocity 3 dimensional vector + bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=()) + # z-left velocity 3 dimensional vector + bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=()) + # z-right velocity 3 dimensional vector + bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=()) + #transforming matrix 19*19 + M = ti.field(ti.f32, shape=(19,19)) + #inverse transforming matrix 19*19 + inv_M = ti.field(ti.f32, shape=(19,19)) + #parameters for calculating the parameter of s diagonal + #=======================================# + lg0, wl, wg = 0.0, 0.0, 0.0 + l1, l2, g1, g2 = 0.0, 0.0, 0.0, 0.0 + wl = 1.0/(niu_l/(1.0/3.0)+0.5) + wg = 1.0/(niu_g/(1.0/3.0)+0.5) + lg0 = 2*wl*wg/(wl+wg) + l1=2*(wl-lg0)*10 + l2=-l1/0.2 + g1=2*(lg0-wg)*10 + g2=g1/0.2 + #=======================================# + + #transformation matrix + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #inverde of transforming matrix + inv_M_np = np.linalg.inv(M_np) + #streaming array + LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]) + #M matrix from the numpy + M.from_numpy(M_np) + #inverse matrix from numpy + inv_M.from_numpy(inv_M_np) + + #steaming array from numpy + LR.from_numpy(LR_np) + #external force with vector three dimensional + ext_f[None] = ti.Vector([fx,fy,fz]) + #set transforming matrix, inverse matrix and streaming vector non-modified + ti.static(inv_M) + ti.static(M) + ti.static(LR) + + #set x,y,z array with nx*ny*nz + x = np.linspace(0, nx, nx) + y = np.linspace(0, ny, ny) + z = np.linspace(0, nz, nz) + #set meshgrid and return three meshgrid matrix X,Y,Z with non-cartesian indexing + X, Y, Z = np.meshgrid(x, y, z, indexing='ij') + +``feq(k,rho_local, u)`` calculate the equilibrium denisty distribution function + +.. code-block:: python + + @ti.func + def feq(k,rho_local, u): + # eu=ts.vector.dot(e[k],u) + # uv=ts.vector.dot(u,u) + eu = e[k].dot(u) + uv = u.dot(u) + #same as single phase equilibrium density distribution function + feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, w[k]) + return feqout + +``init()`` intialize some variable + +.. code-block:: python + + @ti.kernel + def init(): + for i,j,k in solid: + if (solid[i,j,k] == 0): + #if it is fluid intialize the density and velocity be one and zero + rho[i,j,k] = 1.0 + v[i,j,k] = ti.Vector([0,0,0]) + # set density r and density b based on psi + rho_r[i,j,k] = (psi[i,j,k]+1.0)/2.0 + rho_b[i,j,k] = 1.0 - rho_r[i,j,k] + #set another density r and density b + rhor[i,j,k] = 0.0 + rhob[i,j,k] = 0.0 + #set density distribution equals to equilibrium density distribution function + for s in ti.static(range(19)): + f[i,j,k,s] = feq(s,1.0,v[i,j,k]) + F[i,j,k,s] = feq(s,1.0,v[i,j,k]) + +``init_geo(filename, filename2)`` import the geometry data + +.. code-block:: python + + def init_geo(filename, filename2): + #read the solid flag data and set it as an column major array + in_dat = np.loadtxt(filename) + in_dat[in_dat>0] = 1 + in_dat = np.reshape(in_dat, (nx,ny,nz),order='F') + + #read the phase data from file + phase_in_dat = np.loadtxt(filename2) + #set the array from the file with colum major + phase_in_dat = np.reshape(phase_in_dat, (nx,ny,nz), order='F') + + return in_dat, phase_in_dat + +``static_init()`` initialize non-modified variable + +.. code-block:: python + + @ti.kernel + def static_init(): + if ti.static(enable_projection): # No runtime overhead + #define lattice speed + e[0] = ti.Vector([0,0,0]) + e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1]) + e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0]) + e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1]) + e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1]) + #define another lattice speed + e_f[0] = ti.Vector([0,0,0]) + e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1]) + e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0]) + e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1]) + e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1]) + #define a weight parameter + w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0; + w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0; + w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0; + #define the boundary velocity + bc_vel_x_left = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl]) + bc_vel_x_right = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr]) + bc_vel_y_left = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl]) + bc_vel_y_right = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr]) + bc_vel_z_left = ti.Vector([vx_bczl, vy_bczl, vz_bczl]) + bc_vel_z_right = ti.Vector([vx_bczr, vy_bczr, vz_bczr]) + +``multiply_M()`` calculate the density distribution function in momentum space + +.. code-block:: python + + @ti.func + def multiply_M(i,j,k): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + for index in ti.static(range(19)): + for s in ti.static(range(19)): + #calculate here + out[index] += M[index,s]*F[i,j,k,s] + #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s]) + return out + +``GuoF(i,j,k,s,u)`` calculate Guo's force term + +.. code-block:: python + + @ti.func + def GuoF(i,j,k,s,u): + out=0.0 + for l in ti.static(range(19)): + out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l] + + return out + +``meq_vec(rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``Compute_C()`` calculate the color gradient + +.. code-block:: python + + @ti.func + def Compute_C(i): + C = ti.Vector([0.0,0.0,0.0]) + ind_S = 0 + for s in ti.static(range(19)): + ip = periodic_index_for_psi(i+e[s]) + if (solid[ip] == 0): + #if it's fluid calculate the color gradient based on psi + C += 3.0*w[s]*e_f[s]*psi[ip] + else: + #if it is solid and abs(density r-density b) is less than 0.9 + ind_S = 1 + #calculate the color gradient based on psi_solid and set ind_s=1 + C += 3.0*w[s]*e_f[s]*psi_solid + + if (abs(rho_r[i]-rho_b[i]) > 0.9) and (ind_S == 1): + #if abs(density r-density b) is very large and it's solid set color gradient to be zero + C = ti.Vector([0.0,0.0,0.0]) + + return C + +``Compute_S_local`` calculate parameter of s diagonal + +.. code-block:: python + + @ti.func + def Compute_S_local(id): + sv=0.0; sother=0.0 + if (psi[id]>0): + if (psi[id]>0.1): + #if psi>0.1 + #sv=1.0/(niu_l/(1.0/3.0)+0.5) + sv=wl + else: + #if 0-0.1 + sv=lg0+g1*psi[id]+g2*psi[id]*psi[id] + #calculate s other + sother = 8.0*(2.0-sv)/(8.0-sv) + + #set s diagonal to be zero and set certain element to be relatie local parameter + S = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + S[1]=sv;S[2]=sv;S[4]=sother;S[6]=sother;S[8]=sother;S[9]=sv; + S[10]=sv;S[11]=sv;S[12]=sv;S[13]=sv;S[14]=sv;S[15]=sv;S[16]=sother; + S[17]=sother;S[18]=sother; + + + return S; + + +``collision()`` define the collision and recoloring process + +.. code-block:: python + + @ti.kernel + def colission(): + for i,j,k in rho: + #if it is inner fluid, calculate color gradient divided by norm of color gradient + if (i0 : + normal = C/cc + #calculate the M + m_temp = multiply_M(i,j,k) + meq = meq_vec(rho[i,j,k],v[i,j,k]) + #calculate surface tension term + meq[1] += CapA*cc + meq[9] += 0.5*CapA*cc*(2*normal.x*normal.x-normal.y*normal.y-normal.z*normal.z) + meq[11] += 0.5*CapA*cc*(normal.y*normal.y-normal.z*normal.z) + meq[13] += 0.5*CapA*cc*(normal.x*normal.y) + meq[14] += 0.5*CapA*cc*(normal.y*normal.z) + meq[15] += 0.5*CapA*cc*(normal.x*normal.z) + #calculate s local + S_local = Compute_S_local(ti.Vector([i,j,k])) + #calculate s*(m-meq) + for s in ti.static(range(19)): + m_temp[s] -= S_local[s]*(m_temp[s]-meq[s]) + m_temp[s] += (1-0.5*S_local[s])*GuoF(i,j,k,s,v[i,j,k]) + #calculte convection of density filed + g_r = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + g_b = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + + for s in ti.static(range(19)): + f[i,j,k,s] = 0 + for l in ti.static(range(19)): + # 1.single phase collision + f[i,j,k,s] += inv_M[s,l]*m_temp[l] + + g_r[s] = feq(s,rho_r[i,j,k],v[i,j,k]) + g_b[s] = feq(s,rho_b[i,j,k],v[i,j,k]) + + if (cc>0): + for kk in ti.static([1,3,5,7,9,11,13,15,17]): + # ef=ts.vector.dot(e[kk],C) + ef=e[kk].dot(C) + cospsi= g_r[kk] if (g_r[kk]nx-1: iout[0] = 0 + if i[1]<0: iout[1] = ny-1 + if i[1]>ny-1: iout[1] = 0 + if i[2]<0: iout[2] = nz-1 + if i[2]>nz-1: iout[2] = 0 + + return iout + +``periodic_index_for_psi(i)`` defines the index of boundary for psi if using periodic boundary condition + +.. code-block:: python + + @ti.func + def periodic_index_for_psi(i): + iout = i + if i[0]<0: + #if periodic boundary condition set index based on periodic boundary condition + if bc_psi_x_left == 0: + iout[0] = nx-1 + else: + #otherwise set neighbouring index, + #similar for other sides + iout[0] = 0 + + if i[0]>nx-1: + if bc_psi_x_right==0: + iout[0] = 0 + else: + iout[0] = nx-1 + + if i[1]<0: + if bc_psi_y_left == 0: + iout[1] = ny-1 + else: + iout[1] = 0 + + if i[1]>ny-1: + if bc_psi_y_right==0: + iout[1] = 0 + else: + iout[1] = ny-1 + + if i[2]<0: + if bc_psi_z_left==0: + iout[2] = nz-1 + else: + iout[2] = 0 + + if i[2]>nz-1: + if bc_psi_z_right==0: + iout[2] = 0 + else: + iout[2] = nz-1 + + return iout + + +``streaming1()`` defines steaming process of denisty distribution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i,j,k in rho: + #if (solid[i,j,k] == 0): + if (i0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) + + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) + + + # Direction Y + if ti.static(bc_y_left==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + if (solid[i,1,k]>0): + F[i,0,k,s]=feq(s, rho_bcyl, v[i,1,k]) + else: + F[i,0,k,s]=feq(s, rho_bcyl, v[i,0,k]) + + if ti.static(bc_y_left==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + F[i,0,k,s]=feq(LR[s], 1.0, bc_vel_y_left[None])-F[i,0,k,LR[s]]+feq(s,1.0,bc_vel_y_left[None]) + + if ti.static(bc_y_right==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + if (solid[i,ny-2,k]>0): + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-2,k]) + else: + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-1,k]) + + if ti.static(bc_y_right==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + F[i,ny-1,k,s]=feq(LR[s], 1.0, bc_vel_y_right[None])-F[i,ny-1,k,LR[s]]+feq(s,1.0,bc_vel_y_right[None]) + + # Z direction + if ti.static(bc_z_left==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + if (solid[i,j,1]>0): + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,1]) + else: + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,0]) + + if ti.static(bc_z_left==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + F[i,j,0,s]=feq(LR[s], 1.0, bc_vel_z_left[None])-F[i,j,0,LR[s]]+feq(s,1.0,bc_vel_z_left[None]) + + if ti.static(bc_z_right==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + if (solid[i,j,nz-2]>0): + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-2]) + else: + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-1]) + + if ti.static(bc_z_right==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + F[i,j,nz-1,s]=feq(LR[s], 1.0, bc_vel_z_right[None])-F[i,j,nz-1,LR[s]]+feq(s,1.0,bc_vel_z_right[None]) + +``Boundary_condition_psi()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i,j,k, in rho: + #if (solid[i,j,k] == 0): + if (i tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +aside.footnote > span, +div.citation > span { + float: left; +} +aside.footnote > span:last-of-type, +div.citation > span:last-of-type { + padding-right: 0.5em; +} 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// [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff --git a/docs/_build/html/_static/minus.png b/docs/_build/html/_static/minus.png new file mode 100644 index 0000000..d96755f Binary files /dev/null and b/docs/_build/html/_static/minus.png differ diff --git a/docs/_build/html/_static/plus.png b/docs/_build/html/_static/plus.png new file mode 100644 index 0000000..7107cec Binary files /dev/null and b/docs/_build/html/_static/plus.png differ diff --git a/docs/_build/html/_static/pygments.css b/docs/_build/html/_static/pygments.css new file mode 100644 index 0000000..08bec68 --- /dev/null +++ b/docs/_build/html/_static/pygments.css @@ -0,0 +1,74 @@ +pre { line-height: 125%; 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = docUrlRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = docUrlRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; + }); + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/docs/_build/html/_static/sphinx_highlight.js b/docs/_build/html/_static/sphinx_highlight.js new file mode 100644 index 0000000..aae669d --- /dev/null +++ b/docs/_build/html/_static/sphinx_highlight.js @@ -0,0 +1,144 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + parent.insertBefore( + span, + parent.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(SphinxHighlight.highlightSearchWords); +_ready(SphinxHighlight.initEscapeListener); diff --git a/docs/_build/html/aaa.html b/docs/_build/html/aaa.html new file mode 100644 index 0000000..2a18f1c --- /dev/null +++ b/docs/_build/html/aaa.html @@ -0,0 +1,644 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/example_cavity.html b/docs/_build/html/example_cavity.html new file mode 100644 index 0000000..c2e4989 --- /dev/null +++ b/docs/_build/html/example_cavity.html @@ -0,0 +1,173 @@ + + + + + + + example_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_cavity

+

This file use the LBM_3D_SinglePhase_Solver to simulate the cavity flow

+
#import certain packages
+import time
+import taichi as ti
+
+ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#set 50*50*50 cavity based on LB3D_Solver_Single_Phase solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=50,ny=50,nz=50, sparse_storage=False)
+
+#import geometry data
+lb3d.init_geo('./geo_cavity.dat')
+#set the x-right velocity
+lb3d.set_bc_vel_x1([0.0,0.0,0.1])
+#initialize
+lb3d.init_simulation()
+
+#simulation step
+for iter in range(2000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #get the maximum velocity
+        max_v = lb3d.get_max_v()
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the number of time steps, maxiumum force and the force scale=0
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, max_v,  0.0))
+        #every 1000 time steps export the vtk file
+        if (iter%1000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/example_porous_medium.html b/docs/_build/html/example_porous_medium.html new file mode 100644 index 0000000..844419e --- /dev/null +++ b/docs/_build/html/example_porous_medium.html @@ -0,0 +1,170 @@ + + + + + + + example_porous_medium — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_porous_medium

+

This file simulate the porous medium based on the LBM_3D_SinglePhase_Solver

+
#import time and taichi package
+import time
+import taichi as ti
+#taichi intialization
+ti.init(arch=ti.cpu)
+#import the LBM_3D_SinglePhase_Solver
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#create the 131*131*131 gird LBM_3D_SinglePhase_Solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=131,ny=131,nz=131)
+#import the porous medium geometry
+lb3d.init_geo('./img_ftb131.txt')
+#set x-left and x-right density
+lb3d.set_bc_rho_x1(0.99)
+lb3d.set_bc_rho_x0(1.0)
+#initialize the simulation
+lb3d.init_simulation()
+#simulation loop
+for iter in range(50000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the time step, max force=10, force_scale=10
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+        #export VTK every 2000 time step
+        if (iter%2000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/flow_domain_geo_generation_2D.html b/docs/_build/html/flow_domain_geo_generation_2D.html new file mode 100644 index 0000000..526eb37 --- /dev/null +++ b/docs/_build/html/flow_domain_geo_generation_2D.html @@ -0,0 +1,163 @@ + + + + + + + flow_domain_geo_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation_2D

+

This file generate geometry file for solver to read

+
#import certain module
+import numpy as np
+import math
+
+
+#define the input file name
+# INPUT STL FILE NAME
+output_name = 'geo_cavity.dat'
+
+#define the grid resolution
+dnx, dny, dnz = 50, 50, 50
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+
+#define an matrix dnx*dny*dnz with zero values
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#define the boundary to be solid
+out_dat[0,:,:] = 1
+#cout_dat[:,:,0] = 1
+out_dat[:,0,:] = 1
+out_dat[:,-1,:] = 1
+out_dat[:,:,0] = 1
+out_dat[:,:,-1] = 1
+
+#=========================================================
+#reshape the data to be column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+
+
+#output the transfer of out_dat to the file with integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/genindex.html b/docs/_build/html/genindex.html new file mode 100644 index 0000000..08506b6 --- /dev/null +++ b/docs/_build/html/genindex.html @@ -0,0 +1,103 @@ + + + + + + Index — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Index
    • +
  • +
    • +
+
+
+
+
+ + +

Index

+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/index.html b/docs/_build/html/index.html new file mode 100644 index 0000000..f6256d7 --- /dev/null +++ b/docs/_build/html/index.html @@ -0,0 +1,151 @@ + + + + + + + Welcome to taichi-LBM3D’s documentation! — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/lbm_solver_3d.html b/docs/_build/html/lbm_solver_3d.html new file mode 100644 index 0000000..77ad6e0 --- /dev/null +++ b/docs/_build/html/lbm_solver_3d.html @@ -0,0 +1,530 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s Force scheme

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+    #calculate Guo's force here
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) calculate equilibrium density distribution function in momentum space

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

collison() define the prcoess of collision

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is fluid
+        if (solid[i,j,k] == 0):
+            #calculate m
+            m_temp = multiply_M(i,j,k)
+            #calculate meq
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                #calculate -s*(m-meq)
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #add Guo's force
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    #f=-M^-1*S(m-meq)
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

periodic_index(i) set the bounary index with periodic bounary condition

+
@ti.func
+def periodic_index(i):
+    #inner index
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = nx-1
+    #x-right
+    if i[0]>nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = ny-1
+    #y-right
+    if i[1]>ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = nz-1
+    #z-right
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming process of denisty distibution function

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        #if it is fluid
+        if (solid[i] == 0):
+            for s in range(19):
+                #the neighbour index
+                ip = periodic_index(i+e[s])
+                #if neighbour index is fluid just streaming
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                #if neighbour index is solid just bounce back
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

streaming2() a simple streaming process without consideration of solid and boundary

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

Boudary_condition() define the bounary condition of fixed pressure and fixed velocity

+
@ti.kernel
+def Boundary_condition():
+    #pressure-boundary condtion x-left
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #if boundary is fluid but the neighbour is solid
+                #equilibrium density distribution function is calculated based on the neighbour velocity
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                #if boundary is fluid and the neighbour is also fluid
+                #equilibrium density distribution function is calculated based on the boundary velocity
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    #velocity-boundary conditon x-left
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #calculate density distribution fucntion based on equilibrium part and non-equilibrium part
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    #pressure boundary condition x-right similar to x-left
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    #velocity booundary condition x-right similar to x-left
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

streaming3() calculate the macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        #if it is fluid calculate density and velocity based on density distribution function
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+        # if it is solid set denisty equals one and velocity equals zero
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

At the end of the file do the actual simulation and export the data

+
#define some time varible
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+#import the solid flag data
+#solid_np = init_geo('./BC.dat')
+solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+
+# do the initialization
+static_init()
+init()
+
+# do the actual simulation
+for iter in range(50000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    # calculate every 1000 time step
+    if (iter%1000==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        #calculate the time difference between now and previous time step
+        diff_time = int(time_now-time_pre)
+        #calculate the time difference between now and the initial time
+        elap_time = int(time_now-time_init)
+        #divmod function return the quotient and the remainder
+        #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2]))
+                            }
+            )
+# ti.sync()
+# ti.profiler.print_kernel_profiler_info()
+#print the profiler information of every kernel and task of taichi in this file
+ti.profiler.print_scoped_profiler_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/lbm_solver_3d_cavity.html b/docs/_build/html/lbm_solver_3d_cavity.html new file mode 100644 index 0000000..7e051cd --- /dev/null +++ b/docs/_build/html/lbm_solver_3d_cavity.html @@ -0,0 +1,156 @@ + + + + + + + lbm_solver_3d_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_cavity

+

This solver is almost similar to lbm_solver_3d expect several difference as follows: +.. number:: lbm_solver_3d_cavity

+
    +

  1. The Grid resolution in this solver is 50x50x50

    2. +

  2. The viscosity in this solver is 0.16667

    3. +

  3. The boundary condition in this solver is velocity solver on x-right as follows

    4. +
+

boundary condition of this solver

+
#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+
+

x-right is implementated with velocity boundary condition

+

4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary.

+
if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left))
+
+
+
    +

  1. Finally, the definition of the varible is slightly different from lbm_solver_3d

    2. +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/lbm_solver_3d_sparse.html b/docs/_build/html/lbm_solver_3d_sparse.html new file mode 100644 index 0000000..58c9363 --- /dev/null +++ b/docs/_build/html/lbm_solver_3d_sparse.html @@ -0,0 +1,143 @@ + + + + + + + lbm_solver_3d_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_sparse

+

This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible:

+
f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse.

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/modules.html b/docs/_build/html/modules.html new file mode 100644 index 0000000..139c882 --- /dev/null +++ b/docs/_build/html/modules.html @@ -0,0 +1,148 @@ + + + + + + + taichi_LBM3D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/objects.inv b/docs/_build/html/objects.inv new file mode 100644 index 0000000..8b79ea0 Binary files /dev/null and b/docs/_build/html/objects.inv differ diff --git a/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solute_Solver.html b/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solute_Solver.html new file mode 100644 index 0000000..cae5168 --- /dev/null +++ b/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solute_Solver.html @@ -0,0 +1,699 @@ + + + + + + + LBM_3D_SinglePhase_Solute_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

LBM_3D_SinglePhase_Solute_Solver

+

This file is the solver for solute transportation

+

First import the certain package and define the class of LB3D_Solver_Single_Phase_Solute which inheritant from +LB3D_Solver_Single_Phase_Solute

+
from sympy import inverse_mellin_transform
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+
+#ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3d
+
+@ti.data_oriented
+class LB3D_Solver_Single_Phase_Solute(lb3d.LB3D_Solver_Single_Phase):
+    def __init__(self, nx, ny, nz):
+        super(LB3D_Solver_Single_Phase_Solute, self).__init__(nx, ny, nz, sparse_storage = False)
+        #define solute boundary condition
+        self.solute_bc_x_left, self.solute_bcxl = 0, 0.0
+        self.solute_bc_x_right, self.solute_bcxr = 0, 0.0
+        self.solute_bc_y_left, self.solute_bcyl = 0, 0.0
+        self.solute_bc_y_right, self.solute_bcyr = 0, 0.0
+        self.solute_bc_z_left, self.solute_bczl = 0, 0.0
+        self.solute_bc_z_right, self.solute_bczr = 0, 0.0
+
+        #define parameters for bouyancy force
+        self.buoyancy_parameter = 20.0   #Buoyancy Parameter (0= no buoyancy)
+        self.ref_T = 20.0              #reference_psi F=/rho*g+Bouyancy*(/psi-reference_psi)*g)
+        #define gravity
+        self.gravity = 5e-7
+
+        #define concentration distribution function
+        self.fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define another concentration distribution function
+        self.Fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define external force
+        self.forcexyz = ti.Vector.field(3,ti.f32,shape=(nx,ny,nz))
+        #define entropy
+        self.rho_H = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define temperature
+        self.rho_T = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define liquid volumn fraction
+        self.rho_fl = ti.field(ti.f32, shape=(nx,ny,nz))
+
+        #define specific heat of liquid
+        self.Cp_l= 1.0
+        #define specific heat of solid
+        self.Cp_s = 1.0
+        #define latent heat
+        self.Lt = 1.0
+        #define solid temperature
+        self.T_s = -10.0
+        #define liquid temperature
+        self.T_l = -10.0
+        #define viscosity of solid
+        self.niu_s = 0.002
+        #define viscosity of liquid
+        self.niu_l = 0.002
+
+        #define energy of solid
+        self.H_s = None
+        #define energy of liquid
+        self.H_l = None
+
+        #define rock thermal diffusivity
+        self.niu_solid = 0.001
+        #define specific heat of rock
+        self.Cp_solid = 1.0
+
+
+

An then it sets these parameters with functions

+
#set gravity
+def set_gravity(self, gravity):
+self.gravity = gravity
+#set buoyancy force parameter
+def set_buoyancy_parameter(self, buoyancy_param):
+    self.buoyancy_parameter = buoyancy_param
+#set reference temperature
+def set_ref_T(self, ref_t):
+    self.ref_T = ref_t
+#set specific heat of solid
+def set_specific_heat_solid(self, cps):
+    self.Cp_s = cps
+#set specfic heat of liquid
+def set_specific_heat_liquid(self, cpl):
+    self.Cp_l = cpl
+#set specfic heat of rock
+def set_specific_heat_rock(self, cprock):
+    self.Cp_solid = cprock
+#set latent heat
+def set_latent_heat(self, ltheat):
+    self.Lt = ltheat
+#set solidus temperature
+def set_solidus_temperature(self, ts):
+    self.T_s = ts
+#set liquidus temperature
+def set_liquidus_temperature(self, tl):
+    self.T_l = tl
+#set solid thermal diffusivity
+def set_solid_thermal_diffusivity(self, nius):
+    self.niu_s = nius
+#set liquid thermal diffusivity
+def set_liquid_thermal_diffusivity(self, niul):
+    self.niu_l = niul
+#set rock thermal diffusivity
+def set_rock_thermal_diffusivity(self, niurock):
+    self.niu_solid = niurock
+#set adiabatic boundary on x-left
+def set_bc_adiabatic_x_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_x_left = 2
+#set adiabatic boundary on x-right
+def set_bc_adiabatic_x_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_x_right = 2
+#set adiabatic boundary on y-left
+def set_bc_adiabatic_y_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_y_left = 2
+#set adiabatic boundary on y-right
+def set_bc_adiabatic_y_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_y_right = 2
+#set adiabatic boundary on z-left
+def set_bc_adiabatic_z_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_z_left = 2
+#set adiabatic boundary on z-right
+def set_bc_adiabatic_z_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_z_right = 2
+#set constant temperature on x-left
+def set_bc_constant_temperature_x_left(self,xl):
+    self.solute_bc_x_left = 1
+    self.solute_bcxl = xl
+#set constant temperature on x-right
+def set_bc_constant_temperature_x_right(self,xr):
+    self.solute_bc_x_right = 1
+    self.solute_bcxr = xr
+#set constant temperature on y-left
+def set_bc_constant_temperature_y_left(self,yl):
+    self.solute_bc_y_left = 1
+    self.solute_bcyl = yl
+#set constant temperature on y-right
+def set_bc_constant_temperature_y_right(self,yr):
+    self.solute_bc_y_right = 1
+    self.solute_bcyr = yr
+#set constant temperature on z-left
+def set_bc_constant_temperature_z_left(self,zl):
+    self.solute_bc_z_left = 1
+    self.solute_bczl = zl
+#set constant temperature on z-right
+def set_bc_constant_temperature_z_right(self,zr):
+    self.solute_bc_y_right = 1
+    self.solute_bczr = zr
+
+# update energy of solid and liquid
+def update_H_sl(self):
+    #energy of solid
+    self.H_s = self.Cp_s*self.T_s
+    #energy of liquid
+    self.H_l = self.H_s+self.Lt
+    print('H_s',self.H_s)
+    print('H_l',self.H_l)
+
+
+

Then it initialize some variable or function

+
#intialize the energy
+@ti.kernel
+def init_H(self):
+    for I in ti.grouped(self.rho_T):
+        #calculate the energy, convert_T_H() define later
+        self.rho_H[I] = self.convert_T_H(self.rho_T[I])
+
+#intialize the density distribiution function for solute concentration
+@ti.kernel
+def init_fg(self):
+    for I in ti.grouped(self.fg):
+        #calculate the overall specific heat
+        Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s
+        #intialize the density distribiution function for solute concentration equals equilibrium density distribiution function for solute concentration
+        for s in ti.static(range(19)):
+            self.fg[I][s] = self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])
+            self.Fg[I][s] = self.fg[I][s]
+
+#intialize the volumn fraction of liquid
+@ti.kernel
+def init_fl(self):
+    for I in ti.grouped(self.rho_T):
+        #convert_T_fl define later
+        self.rho_fl[I] = self.convert_T_fl(self.rho_T[I])
+
+
+

g_feq(self, k,local_T,local_H, Cp, u) calculate the equilibrium density distribiution function for thermal energy

+
@ti.func
+def g_feq(self, k,local_T,local_H, Cp, u):
+    eu = self.e[k].dot(u)
+    uv = u.dot(u)
+    feqout = 0.0
+    #calculating the zero-velocity equilibrium thermal distribution function
+    if (k==0):
+        feqout = local_H-Cp*local_T+self.w[k]*Cp*local_T*(1-1.5*uv)
+    else:
+    #calculating other directions equilibrium thermal distribution function
+        feqout = self.w[k]*Cp*local_T*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, self.w[k], feqout, Cp, local_T)
+    return feqout
+
+
+

cal_local_force(i, j, k) calculates buoyancy force

+
#density is the function of temperture delat(rho)=-rho*beta*delta(T)
+@ti.func
+def cal_local_force(self, i, j, k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    f[1] += self.gravity*self.buoyancy_parameter*(self.rho_T[i,j,k]-self.ref_T)
+    #f= delta(rho)*delta(v)*g
+    f *= self.rho_fl[i,j,k]
+    return f
+
+
+

collision_g() defines the the collision of thermal distribution function

+
@ti.kernel
+def colission_g(self):
+    for I in ti.grouped(self.rho_T):
+        #overall relaxation time
+        tau_s = 3*(self.niu_s*(1.0-self.rho_fl[I])+self.niu_l*self.rho_fl[I])+0.5
+        #overall specific heat
+        Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s
+
+        #ROCK overall relaxation time and specific heat
+        if (self.solid[I] >0):
+            tau_s = 3.0*self.niu_solid+0.5
+            Cp = self.Cp_solid
+
+        #f=f-1/tau*(f-feq)
+        for s in ti.static(range(19)):
+            tmp_fg = -1.0/tau_s*(self.fg[I][s]-self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]))
+            #print(self.fg[I][s],tmp_fg,I,s,self.rho_H[I],self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]))
+            self.fg[I][s] += tmp_fg
+
+
+

collision() defines the the collision of density distribution function

+
@ti.kernel
+def colission(self):
+    for i,j,k in self.rho:
+        #if (self.solid[i,j,k] == 0):
+        m_temp = self.M[None]@self.F[i,j,k]
+        meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+        m_temp -= self.S_dig[None]*(m_temp-meq)
+        f = self.cal_local_force(i,j,k)
+        if (ti.static(self.force_flag==1)):
+            for s in ti.static(range(19)):
+            #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #f = self.cal_local_force()
+                f_guo=0.0
+                for l in ti.static(range(19)):
+                    f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+
+        self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+        #calculate the denisty distribution function in momentum space here
+        self.f[i,j,k] += self.inv_M[None]@m_temp
+        #calculate the fluid density distribution function here
+        for s in ti.static(range(19)):
+            self.f[i,j,k][s] = self.f[i,j,k][s]*(self.rho_fl[i,j,k]) + self.w[s]*(1.0-self.rho_fl[i,j,k])
+
+
+

streaming1() and streaming1_g() defines the fluid denisty distribiution function and +thermal density distribiution function

+
@ti.kernel
+def streaming1(self):
+    for i in ti.grouped(self.rho):
+        #if (self.solid[i] == 0):
+        for s in ti.static(range(19)):
+            ip = self.periodic_index(i+self.e[s])
+            self.F[ip][s] = self.f[i][s]
+
+@ti.kernel
+def streaming1_g(self):
+    for i in ti.grouped(self.rho_T):
+        for s in ti.static(range(19)):
+            ip = self.periodic_index(i+self.e[s])
+            self.Fg[ip][s] = self.fg[i][s]
+
+
+

this

+
@ti.kernel
+def BC_concentration(self):
+    #constant temperature boundary condition
+    if ti.static(self.solute_bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            local_T = self.solute_bcxl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[0,j,k]*self.Cp_l + (1-self.rho_fl[0,j,k])*self.Cp_s
+            #the boundary's thermal distribution function equals the equilibrium thermal distribution function on the boundary
+            for s in ti.static(range(19)):
+                self.fg[0,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[0,j,k])
+                self.Fg[0,j,k][s] = self.fg[0,j,k][s]
+    #adiabatic boundary condition
+    elif ti.static(self.solute_bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            for s in ti.static(range(19)):
+            #there is no thermal transfer between the boundaty and neighbouring cell
+                self.fg[0,j,k][s] = self.fg[1,j,k][s]
+                self.Fg[0,j,k][s] = self.fg[1,j,k][s]
+
+    #x-right
+    if ti.static(self.solute_bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            local_T = self.solute_bcxr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[self.nx-1,j,k]*self.Cp_l + (1-self.rho_fl[self.nx-1,j,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[self.nx-1,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[self.nx-1,j,k])
+                self.Fg[self.nx-1,j,k][s]= self.fg[self.nx-1,j,k][s]
+    elif ti.static(self.solute_bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s]
+                self.Fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s]
+
+    #y-left
+    if ti.static(self.solute_bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            local_T = self.solute_bcyl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,0,k]*self.Cp_l + (1-self.rho_fl[i,0,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,0,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,0,k])
+                self.Fg[i,0,k][s] = self.fg[i,0,k][s]
+    elif ti.static(self.solute_bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[i,0,k][s] = self.fg[i,1,k][s]
+                self.Fg[i,0,k][s] = self.fg[i,1,k][s]
+
+    #y-right
+    if ti.static(self.solute_bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            local_T = self.solute_bcyr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,self.ny-1,k]*self.Cp_l + (1-self.rho_fl[i,self.ny-1,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,self.ny-1,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,self.ny-1,k])
+                self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-1,k][s]
+    elif ti.static(self.solute_bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s]
+                self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s]
+
+    #z-left
+    if ti.static(self.solute_bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            local_T = self.solute_bczl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,j,0]*self.Cp_l + (1-self.rho_fl[i,j,0])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,j,0][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,0])
+                self.Fg[i,j,0][s] = self.fg[i,j,0][s]
+    elif ti.static(self.solute_bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            for s in ti.static(range(19)):
+                self.fg[i,j,0][s] = self.fg[i,j,1][s]
+                self.Fg[i,j,0][s] = self.fg[i,j,1][s]
+
+    #z-right
+    if ti.static(self.solute_bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            local_T = self.solute_bczr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,j,self.nz-1]*self.Cp_l + (1-self.rho_fl[i,j,self.nz-1])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,j,self.nz-1][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,self.nz-1])
+                self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-1][s]
+    elif ti.static(self.solute_bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            for s in ti.static(range(19)):
+                self.fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s]
+                self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s]
+
+
+

convert_H_T() calculate the temperature

+
@ti.func
+def convert_H_T(self,local_H):
+    new_T=0.0
+    #if local enthalpy is less than solid enthalpy
+    #T= enthalpy/specific heat
+    if (local_H<self.H_s):
+        new_T = local_H/self.Cp_s
+    #if if local enthalpy is greater than liquid enthalpy
+    #T= Tliquid+(enthalpy-liquid enthalpy)/speific heat of liquid
+    elif (local_H>self.H_l):
+        new_T = self.T_l+(local_H-self.H_l)/self.Cp_l
+    #if if temperature is greater than solid temperature
+    #T= Tsolid+(enthalpy-solid enthalpy)/(enthalpy of liquid-enthalpy of solid)*(temperature of liquid- temperature of solid)
+    elif (self.T_l>self.T_s):
+        new_T = self.T_s+(local_H-self.H_s)/(self.H_l-self.H_s)*(self.T_l-self.T_s)
+    else:
+    #else T= temperature of solid
+        new_T = self.T_s
+
+    return new_T
+
+
+

convert_H_fl() calculate the volumn fraction of liquid

+
@ti.func
+def convert_H_fl(self,local_H):
+    new_fl=0.0
+    #if enthalpy is less than solid enthalpy
+    #it is zero
+    if (local_H<self.H_s):
+        new_fl = 0.0
+    #if it is greater than liquid enthalpy
+    #it is one
+    elif (local_H>self.H_l):
+        new_fl = 1.0
+    #else
+    #it equals to (enthaply- soid enthaply)/(enthaply of liquid- enthalpy of solid)
+    else:
+        new_fl = (local_H-self.H_s)/(self.H_l-self.H_s)
+
+    return new_fl
+
+
+

convert_T_H() calculate the enthaply from temperature

+
@ti.func
+def convert_T_H(self,local_T):
+    new_H = 0.0
+    # calculate enthaply for three different conditions
+    if (local_T<=self.T_s):
+        new_H = self.Cp_s*local_T
+    elif (local_T>self.T_l):
+        new_H = (local_T-self.T_l)*self.Cp_l+self.H_l
+    else:
+        fluid_frc = (local_T-self.T_s)/(self.T_l-self.T_s)
+        new_H = self.H_s*(1-fluid_frc) + self.H_l*fluid_frc
+    return new_H
+
+
+

convert_T_fl() calculate volumn fraction from temperature

+
@ti.func
+def convert_T_fl(self,local_T):
+    new_fl = 0.0
+    # calculate volumn fraction for three different conditions
+    if (local_T<=self.T_s):
+        new_fl = 0.0
+    elif (local_T>=self.T_l):
+        new_fl = 1.0
+    elif (self.T_l>self.T_s):
+        new_fl = (local_T-self.T_s)/(self.T_l-self.T_s)
+    else:
+        new_fl = 1.0
+
+    return new_fl
+
+
+

streaming3() calculate macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        self.forcexyz[i] = self.cal_local_force(i.x, i.y, i.z)
+        #print(i.x, i.y, i.z)
+        if ((self.solid[i]==0) or (self.rho_fl[i]>0.0)):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            for s in ti.static(range(19)):
+                self.f[i][s] = self.f[i][s]*self.rho_fl[i]+self.w[s]*(1.0-self.rho_fl[i])
+            #density for fluid
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+            #velocity for fluid
+            self.v[i] /= self.rho[i]
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        #density and velocity for solid
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

streaming3() calculate enthalpy

+
@ti.kernel
+def streaming3_g(self):
+    for i in ti.grouped(self.rho_T):
+        self.rho_H[i] = 0.0
+        #enthalpy here
+        self.rho_H[i] = self.Fg[i].sum()
+        #for s in ti.static(range(19)):
+        #    self.rho_H[i] += self.Fg[i][s]
+        self.fg[i] = self.Fg[i]
+
+
+

update_T_fl() calculate volumn fraction and temperature

+
@ti.kernel
+def update_T_fl(self):
+    for I in ti.grouped(self.rho_T):
+        self.rho_T[I] = self.convert_H_T(self.rho_H[I])
+        self.rho_fl[I] = self.convert_H_fl(self.rho_H[I])
+        if (self.solid[I]>0):
+            self.rho_fl[I] = 0.0
+
+
+

init_solute_simulation() initialize the solute simulation

+
def init_solute_simulation(self):
+
+    self.init_simulation()
+    self.update_H_sl()
+    #ethalpy
+    self.init_H()
+    #volumn fraction
+    self.init_fl()
+    #thermal distribution function
+    self.init_fg()
+
+
+

init_concentration(filename) import concentration data from file

+
def init_concentration(self,filename):
+    in_dat = np.loadtxt(filename)
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    self.rho_T.from_numpy(in_dat)
+
+
+

this

+
def step(self):
+    self.colission()
+    self.colission_g()
+
+    self.streaming1()
+    self.streaming1_g()
+
+    self.Boundary_condition()
+    self.BC_concentration()
+
+    self.streaming3_g()
+    self.streaming3()
+    self.streaming3_g()
+
+    self.update_T_fl()
+
+
+

this

+
def export_VTK(self, n):
+    gridToVTK(
+            "./LB_SingelPhase_"+str(n),
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "Solid_Liquid": np.ascontiguousarray(self.rho_fl.to_numpy()),
+                        "Tempreture": np.ascontiguousarray(self.rho_T.to_numpy()),
+                        "Entropy": np.ascontiguousarray(self.rho_H.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])),
+                        "Force": (      np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

this

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solver.html b/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..2ee3a59 --- /dev/null +++ b/docs/_build/html/phasechange/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,125 @@ + + + + + + + LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

LBM_3D_SinglePhase_Solver

+

This file is the same as LBM_3D_SinglePhase_Solver in Single_phase folder

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/example_cavity_melting.html b/docs/_build/html/phasechange/example_cavity_melting.html new file mode 100644 index 0000000..ae9d24d --- /dev/null +++ b/docs/_build/html/phasechange/example_cavity_melting.html @@ -0,0 +1,124 @@ + + + + + + + example_cavity_melting — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_cavity_melting

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/example_phase_change.html b/docs/_build/html/phasechange/example_phase_change.html new file mode 100644 index 0000000..90da0ca --- /dev/null +++ b/docs/_build/html/phasechange/example_phase_change.html @@ -0,0 +1,124 @@ + + + + + + + example_phase_change — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_phase_change

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/read_img_solute_psi_generation_2D.html b/docs/_build/html/phasechange/read_img_solute_psi_generation_2D.html new file mode 100644 index 0000000..1bf9ec6 --- /dev/null +++ b/docs/_build/html/phasechange/read_img_solute_psi_generation_2D.html @@ -0,0 +1,124 @@ + + + + + + + read_img_solute_psi_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

read_img_solute_psi_generation_2D

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/solute_psi_generation_2D.html b/docs/_build/html/phasechange/solute_psi_generation_2D.html new file mode 100644 index 0000000..7f736fb --- /dev/null +++ b/docs/_build/html/phasechange/solute_psi_generation_2D.html @@ -0,0 +1,124 @@ + + + + + + + solute_psi_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

solute_psi_generation_2D

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/phasechange/test1.html b/docs/_build/html/phasechange/test1.html new file mode 100644 index 0000000..9141c6e --- /dev/null +++ b/docs/_build/html/phasechange/test1.html @@ -0,0 +1,122 @@ + + + + + + + test1 — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + +
+ + +
+ +
+
+ +
+
+ +
+

test1

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/search.html b/docs/_build/html/search.html new file mode 100644 index 0000000..1eb12ca --- /dev/null +++ b/docs/_build/html/search.html @@ -0,0 +1,118 @@ + + + + + + Search — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Search
    • +
  • +
    • +
+
+
+
+
+ + + + +
+ +
+ +
+
+ +
+
+
+
+ + + + + + + + + \ No newline at end of file diff --git a/docs/_build/html/searchindex.js b/docs/_build/html/searchindex.js new file mode 100644 index 0000000..ee84f2a --- /dev/null +++ b/docs/_build/html/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"docnames": ["2phase", "Grey_Scale", "Grey_scale/flow_domain_geo_generation", "Grey_scale/lbm_solver_3d_Macro_Sukop", "Phase_change", "Single_phase", "Single_phase/Convert_stl_to_binary", "Single_phase/LBM_3D_SinglePhase_Solver", "Single_phase/example_cavity", "Single_phase/example_porous_medium", "Single_phase/flow_domain_geo_generation_2D", "Single_phase/lbm_solver_3d", "Single_phase/lbm_solver_3d_cavity", "Single_phase/lbm_solver_3d_sparse", "index", "modules", "phasechange/LBM_3D_SinglePhase_Solute_Solver", "phasechange/LBM_3D_SinglePhase_Solver", "phasechange/example_cavity_melting", "phasechange/example_phase_change", "phasechange/read_img_solute_psi_generation_2D", "phasechange/solute_psi_generation_2D", "phasechange/test1", 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and tables": [[14, "indices-and-tables"]], "Grey_Scale": [[1, "grey-scale"]], "Single_phase": [[5, "single-phase"]], "Convert_stl_to_binary": [[6, "convert-stl-to-binary"]], "Single_phase.LBM_3D_SinglePhase_Solver": [[7, "single-phase-lbm-3d-singlephase-solver"]], "example_cavity": [[8, "example-cavity"]], "example_porous_medium": [[9, "example-porous-medium"]], "flow_domain_geo_generation_2D": [[10, "flow-domain-geo-generation-2d"]], "Single_phase.lbm_solver_3d": [[11, "single-phase-lbm-solver-3d"]], "lbm_solver_3d_sparse": [[13, "lbm-solver-3d-sparse"]], "flow_domain_geo_generation": [[2, "flow-domain-geo-generation"]], "lbm_solver_3d_cavity": [[12, "lbm-solver-3d-cavity"]], "lbm_solver_3d_Macro_Sukop": [[3, "lbm-solver-3d-macro-sukop"]], "2phase": [[0, "phase"]], "example_cavity_melting": [[18, "example-cavity-melting"]], "example_phase_change": [[19, "example-phase-change"]], "read_img_solute_psi_generation_2D": [[20, "read-img-solute-psi-generation-2d"]], "solute_psi_generation_2D": [[21, "solute-psi-generation-2d"]], "test1": [[22, "test1"]], "lbm_solver_3d_2phase": [[23, "lbm-solver-3d-2phase"]], "lbm_solver_3d_2phase_sparse": [[24, "lbm-solver-3d-2phase-sparse"]], "Phase_change": [[4, "phase-change"]], "LBM_3D_SinglePhase_Solver": [[17, "lbm-3d-singlephase-solver"]], "LBM_3D_SinglePhase_Solute_Solver": [[16, "lbm-3d-singlephase-solute-solver"]]}, "indexentries": {}}) \ No newline at end of file diff --git a/docs/_build/html/twophase/lbm_solver_3d_2phase.html b/docs/_build/html/twophase/lbm_solver_3d_2phase.html new file mode 100644 index 0000000..65b85a2 --- /dev/null +++ b/docs/_build/html/twophase/lbm_solver_3d_2phase.html @@ -0,0 +1,813 @@ + + + + + + + lbm_solver_3d_2phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_2phase

+

This solver is the multiphase model based on color gradient model +Firstly, it defines some parameters

+
# NOTE: THIS CODE NEED taichi_glsl, so please use taichi version <=0.8.5
+#import taichi, numpy, pyevtk and time package
+import taichi as ti
+import numpy as np
+#import taichi_glsl as ts
+from pyevtk.hl import gridToVTK
+import time
+#from taichi_glsl import scalar
+
+#from taichi_glsl.scalar import isinf, isnan
+#from taichi_glsl.vector import vecFill
+#intialize taichi
+ti.init(arch=ti.cpu)
+#ti.init(arch=ti.gpu, dynamic_index=True,offline_cache=True)
+
+#enable projection
+enable_projection = True
+# 131*131*131
+nx,ny,nz = 131,131,131
+#nx,ny,nz = 131,131,131
+#external force in x,y,z direction
+fx,fy,fz = 5.0e-5,-2e-5,0.0
+#niu = 0.1
+#liquid viscosity
+niu_l = 0.1         #psi>0
+#gas viscosity
+niu_g = 0.1         #psi<0
+#psi in color gradient calculation
+psi_solid = 0.7
+#surface tension
+CapA = 0.005
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 0, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+bc_psi_x_left, psi_x_left = 1, -1.0          #   boundary condition for phase-field: 0 = periodic,
+bc_psi_x_right, psi_x_right = 0, 1.0        #   1 = constant value on the boundary, value = -1.0 phase1 or 1.0 = phase 2
+bc_psi_y_left, psi_y_left = 0, 1.0
+bc_psi_y_right, psi_y_right = 0, 1.0
+bc_psi_z_left, psi_z_left = 0, 1.0
+bc_psi_z_right, psi_z_right = 0, 1.0
+
+# Non Sparse memory allocation
+#density distribution function nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#velocity nx*ny*nz vector
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#psi nx*ny*nz
+psi = ti.field(ti.f32, shape=(nx,ny,nz))
+#density r nx*ny*nz
+rho_r = ti.field(ti.f32, shape=(nx,ny,nz))
+#density b nx*ny*nz
+rho_b = ti.field(ti.f32, shape=(nx,ny,nz))
+#density r nx*ny*nz
+rhor = ti.field(ti.f32, shape=(nx,ny,nz))
+#density b nx*ny*nz
+rhob = ti.field(ti.f32, shape=(nx,ny,nz))
+#lattice speed 19 dimensional vector
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#S_dig = ti.field(ti.f32,shape=(19))
+#lattice speed 19 dimensional vector
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#weight parameter 19 dimensional vector
+w = ti.field(ti.f32, shape=(19))
+#solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#streaming vector 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+
+#external force 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+# x-left velocity 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+# x-right velocity 3 dimensional vector
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+# y-left velocity 3 dimensional vector
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+# y-right velocity 3 dimensional vector
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+# z-left velocity 3 dimensional vector
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+# z-right velocity 3 dimensional vector
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#inverse transforming matrix 19*19
+inv_M = ti.field(ti.f32, shape=(19,19))
+#parameters for calculating the parameter of s diagonal
+#=======================================#
+lg0, wl, wg = 0.0, 0.0, 0.0
+l1, l2, g1, g2 = 0.0, 0.0, 0.0, 0.0
+wl = 1.0/(niu_l/(1.0/3.0)+0.5)
+wg = 1.0/(niu_g/(1.0/3.0)+0.5)
+lg0 = 2*wl*wg/(wl+wg)
+l1=2*(wl-lg0)*10
+l2=-l1/0.2
+g1=2*(lg0-wg)*10
+g2=g1/0.2
+#=======================================#
+
+#transformation matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#inverde of transforming matrix
+inv_M_np = np.linalg.inv(M_np)
+#streaming array
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#M matrix from the numpy
+M.from_numpy(M_np)
+#inverse matrix from numpy
+inv_M.from_numpy(inv_M_np)
+
+#steaming array from numpy
+LR.from_numpy(LR_np)
+#external force with vector three dimensional
+ext_f[None] = ti.Vector([fx,fy,fz])
+#set transforming matrix, inverse matrix and streaming vector non-modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+
+#set x,y,z array with nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#set meshgrid and return three meshgrid matrix X,Y,Z with non-cartesian indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local, u) calculate the equilibrium denisty distribution function

+
@ti.func
+def feq(k,rho_local, u):
+    # eu=ts.vector.dot(e[k],u)
+    # uv=ts.vector.dot(u,u)
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #same as single phase equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() intialize some variable

+
@ti.kernel
+def init():
+    for i,j,k in solid:
+        if (solid[i,j,k] == 0):
+        #if it is fluid intialize the density and velocity be one and zero
+            rho[i,j,k] = 1.0
+            v[i,j,k] = ti.Vector([0,0,0])
+            # set density r and density b based on psi
+            rho_r[i,j,k] = (psi[i,j,k]+1.0)/2.0
+            rho_b[i,j,k] = 1.0 - rho_r[i,j,k]
+            #set another density r and density b
+            rhor[i,j,k] = 0.0
+            rhob[i,j,k] = 0.0
+            #set density distribution equals to equilibrium density distribution function
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+                F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+
+
+

init_geo(filename, filename2) import the geometry data

+
def init_geo(filename, filename2):
+    #read the solid flag data and set it as an column major array
+    in_dat = np.loadtxt(filename)
+    in_dat[in_dat>0] = 1
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+
+    #read the phase data from file
+    phase_in_dat = np.loadtxt(filename2)
+    #set the array from the file with colum major
+    phase_in_dat = np.reshape(phase_in_dat, (nx,ny,nz), order='F')
+
+    return in_dat, phase_in_dat
+
+
+

static_init() initialize non-modified variable

+
@ti.kernel
+def static_init():
+    if ti.static(enable_projection): # No runtime overhead
+    #define lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #define another lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #define a weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #define the boundary velocity
+    bc_vel_x_left = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M() calculate the density distribution function in momentum space

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in ti.static(range(19)):
+        for s in ti.static(range(19)):
+            #calculate here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s force term

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in ti.static(range(19)):
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

Compute_C() calculate the color gradient

+
@ti.func
+def Compute_C(i):
+    C = ti.Vector([0.0,0.0,0.0])
+    ind_S = 0
+    for s in ti.static(range(19)):
+        ip = periodic_index_for_psi(i+e[s])
+        if (solid[ip] == 0):
+            #if it's fluid calculate the color gradient based on psi
+            C += 3.0*w[s]*e_f[s]*psi[ip]
+        else:
+            #if it is solid and abs(density r-density b) is less than 0.9
+            ind_S = 1
+            #calculate the color gradient based on psi_solid and set ind_s=1
+            C += 3.0*w[s]*e_f[s]*psi_solid
+
+    if (abs(rho_r[i]-rho_b[i]) > 0.9) and (ind_S == 1):
+        #if abs(density r-density b) is very large and it's solid set color gradient to be zero
+        C = ti.Vector([0.0,0.0,0.0])
+
+    return C
+
+
+

Compute_S_local calculate parameter of s diagonal

+
@ti.func
+def Compute_S_local(id):
+    sv=0.0; sother=0.0
+    if (psi[id]>0):
+        if (psi[id]>0.1):
+        #if psi>0.1
+        #sv=1.0/(niu_l/(1.0/3.0)+0.5)
+            sv=wl
+        else:
+        #if 0<psi<0.1   calculate sv
+            sv=lg0+l1*psi[id]+l2*psi[id]*psi[id]
+    else:
+        #if psi <-0.1
+        if (psi[id]<-0.1):
+        #calculate sv
+            sv=wg
+        else:
+        #if psi >-0.1
+            sv=lg0+g1*psi[id]+g2*psi[id]*psi[id]
+    #calculate s other
+    sother = 8.0*(2.0-sv)/(8.0-sv)
+
+    #set s diagonal to be zero and set certain element to be relatie local parameter
+    S = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    S[1]=sv;S[2]=sv;S[4]=sother;S[6]=sother;S[8]=sother;S[9]=sv;
+    S[10]=sv;S[11]=sv;S[12]=sv;S[13]=sv;S[14]=sv;S[15]=sv;S[16]=sother;
+    S[17]=sother;S[18]=sother;
+
+
+    return S;
+
+
+

collision() define the collision and recoloring process

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is inner fluid, calculate color gradient divided by norm of color gradient
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            uu = v[i,j,k].norm_sqr()
+            C = Compute_C(ti.Vector([i,j,k]))
+            cc = C.norm()
+            normal = ti.Vector([0.0,0.0,0.0])
+            if cc>0 :
+                normal = C/cc
+            #calculate the M
+            m_temp = multiply_M(i,j,k)
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            #calculate surface tension term
+            meq[1] += CapA*cc
+            meq[9] += 0.5*CapA*cc*(2*normal.x*normal.x-normal.y*normal.y-normal.z*normal.z)
+            meq[11] += 0.5*CapA*cc*(normal.y*normal.y-normal.z*normal.z)
+            meq[13] += 0.5*CapA*cc*(normal.x*normal.y)
+            meq[14] += 0.5*CapA*cc*(normal.y*normal.z)
+            meq[15] += 0.5*CapA*cc*(normal.x*normal.z)
+            #calculate s local
+            S_local = Compute_S_local(ti.Vector([i,j,k]))
+            #calculate s*(m-meq)
+            for s in ti.static(range(19)):
+                m_temp[s] -= S_local[s]*(m_temp[s]-meq[s])
+                m_temp[s] += (1-0.5*S_local[s])*GuoF(i,j,k,s,v[i,j,k])
+            #calculte convection of density filed
+            g_r = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            g_b = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = 0
+                for l in ti.static(range(19)):
+                # 1.single phase collision
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+                g_r[s] = feq(s,rho_r[i,j,k],v[i,j,k])
+                g_b[s] = feq(s,rho_b[i,j,k],v[i,j,k])
+
+            if (cc>0):
+                for kk in ti.static([1,3,5,7,9,11,13,15,17]):
+                    # ef=ts.vector.dot(e[kk],C)
+                    ef=e[kk].dot(C)
+                    cospsi= g_r[kk] if (g_r[kk]<g_r[kk+1]) else g_r[kk+1]
+                    cospsi= cospsi if (cospsi<g_b[kk]) else g_b[kk]
+                    cospsi=cospsi if (cospsi<g_b[kk+1]) else g_b[kk+1]
+                    cospsi*=ef/cc
+                    #2.surface tension perturbation
+                    g_r[kk]+=cospsi
+                    g_r[kk+1]-=cospsi
+                    g_b[kk]-=cospsi
+                    g_b[kk+1]+=cospsi
+            # recoloring
+            for s in ti.static(range(19)):
+                ip = periodic_index(ti.Vector([i,j,k])+e[s])
+                if (solid[ip]==0):
+                    rhor[ip] += g_r[s]
+                    rhob[ip] += g_b[s]
+                else:
+                    rhor[i,j,k] += g_r[s]
+                    rhob[i,j,k] += g_b[s]
+
+
+

periodic_index() defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(i):
+    iout = i
+    if i[0]<0:     iout[0] = nx-1
+    if i[0]>nx-1:  iout[0] = 0
+    if i[1]<0:     iout[1] = ny-1
+    if i[1]>ny-1:  iout[1] = 0
+    if i[2]<0:     iout[2] = nz-1
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

periodic_index_for_psi(i) defines the index of boundary for psi if using periodic boundary condition

+
@ti.func
+def periodic_index_for_psi(i):
+    iout = i
+    if i[0]<0:
+    #if periodic boundary condition set index based on periodic boundary condition
+        if bc_psi_x_left == 0:
+            iout[0] = nx-1
+        else:
+    #otherwise set neighbouring index,
+    #similar for other sides
+            iout[0] = 0
+
+    if i[0]>nx-1:
+        if bc_psi_x_right==0:
+            iout[0] = 0
+        else:
+            iout[0] = nx-1
+
+    if i[1]<0:
+        if bc_psi_y_left == 0:
+            iout[1] = ny-1
+        else:
+            iout[1] = 0
+
+    if i[1]>ny-1:
+        if bc_psi_y_right==0:
+            iout[1] = 0
+        else:
+            iout[1] = ny-1
+
+    if i[2]<0:
+        if bc_psi_z_left==0:
+            iout[2] = nz-1
+        else:
+            iout[2] = 0
+
+    if i[2]>nz-1:
+        if bc_psi_z_right==0:
+            iout[2] = 0
+        else:
+            iout[2] = nz-1
+
+    return iout
+
+
+

streaming1() defines steaming process of denisty distribution function

+
@ti.kernel
+def streaming1():
+    for i,j,k in rho:
+        #if (solid[i,j,k] == 0):
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            ci = ti.Vector([i,j,k])
+            for s in ti.static(range(19)):
+                ip = periodic_index(ci+e[s])
+                if (solid[ip]==0):
+                #if it is fluid,streaming along certain direction
+                    F[ip,s] = f[ci,s]
+                else:
+                #if it is on the solid, bounce back to the opposite
+                    F[ci,LR[s]] = f[ci,s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition_psi() defines boundary condition for psi

+
@ti.kernel
+def Boundary_condition_psi():
+    if bc_psi_x_left == 1:
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+            #if it is fluid the value of psi equals to the psi_x_left
+                psi[0,j,k] = psi_x_left
+            #calculate density according to psi
+            #similar for other sides
+                rho_r[0,j,k] = (psi_x_left + 1.0)/2.0
+                rho_b[0,j,k] = 1.0 - rho_r[0,j,k]
+
+    if bc_psi_x_right == 1:
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                psi[nx-1,j,k] = psi_x_right
+                rho_r[nx-1,j,k] = (psi_x_right + 1.0)/2.0
+                rho_b[nx-1,j,k] = 1.0 - rho_r[nx-1,j,k]
+
+    if bc_psi_y_left == 1:
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                psi[i,0,k] = psi_y_left
+                rho_r[i,0,k] = (psi_y_left + 1.0)/2.0
+                rho_b[i,0,k] = 1.0 - rho_r[i,0,k]
+
+    if bc_psi_y_right == 1:
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                psi[i,ny-1,k] = psi_y_right
+                rho_r[i,ny-1,k] = (psi_y_right + 1.0)/2.0
+                rho_b[i,ny-1,k] = 1.0 - rho_r[i,ny-1,k]
+
+    if bc_psi_z_left == 1:
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                psi[i,j,0] = psi_z_left
+                rho_r[i,j,0] = (psi_z_left + 1.0)/2.0
+                rho_b[i,j,0] = 1.0 - rho_r[i,j,0]
+
+    if bc_psi_z_right == 1:
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                psi[i,j,nz-1] = psi_z_right
+                rho_r[i,j,nz-1] = (psi_z_right + 1.0)/2.0
+                rho_b[i,j,nz-1] = 1.0 - rho_r[i,j,nz-1]
+
+
+

Boundary_condition defines boundary condition and the same as single_phase solver

+
@ti.kernel
+def Boundary_condition():
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])
+
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])
+
+
+    # Direction Y
+    if ti.static(bc_y_left==1):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,1,k]>0):
+                        F[i,0,k,s]=feq(s, rho_bcyl, v[i,1,k])
+                    else:
+                        F[i,0,k,s]=feq(s, rho_bcyl, v[i,0,k])
+
+    if ti.static(bc_y_left==2):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    F[i,0,k,s]=feq(LR[s], 1.0, bc_vel_y_left[None])-F[i,0,k,LR[s]]+feq(s,1.0,bc_vel_y_left[None])
+
+    if ti.static(bc_y_right==1):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,ny-2,k]>0):
+                        F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-2,k])
+                    else:
+                        F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-1,k])
+
+    if ti.static(bc_y_right==2):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    F[i,ny-1,k,s]=feq(LR[s], 1.0, bc_vel_y_right[None])-F[i,ny-1,k,LR[s]]+feq(s,1.0,bc_vel_y_right[None])
+
+    # Z direction
+    if ti.static(bc_z_left==1):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,j,1]>0):
+                        F[i,j,0,s]=feq(s, rho_bczl, v[i,j,1])
+                    else:
+                        F[i,j,0,s]=feq(s, rho_bczl, v[i,j,0])
+
+    if ti.static(bc_z_left==2):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    F[i,j,0,s]=feq(LR[s], 1.0, bc_vel_z_left[None])-F[i,j,0,LR[s]]+feq(s,1.0,bc_vel_z_left[None])
+
+    if ti.static(bc_z_right==1):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,j,nz-2]>0):
+                        F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-2])
+                    else:
+                        F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-1])
+
+    if ti.static(bc_z_right==2):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                for s in ti.static(range(19)):
+                    F[i,j,nz-1,s]=feq(LR[s], 1.0, bc_vel_z_right[None])-F[i,j,nz-1,LR[s]]+feq(s,1.0,bc_vel_z_right[None])
+
+
+

Boundary_condition_psi() calculate macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i,j,k, in rho:
+        #if (solid[i,j,k] == 0):
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            rho[i,j,k] = 0
+            v[i,j,k] = ti.Vector([0,0,0])
+            #define denisty r and density b
+            rho_r[i,j,k] = rhor[i,j,k]
+            rho_b[i,j,k] = rhob[i,j,k]
+            rhor[i,j,k] = 0.0; rhob[i,j,k] = 0.0
+
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = F[i,j,k,s]
+                rho[i,j,k] += f[i,j,k,s]
+                v[i,j,k] += e_f[s]*f[i,j,k,s]
+            #calculate velocity and psi
+            v[i,j,k] /= rho[i,j,k]
+            v[i,j,k] += (ext_f[None]/2)/rho[i,j,k]
+            psi[i,j,k] = rho_r[i,j,k]-rho_b[i,j,k]/(rho_r[i,j,k] + rho_b[i,j,k])
+
+
+

The code snippts below define time, read file do the simulation and export results +It is almost the same as the single-phase solver except two input file and export phase variable

+
time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+
+solid_np, phase_np = init_geo('./img_ftb131.txt','./phase_ftb131.dat')
+
+#solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+psi.from_numpy(phase_np)
+
+static_init()
+init()
+
+#print(wl,wg, lg0, l1, l2,'~@@@@@~@~@~@~@')
+
+for iter in range(80000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    Boundary_condition_psi()
+
+
+    if (iter%500==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()[0:nx,0:ny,0:nz]),
+                            "phase": np.ascontiguousarray(psi.to_numpy()[0:nx,0:ny,0:nz]),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,0]), np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,1]),np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,2]))
+                            }
+            )
+
+#ti.print_kernel_profile_info()
+#ti.print_profile_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/twophase/lbm_solver_3d_2phase_sparse.html b/docs/_build/html/twophase/lbm_solver_3d_2phase_sparse.html new file mode 100644 index 0000000..6fe7cea --- /dev/null +++ b/docs/_build/html/twophase/lbm_solver_3d_2phase_sparse.html @@ -0,0 +1,146 @@ + + + + + + + lbm_solver_3d_2phase_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_2phase_sparse

+

This file is almost the same as the lbm_solver_3d_2phase.py file execpt sparse storage definition of some varibles

+
# Sparse Storage memory allocation
+f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+rhor = ti.field(ti.f32)
+rhob = ti.field(ti.f32)
+rho_r = ti.field(ti.f32)
+rho_b = ti.field(ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhor)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhob)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_r)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_b)
+
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

Above code snippts define the sparse storage of some varibles

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_sources/2phase.rst.txt b/docs/_sources/2phase.rst.txt new file mode 100644 index 0000000..d0d402f --- /dev/null +++ b/docs/_sources/2phase.rst.txt @@ -0,0 +1,11 @@ +2phase +============== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + twophase/lbm_solver_3d_2phase_sparse + twophase/lbm_solver_3d_2phase + + diff --git a/docs/_sources/Convert_stl_to_binary.rst.txt b/docs/_sources/Convert_stl_to_binary.rst.txt new file mode 100644 index 0000000..edf04e6 --- /dev/null +++ b/docs/_sources/Convert_stl_to_binary.rst.txt @@ -0,0 +1,4 @@ +Convert_stl_to_binary +================================= + +This file reads the stl file and output to vtk file \ No newline at end of file diff --git a/docs/_sources/Grey_Scale.rst.txt b/docs/_sources/Grey_Scale.rst.txt new file mode 100644 index 0000000..ef21d69 --- /dev/null +++ b/docs/_sources/Grey_Scale.rst.txt @@ -0,0 +1,10 @@ +Grey\_Scale +=================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Grey_scale/flow_domain_geo_generation + Grey_scale/lbm_solver_3d_Macro_Sukop + diff --git a/docs/_sources/Grey_scale/flow_domain_geo_generation.rst.txt b/docs/_sources/Grey_scale/flow_domain_geo_generation.rst.txt new file mode 100644 index 0000000..bf4c4a7 --- /dev/null +++ b/docs/_sources/Grey_scale/flow_domain_geo_generation.rst.txt @@ -0,0 +1,34 @@ +flow_domain_geo_generation +================================= + +This file output geometry data + +.. code-block:: python + + #import numpy and math packahe + import numpy as np + import math + + + # INPUT STL FILE NAME + output_name = 'geo.dat' + + # POINT SEARCHING RESOLUTION IN X direction, Y,Z direction will be calculate by the code + # the bigger value ~ more points will be found inside STL + dnx, dny, dnz = 60, 60, 60 + + + #========================================================== + # DO NOT CHANGE BELOW + #========================================================== + #create np matrix with dnx*dny*dnz zero + out_dat = np.zeros((dnx,dny,dnz)) + + #=======Can define some geometry here to out_dat========= + #out_dat[1,:,:] = 1 + + #========================================================= + #reshape out_dat with column major + out_dat = out_dat.reshape(out_dat.size, order = 'F') + #save the file with the transfer of out_dat based on integer type + np.savetxt(output_name,out_dat.T,fmt='%d') \ No newline at end of file diff --git a/docs/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt b/docs/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt new file mode 100644 index 0000000..26eb0cc --- /dev/null +++ b/docs/_sources/Grey_scale/lbm_solver_3d_Macro_Sukop.rst.txt @@ -0,0 +1,70 @@ +lbm_solver_3d_Macro_Sukop +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. Some parameter is different + +.. code-block:: python + + #grid resolution + nx,ny,nz = 60,50,5 + #external force + fx,fy,fz = 1.0e-6,0.0,0.0 + #viscosity + niu = 0.1 + #import geometry + geo_name = './BC.dat' + #maximum timestep + max_timestep = 5000 + #output frequency + output_fre = 100 + #vtk file output frequency + vtk_fre = 500 + +2. There are two array for solid flag data. + +.. code-block:: python + + ns_np = init_geo(geo_name) + solid_np = ns_np.astype(int) + #solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + ns.from_numpy(ns_np) + +3. The streaming function is different + +.. code-block:: python + + @ti.kernel + def streaming0(): + for i in ti.grouped(rho): + if (solid[i] == 0): + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + #if it is fluid f2=f otherwise apply bounce-back f2[i,s]=f[ip,LR[s]] + f2[i,s] = f[i,s] + ns[i]*(f[ip,LR[s]] - f[i,s]) + + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + if (solid[i] == 0): + #if it is fluid apply streaming + for s in ti.static(range(19)): + ip = periodic_index(i+e[s]) + F[ip,s] = f2[i,s] + + #if (solid[ip]==0): + # F[ip,s] = f[i,s] + #else: + # F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + #not used + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in ti.static(range(19)): + f[i,s] = F[i,s] + +``streaming3()`` calculates the macroscopic variable \ No newline at end of file diff --git a/docs/_sources/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_sources/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_sources/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.x0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + if i[1]<0: iout[1] = ny-1 + if i[1]>ny-1: iout[1] = 0 + if i[2]<0: iout[2] = nz-1 + if i[2]>nz-1: iout[2] = 0 + + return iout + +this + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + if (solid[i] == 0): + for s in range(19): + ip = periodic_index(i+e[s]) + if (solid[ip]==0): + F[ip,s] = f[i,s] + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +this + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +this + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + +this + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +this \ No newline at end of file diff --git a/docs/_sources/Single_phase.rst.txt b/docs/_sources/Single_phase.rst.txt new file mode 100644 index 0000000..d66928e --- /dev/null +++ b/docs/_sources/Single_phase.rst.txt @@ -0,0 +1,20 @@ +Single\_phase +===================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + Single_phase/LBM_3D_SinglePhase_Solver + Single_phase/lbm_solver_3d + Single_phase/lbm_solver_3d_cavity + Single_phase/lbm_solver_3d_sparse + Single_phase/flow_domain_geo_generation_2D + Single_phase/example_cavity + Single_phase/example_porous_medium + Single_phase/Convert_stl_to_binary + + + + + diff --git a/docs/_sources/Single_phase/Convert_stl_to_binary.rst.txt b/docs/_sources/Single_phase/Convert_stl_to_binary.rst.txt new file mode 100644 index 0000000..edf04e6 --- /dev/null +++ b/docs/_sources/Single_phase/Convert_stl_to_binary.rst.txt @@ -0,0 +1,4 @@ +Convert_stl_to_binary +================================= + +This file reads the stl file and output to vtk file \ No newline at end of file diff --git a/docs/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_sources/Single_phase/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = ny-1 + #y-right + if i[1]>ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = nz-1 + #z-right + if i[2]>nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming process of denisty distibution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + #if it is fluid + if (solid[i] == 0): + for s in range(19): + #the neighbour index + ip = periodic_index(i+e[s]) + #if neighbour index is fluid just streaming + if (solid[ip]==0): + F[ip,s] = f[i,s] + #if neighbour index is solid just bounce back + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +``streaming2()`` a simple streaming process without consideration of solid and boundary + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +``Boudary_condition()`` define the bounary condition of fixed pressure and fixed velocity + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + #pressure-boundary condtion x-left + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #if boundary is fluid but the neighbour is solid + #equilibrium density distribution function is calculated based on the neighbour velocity + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + #if boundary is fluid and the neighbour is also fluid + #equilibrium density distribution function is calculated based on the boundary velocity + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + #velocity-boundary conditon x-left + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #calculate density distribution fucntion based on equilibrium part and non-equilibrium part + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + #pressure boundary condition x-right similar to x-left + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + #velocity booundary condition x-right similar to x-left + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + + +``streaming3()`` calculate the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + #if it is fluid calculate density and velocity based on density distribution function + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + # if it is solid set denisty equals one and velocity equals zero + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +At the end of the file do the actual simulation and export the data + +.. code-block:: python + + #define some time varible + time_init = time.time() + time_now = time.time() + time_pre = time.time() + dt_count = 0 + + #import the solid flag data + #solid_np = init_geo('./BC.dat') + solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + + # do the initialization + static_init() + init() + + # do the actual simulation + for iter in range(50000+1): + colission() + streaming1() + Boundary_condition() + #streaming2() + streaming3() + # calculate every 1000 time step + if (iter%1000==0): + + time_pre = time_now + time_now = time.time() + #calculate the time difference between now and previous time step + diff_time = int(time_now-time_pre) + #calculate the time difference between now and the initial time + elap_time = int(time_now-time_init) + #divmod function return the quotient and the remainder + #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + + #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable + if (iter%10000==0): + gridToVTK( + "./structured"+str(iter), + x, + y, + z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()), + "rho": np.ascontiguousarray(rho.to_numpy()), + "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2])) + } + ) + # ti.sync() + # ti.profiler.print_kernel_profiler_info() + #print the profiler information of every kernel and task of taichi in this file + ti.profiler.print_scoped_profiler_info() diff --git a/docs/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt b/docs/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt new file mode 100644 index 0000000..08d16d9 --- /dev/null +++ b/docs/_sources/Single_phase/lbm_solver_3d_cavity.rst.txt @@ -0,0 +1,37 @@ +lbm_solver_3d_cavity +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: + +1. The Grid resolution in this solver is 50x50x50 +2. The viscosity in this solver is 0.16667 +3. The boundary condition in this solver is velocity solver on x-right as follows + +boundary condition of this solver + +.. code-block:: python + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + +x-right is implementated with velocity boundary condition + +4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary. + +.. code-block:: python + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left)) + + +5. Finally, the definition of the varible is slightly different from lbm_solver_3d \ No newline at end of file diff --git a/docs/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt b/docs/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt new file mode 100644 index 0000000..d76a344 --- /dev/null +++ b/docs/_sources/Single_phase/lbm_solver_3d_sparse.rst.txt @@ -0,0 +1,24 @@ +lbm_solver_3d_sparse +================================= + + +This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible: + +.. code-block:: python + + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse. \ No newline at end of file diff --git a/docs/_sources/aaa.rst.txt b/docs/_sources/aaa.rst.txt new file mode 100644 index 0000000..d136b12 --- /dev/null +++ b/docs/_sources/aaa.rst.txt @@ -0,0 +1,575 @@ +Single\_phase.LBM\_3D\_SinglePhase\_Solver +============================================== +This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called ``LB3D_Solver_Single_Phase``. The Class has a default function +``__init__()`` as normal python class. + +.. code-block:: python + + class LB3D_Solver_Single_Phase: + def __init__(self, nx, ny, nz, sparse_storage = False): + #enable projection, define a sparse_storage flag + self.enable_projection = True + self.sparse_storage = sparse_storage + #the grid of the simulation in three direction + self.nx,self.ny,self.nz = nx,ny,nz + #nx,ny,nz = 120,120,120 + #density distribution function in three direction + self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0 + #kinematic viscosity in lattice unit + self.niu = 0.16667 + #define a taichi field of float scalar which is the maximum velocity + self.max_v=ti.field(ti.f32,shape=()) + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary x-axis right side + self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + if sparse_storage == False: + #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define density with taichi field which has nx*ny*nz element and each element is a scalar + self.rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector + self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + else: + #sparse storage the variable + #define old density distribution function by taichi field with one element and which is a 19 dimensional vector + self.f = ti.Vector.field(19, ti.f32) + #define new density distribution function by taichi field with one element and which is a 19 dimensional vector + self.F = ti.Vector.field(19,ti.f32) + #define density by taichi field with one element which is a scalar + self.rho = ti.field(ti.f32) + #define velocity by taichi field with one element which is a scalar + self.v = ti.Vector.field(3, ti.f32) + #define partition equals 3 + n_mem_partition = 3 + #every index has four variable rho, v, f, F + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F) + #define lattice speed 3x19 + self.e = ti.Vector.field(3,ti.i32, shape=(19)) + #define s diagnol vector + self.S_dig = ti.Vector.field(19,ti.f32,shape=()) + #define another lattice speed 3x19 + self.e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #define weight parameter + self.w = ti.field(ti.f32, shape=(19)) + #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid + self.solid = ti.field(ti.i8,shape=(nx,ny,nz)) + #define external force which is a three dimensional vector + self.ext_f = ti.Vector.field(3,ti.f32,shape=()) + #define transforming matrix M which is a 19x19 dimension matrix + self.M = ti.Matrix.field(19, 19, ti.f32, shape=()) + #define the inverse transforming matrix M^-1 + self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=()) + #define the numpy version of M. + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define the numpy version of M^-1 + inv_M_np = np.linalg.inv(M_np) + #define the index of 19 lattice node for bounce back + self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17] + #define taichi field version of M + self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #define taichi field version of M^-1 + self.inv_M[None] = ti.Matrix(inv_M_np) + #define coordinate nx*ny*nz + self.x = np.linspace(0, nx, nx) + self.y = np.linspace(0, ny, ny) + self.z = np.linspace(0, nz, nz) + #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij') + +Following is the ``init_simulation()`` function which initialize some simulation parameter + +.. code-block:: python + + def init_simulation(self): + #x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl + self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl] + self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr] + self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl] + self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr] + self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl] + self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr] + #define single relaxation time tau + self.tau_f=3.0*self.niu+0.5 + #define single relaxation frequency + self.s_v=1.0/self.tau_f + #define other parameter in the s diagonal + self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v) + #define the s diagonal + self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other]) + #define external force + #self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz]) + self.ext_f[None][0] = self.fx + self.ext_f[None][1] = self.fy + self.ext_f[None][2] = self.fz + #if external force greater than zero define force_flag equals 1 + #other wise force_flag equals 0 + if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)): + self.force_flag = 1 + else: + self.force_flag = 0 + + #define M M^-1 S diagonal not been modified. + ti.static(self.inv_M) + ti.static(self.M) + #ti.static(LR) + ti.static(self.S_dig) + #statically initialize + self.static_init() + self.init() + +``feq()`` calculate the equilibrium density distribution function in velocity space + +.. code-block:: python + + #taichi function + @ti.func + def feq(self, k,rho_local, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + #calculate the equilibrium density distribution function + feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, self.w[k]) + return feqout + +``init()`` initialize density velocity and density distribution function + +.. code-block:: python + + @ti.kernel + def init(self): + for i,j,k in self.solid: + #print(i,j,k) + if (self.sparse_storage==False or self.solid[i,j,k]==0): + #if it is fluid then initialize density equals one + self.rho[i,j,k] = 1.0 + #initialize the velocity to be zero in all the direction + self.v[i,j,k] = ti.Vector([0,0,0]) + for s in ti.static(range(19)): + #initialize 19 denisty distribution function equals the equilibrium density distribution function + self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k]) + #print(F[i,j,k,s], feq(s,1.0,v[i,j,k])) + +``init_geo()`` import data from a file + +.. code-block:: python + + def init_geo(self,filename): + #load data from a file + in_dat = np.loadtxt(filename) + #set any positive value to be one + in_dat[in_dat>0] = 1 + #reshape it as a nx*ny*nz vector with column major + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + #assign it to solid varible + self.solid.from_numpy(in_dat) + +``static_init()`` initialize lattice speeed and weight parameter. These parameter is not modified during the simulation + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def static_init(self): + if ti.static(self.enable_projection): # No runtime overhead + #initialize the lattice speed + self.e[0] = ti.Vector([0,0,0]) + self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1]) + self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0]) + self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1]) + self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1]) + + self.e_f[0] = ti.Vector([0,0,0]) + self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1]) + self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0]) + self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1]) + self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1]) + #initialize the weight parameter + self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0; + self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0; + self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0; + +``meq_vec(self, rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(self, rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``cal_local_force(self,i,j,k)`` transfer the external force to a vector + +.. code-block:: python + + @ti.func + def cal_local_force(self,i,j,k): + f = ti.Vector([self.fx, self.fy, self.fz]) + return f + +``collision()`` defines the collision of LBM process + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def colission(self): + #outer loop for every index in rho field + for i,j,k in self.rho: + #if is not solid and it is not on the boundary + if (self.solid[i,j,k] == 0 and iself.nx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = self.ny-1 + #y-right + if i[1]>self.ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = self.nz-1 + #z-right + if i[2]>self.nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming prcoess of denisty distribution function + +.. code-block:: python + + #taichi kernel for parallization + @ti.kernel + def streaming1(self): + #grouped index which loop the index of rho + for i in ti.grouped(self.rho): + # streaming for fluid and non-boundary + if (self.solid[i] == 0 and i.x0): + # if the boundary is fluid but the neighbour is solid then the density distribution + #function equals to the solid velcity equilibrium density distribution fucntion + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k]) + else: + # if the boundary is fluid and the neighbour is fluid then the density distribution + #function equals to equilibrium density distribution fucntion on the boundary + self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k]) + #fixed velocity boundary condition + if ti.static(self.bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + # if the boundary is fluid new density distribution fucntion equals to equilibrium density + #distibution function with fixed velocity + if (self.solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left)) + # fixed pressure boundary condition on x-right similar for x-left + if ti.static(self.bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + if (self.solid[self.nx-2,j,k]>0): + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k]) + else: + self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k]) + # fixed velocity boubndary condition on x-right similar for x-left + if ti.static(self.bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + if (self.solid[self.nx-1,j,k]==0): + for s in ti.static(range(19)): + #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right)) + + # Direction Y + #fixed pressure boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,1,k]>0): + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k]) + else: + self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k]) + #fixed velocity boundary condition on y-left similar for x direction + if ti.static(self.bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,0,k]==0): + for s in ti.static(range(19)): + #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None]) + self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left)) + #fixed pressure boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + if (self.solid[i,self.ny-2,k]>0): + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k]) + else: + self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k]) + #fixed velocity boundary condition on y-right similar for x direction + if ti.static(self.bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + if (self.solid[i,self.ny-1,k]==0): + for s in ti.static(range(19)): + #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None]) + self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right)) + + # Z direction + #fixed pressure boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,1]>0): + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1]) + else: + self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0]) + #fixed velocity boundary condition on z-left similar for x direction + if ti.static(self.bc_z_left==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,0]==0): + for s in ti.static(range(19)): + #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None]) + self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left)) + #fixed pressure boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + if (self.solid[i,j,self.nz-2]>0): + self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2]) + else: + self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1]) + #fixed velocity boundary condition on z-right similar for x direction + if ti.static(self.bc_z_right==2): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + if (self.solid[i,j,self.nz-1]==0): + for s in ti.static(range(19)): + #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None]) + self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right)) + +``streaming3()`` calculatet the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + #print(i.x, i.y, i.z) + #if it is fluid and not on the boundary + if (self.solid[i]==0 and i.xnx-1: iout[0] = 0 + #y-left + if i[1]<0: iout[1] = ny-1 + #y-right + if i[1]>ny-1: iout[1] = 0 + #z-left + if i[2]<0: iout[2] = nz-1 + #z-right + if i[2]>nz-1: iout[2] = 0 + + return iout + +``streaming1()`` defines the streaming process of denisty distibution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i in ti.grouped(rho): + #if it is fluid + if (solid[i] == 0): + for s in range(19): + #the neighbour index + ip = periodic_index(i+e[s]) + #if neighbour index is fluid just streaming + if (solid[ip]==0): + F[ip,s] = f[i,s] + #if neighbour index is solid just bounce back + else: + F[i,LR[s]] = f[i,s] + #print(i, ip, "@@@") + +``streaming2()`` a simple streaming process without consideration of solid and boundary + +.. code-block:: python + + @ti.kernel + def streaming2(): + for i in ti.grouped(rho): + for s in range(19): + f[i,s] = F[i,s] + +``Boudary_condition()`` define the bounary condition of fixed pressure and fixed velocity + +.. code-block:: python + + @ti.kernel + def Boundary_condition(): + #pressure-boundary condtion x-left + if ti.static(bc_x_left==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #if boundary is fluid but the neighbour is solid + #equilibrium density distribution function is calculated based on the neighbour velocity + if (solid[1,j,k]>0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + #if boundary is fluid and the neighbour is also fluid + #equilibrium density distribution function is calculated based on the boundary velocity + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + #velocity-boundary conditon x-left + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in range(19): + #calculate density distribution fucntion based on equilibrium part and non-equilibrium part + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + + #pressure boundary condition x-right similar to x-left + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + #velocity booundary condition x-right similar to x-left + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in range(19): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) #!!!!!!change velocity in feq into vector + + +``streaming3()`` calculate the macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i in ti.grouped(rho): + #if it is fluid calculate density and velocity based on density distribution function + if (solid[i]==0): + rho[i] = 0 + v[i] = ti.Vector([0,0,0]) + for s in range(19): + f[i,s] = F[i,s] + rho[i] += f[i,s] + v[i] += e_f[s]*f[i,s] + + v[i] /= rho[i] + v[i] += (ext_f[None]/2)/rho[i] + # if it is solid set denisty equals one and velocity equals zero + else: + rho[i] = 1.0 + v[i] = ti.Vector([0,0,0]) + +At the end of the file do the actual simulation and export the data + +.. code-block:: python + + #define some time varible + time_init = time.time() + time_now = time.time() + time_pre = time.time() + dt_count = 0 + + #import the solid flag data + #solid_np = init_geo('./BC.dat') + solid_np = init_geo('./img_ftb131.txt') + solid.from_numpy(solid_np) + + # do the initialization + static_init() + init() + + # do the actual simulation + for iter in range(50000+1): + colission() + streaming1() + Boundary_condition() + #streaming2() + streaming3() + # calculate every 1000 time step + if (iter%1000==0): + + time_pre = time_now + time_now = time.time() + #calculate the time difference between now and previous time step + diff_time = int(time_now-time_pre) + #calculate the time difference between now and the initial time + elap_time = int(time_now-time_init) + #divmod function return the quotient and the remainder + #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap + m_diff, s_diff = divmod(diff_time, 60) + h_diff, m_diff = divmod(m_diff, 60) + m_elap, s_elap = divmod(elap_time, 60) + h_elap, m_elap = divmod(m_elap, 60) + + print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap)) + print('The %dth iteration, Max Force = %f, force_scale = %f\n\n ' %(iter, 10.0, 10.0)) + + #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable + if (iter%10000==0): + gridToVTK( + "./structured"+str(iter), + x, + y, + z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()), + "rho": np.ascontiguousarray(rho.to_numpy()), + "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2])) + } + ) + # ti.sync() + # ti.profiler.print_kernel_profiler_info() + #print the profiler information of every kernel and task of taichi in this file + ti.profiler.print_scoped_profiler_info() diff --git a/docs/_sources/lbm_solver_3d_cavity.rst.txt b/docs/_sources/lbm_solver_3d_cavity.rst.txt new file mode 100644 index 0000000..a1861dc --- /dev/null +++ b/docs/_sources/lbm_solver_3d_cavity.rst.txt @@ -0,0 +1,38 @@ +lbm_solver_3d_cavity +================================= + +This solver is almost similar to lbm_solver_3d expect several difference as follows: +.. number:: lbm_solver_3d_cavity + +1. The Grid resolution in this solver is 50x50x50 +2. The viscosity in this solver is 0.16667 +3. The boundary condition in this solver is velocity solver on x-right as follows + +boundary condition of this solver + +.. code-block:: python + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + +x-right is implementated with velocity boundary condition + +4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary. + +.. code-block:: python + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) #!!!!!!change velocity in feq into vector + F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left)) + + +5. Finally, the definition of the varible is slightly different from lbm_solver_3d \ No newline at end of file diff --git a/docs/_sources/lbm_solver_3d_sparse.rst.txt b/docs/_sources/lbm_solver_3d_sparse.rst.txt new file mode 100644 index 0000000..d76a344 --- /dev/null +++ b/docs/_sources/lbm_solver_3d_sparse.rst.txt @@ -0,0 +1,24 @@ +lbm_solver_3d_sparse +================================= + + +This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible: + +.. code-block:: python + + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse. \ No newline at end of file diff --git a/docs/_sources/modules.rst.txt b/docs/_sources/modules.rst.txt new file mode 100644 index 0000000..b9bfd06 --- /dev/null +++ b/docs/_sources/modules.rst.txt @@ -0,0 +1,10 @@ +taichi_LBM3D +============ + +.. toctree:: + :maxdepth: 4 + + Single_phase + Grey_Scale + 2phase + Phase_change diff --git a/docs/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt b/docs/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt new file mode 100644 index 0000000..04dbf54 --- /dev/null +++ b/docs/_sources/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst.txt @@ -0,0 +1,619 @@ +LBM_3D_SinglePhase_Solute_Solver +====================================== + +This file is the solver for solute transportation + +First import the certain package and define the class of ``LB3D_Solver_Single_Phase_Solute`` which inheritant from +``LB3D_Solver_Single_Phase_Solute`` + +.. code-block:: python + + from sympy import inverse_mellin_transform + import taichi as ti + import numpy as np + from pyevtk.hl import gridToVTK + import time + + #ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False) + import LBM_3D_SinglePhase_Solver as lb3d + + @ti.data_oriented + class LB3D_Solver_Single_Phase_Solute(lb3d.LB3D_Solver_Single_Phase): + def __init__(self, nx, ny, nz): + super(LB3D_Solver_Single_Phase_Solute, self).__init__(nx, ny, nz, sparse_storage = False) + #define solute boundary condition + self.solute_bc_x_left, self.solute_bcxl = 0, 0.0 + self.solute_bc_x_right, self.solute_bcxr = 0, 0.0 + self.solute_bc_y_left, self.solute_bcyl = 0, 0.0 + self.solute_bc_y_right, self.solute_bcyr = 0, 0.0 + self.solute_bc_z_left, self.solute_bczl = 0, 0.0 + self.solute_bc_z_right, self.solute_bczr = 0, 0.0 + + #define parameters for bouyancy force + self.buoyancy_parameter = 20.0 #Buoyancy Parameter (0= no buoyancy) + self.ref_T = 20.0 #reference_psi F=/rho*g+Bouyancy*(/psi-reference_psi)*g) + #define gravity + self.gravity = 5e-7 + + #define concentration distribution function + self.fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define another concentration distribution function + self.Fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define external force + self.forcexyz = ti.Vector.field(3,ti.f32,shape=(nx,ny,nz)) + #define entropy + self.rho_H = ti.field(ti.f32, shape=(nx,ny,nz)) + #define temperature + self.rho_T = ti.field(ti.f32, shape=(nx,ny,nz)) + #define liquid volumn fraction + self.rho_fl = ti.field(ti.f32, shape=(nx,ny,nz)) + + #define specific heat of liquid + self.Cp_l= 1.0 + #define specific heat of solid + self.Cp_s = 1.0 + #define latent heat + self.Lt = 1.0 + #define solid temperature + self.T_s = -10.0 + #define liquid temperature + self.T_l = -10.0 + #define viscosity of solid + self.niu_s = 0.002 + #define viscosity of liquid + self.niu_l = 0.002 + + #define energy of solid + self.H_s = None + #define energy of liquid + self.H_l = None + + #define rock thermal diffusivity + self.niu_solid = 0.001 + #define specific heat of rock + self.Cp_solid = 1.0 + +An then it sets these parameters with functions + +.. code-block:: python + + #set gravity + def set_gravity(self, gravity): + self.gravity = gravity + #set buoyancy force parameter + def set_buoyancy_parameter(self, buoyancy_param): + self.buoyancy_parameter = buoyancy_param + #set reference temperature + def set_ref_T(self, ref_t): + self.ref_T = ref_t + #set specific heat of solid + def set_specific_heat_solid(self, cps): + self.Cp_s = cps + #set specfic heat of liquid + def set_specific_heat_liquid(self, cpl): + self.Cp_l = cpl + #set specfic heat of rock + def set_specific_heat_rock(self, cprock): + self.Cp_solid = cprock + #set latent heat + def set_latent_heat(self, ltheat): + self.Lt = ltheat + #set solidus temperature + def set_solidus_temperature(self, ts): + self.T_s = ts + #set liquidus temperature + def set_liquidus_temperature(self, tl): + self.T_l = tl + #set solid thermal diffusivity + def set_solid_thermal_diffusivity(self, nius): + self.niu_s = nius + #set liquid thermal diffusivity + def set_liquid_thermal_diffusivity(self, niul): + self.niu_l = niul + #set rock thermal diffusivity + def set_rock_thermal_diffusivity(self, niurock): + self.niu_solid = niurock + #set adiabatic boundary on x-left + def set_bc_adiabatic_x_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_left = 2 + #set adiabatic boundary on x-right + def set_bc_adiabatic_x_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_right = 2 + #set adiabatic boundary on y-left + def set_bc_adiabatic_y_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_left = 2 + #set adiabatic boundary on y-right + def set_bc_adiabatic_y_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_right = 2 + #set adiabatic boundary on z-left + def set_bc_adiabatic_z_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_left = 2 + #set adiabatic boundary on z-right + def set_bc_adiabatic_z_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_right = 2 + #set constant temperature on x-left + def set_bc_constant_temperature_x_left(self,xl): + self.solute_bc_x_left = 1 + self.solute_bcxl = xl + #set constant temperature on x-right + def set_bc_constant_temperature_x_right(self,xr): + self.solute_bc_x_right = 1 + self.solute_bcxr = xr + #set constant temperature on y-left + def set_bc_constant_temperature_y_left(self,yl): + self.solute_bc_y_left = 1 + self.solute_bcyl = yl + #set constant temperature on y-right + def set_bc_constant_temperature_y_right(self,yr): + self.solute_bc_y_right = 1 + self.solute_bcyr = yr + #set constant temperature on z-left + def set_bc_constant_temperature_z_left(self,zl): + self.solute_bc_z_left = 1 + self.solute_bczl = zl + #set constant temperature on z-right + def set_bc_constant_temperature_z_right(self,zr): + self.solute_bc_y_right = 1 + self.solute_bczr = zr + + # update energy of solid and liquid + def update_H_sl(self): + #energy of solid + self.H_s = self.Cp_s*self.T_s + #energy of liquid + self.H_l = self.H_s+self.Lt + print('H_s',self.H_s) + print('H_l',self.H_l) + +Then it initialize some variable or function + +.. code-block:: python + + #intialize the energy + @ti.kernel + def init_H(self): + for I in ti.grouped(self.rho_T): + #calculate the energy, convert_T_H() define later + self.rho_H[I] = self.convert_T_H(self.rho_T[I]) + + #intialize the density distribiution function for solute concentration + @ti.kernel + def init_fg(self): + for I in ti.grouped(self.fg): + #calculate the overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + #intialize the density distribiution function for solute concentration equals equilibrium density distribiution function for solute concentration + for s in ti.static(range(19)): + self.fg[I][s] = self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]) + self.Fg[I][s] = self.fg[I][s] + + #intialize the volumn fraction of liquid + @ti.kernel + def init_fl(self): + for I in ti.grouped(self.rho_T): + #convert_T_fl define later + self.rho_fl[I] = self.convert_T_fl(self.rho_T[I]) + +``g_feq(self, k,local_T,local_H, Cp, u)`` calculate the equilibrium density distribiution function for thermal energy + +.. code-block:: python + + @ti.func + def g_feq(self, k,local_T,local_H, Cp, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + feqout = 0.0 + #calculating the zero-velocity equilibrium thermal distribution function + if (k==0): + feqout = local_H-Cp*local_T+self.w[k]*Cp*local_T*(1-1.5*uv) + else: + #calculating other directions equilibrium thermal distribution function + feqout = self.w[k]*Cp*local_T*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, self.w[k], feqout, Cp, local_T) + return feqout + +``cal_local_force(i, j, k)`` calculates buoyancy force + +.. code-block:: python + + #density is the function of temperture delat(rho)=-rho*beta*delta(T) + @ti.func + def cal_local_force(self, i, j, k): + f = ti.Vector([self.fx, self.fy, self.fz]) + f[1] += self.gravity*self.buoyancy_parameter*(self.rho_T[i,j,k]-self.ref_T) + #f= delta(rho)*delta(v)*g + f *= self.rho_fl[i,j,k] + return f + +``collision_g()`` defines the the collision of thermal distribution function + +.. code-block:: python + + @ti.kernel + def colission_g(self): + for I in ti.grouped(self.rho_T): + #overall relaxation time + tau_s = 3*(self.niu_s*(1.0-self.rho_fl[I])+self.niu_l*self.rho_fl[I])+0.5 + #overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + + #ROCK overall relaxation time and specific heat + if (self.solid[I] >0): + tau_s = 3.0*self.niu_solid+0.5 + Cp = self.Cp_solid + + #f=f-1/tau*(f-feq) + for s in ti.static(range(19)): + tmp_fg = -1.0/tau_s*(self.fg[I][s]-self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + #print(self.fg[I][s],tmp_fg,I,s,self.rho_H[I],self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + self.fg[I][s] += tmp_fg + +``collision()`` defines the the collision of density distribution function + +.. code-block:: python + + @ti.kernel + def colission(self): + for i,j,k in self.rho: + #if (self.solid[i,j,k] == 0): + m_temp = self.M[None]@self.F[i,j,k] + meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k]) + m_temp -= self.S_dig[None]*(m_temp-meq) + f = self.cal_local_force(i,j,k) + if (ti.static(self.force_flag==1)): + for s in ti.static(range(19)): + # m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s]) + #f = self.cal_local_force() + f_guo=0.0 + for l in ti.static(range(19)): + f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l] + #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force) + m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo + + self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + #calculate the denisty distribution function in momentum space here + self.f[i,j,k] += self.inv_M[None]@m_temp + #calculate the fluid density distribution function here + for s in ti.static(range(19)): + self.f[i,j,k][s] = self.f[i,j,k][s]*(self.rho_fl[i,j,k]) + self.w[s]*(1.0-self.rho_fl[i,j,k]) + +``streaming1()`` and ``streaming1_g()`` defines the fluid denisty distribiution function and +thermal density distribiution function + +.. code-block:: python + + @ti.kernel + def streaming1(self): + for i in ti.grouped(self.rho): + #if (self.solid[i] == 0): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.F[ip][s] = self.f[i][s] + + @ti.kernel + def streaming1_g(self): + for i in ti.grouped(self.rho_T): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.Fg[ip][s] = self.fg[i][s] + +this + +.. code-block:: python + + @ti.kernel + def BC_concentration(self): + #constant temperature boundary condition + if ti.static(self.solute_bc_x_left==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[0,j,k]*self.Cp_l + (1-self.rho_fl[0,j,k])*self.Cp_s + #the boundary's thermal distribution function equals the equilibrium thermal distribution function on the boundary + for s in ti.static(range(19)): + self.fg[0,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[0,j,k]) + self.Fg[0,j,k][s] = self.fg[0,j,k][s] + #adiabatic boundary condition + elif ti.static(self.solute_bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + #there is no thermal transfer between the boundaty and neighbouring cell + self.fg[0,j,k][s] = self.fg[1,j,k][s] + self.Fg[0,j,k][s] = self.fg[1,j,k][s] + + #x-right + if ti.static(self.solute_bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[self.nx-1,j,k]*self.Cp_l + (1-self.rho_fl[self.nx-1,j,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[self.nx-1,j,k]) + self.Fg[self.nx-1,j,k][s]= self.fg[self.nx-1,j,k][s] + elif ti.static(self.solute_bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + self.Fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + + #y-left + if ti.static(self.solute_bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,0,k]*self.Cp_l + (1-self.rho_fl[i,0,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,0,k]) + self.Fg[i,0,k][s] = self.fg[i,0,k][s] + elif ti.static(self.solute_bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.fg[i,1,k][s] + self.Fg[i,0,k][s] = self.fg[i,1,k][s] + + #y-right + if ti.static(self.solute_bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,self.ny-1,k]*self.Cp_l + (1-self.rho_fl[i,self.ny-1,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,self.ny-1,k]) + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-1,k][s] + elif ti.static(self.solute_bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + + #z-left + if ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,0]*self.Cp_l + (1-self.rho_fl[i,j,0])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,0]) + self.Fg[i,j,0][s] = self.fg[i,j,0][s] + elif ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.fg[i,j,1][s] + self.Fg[i,j,0][s] = self.fg[i,j,1][s] + + #z-right + if ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,self.nz-1]*self.Cp_l + (1-self.rho_fl[i,j,self.nz-1])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,self.nz-1]) + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-1][s] + elif ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + +``convert_H_T()`` calculate the temperature + +.. code-block:: python + + @ti.func + def convert_H_T(self,local_H): + new_T=0.0 + #if local enthalpy is less than solid enthalpy + #T= enthalpy/specific heat + if (local_Hself.H_l): + new_T = self.T_l+(local_H-self.H_l)/self.Cp_l + #if if temperature is greater than solid temperature + #T= Tsolid+(enthalpy-solid enthalpy)/(enthalpy of liquid-enthalpy of solid)*(temperature of liquid- temperature of solid) + elif (self.T_l>self.T_s): + new_T = self.T_s+(local_H-self.H_s)/(self.H_l-self.H_s)*(self.T_l-self.T_s) + else: + #else T= temperature of solid + new_T = self.T_s + + return new_T + +``convert_H_fl()`` calculate the volumn fraction of liquid + +.. code-block:: python + + @ti.func + def convert_H_fl(self,local_H): + new_fl=0.0 + #if enthalpy is less than solid enthalpy + #it is zero + if (local_Hself.H_l): + new_fl = 1.0 + #else + #it equals to (enthaply- soid enthaply)/(enthaply of liquid- enthalpy of solid) + else: + new_fl = (local_H-self.H_s)/(self.H_l-self.H_s) + + return new_fl + +``convert_T_H()`` calculate the enthaply from temperature + +.. code-block:: python + + @ti.func + def convert_T_H(self,local_T): + new_H = 0.0 + # calculate enthaply for three different conditions + if (local_T<=self.T_s): + new_H = self.Cp_s*local_T + elif (local_T>self.T_l): + new_H = (local_T-self.T_l)*self.Cp_l+self.H_l + else: + fluid_frc = (local_T-self.T_s)/(self.T_l-self.T_s) + new_H = self.H_s*(1-fluid_frc) + self.H_l*fluid_frc + return new_H + +``convert_T_fl()`` calculate volumn fraction from temperature + +.. code-block:: python + + @ti.func + def convert_T_fl(self,local_T): + new_fl = 0.0 + # calculate volumn fraction for three different conditions + if (local_T<=self.T_s): + new_fl = 0.0 + elif (local_T>=self.T_l): + new_fl = 1.0 + elif (self.T_l>self.T_s): + new_fl = (local_T-self.T_s)/(self.T_l-self.T_s) + else: + new_fl = 1.0 + + return new_fl + +``streaming3()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + self.forcexyz[i] = self.cal_local_force(i.x, i.y, i.z) + #print(i.x, i.y, i.z) + if ((self.solid[i]==0) or (self.rho_fl[i]>0.0)): + self.rho[i] = 0 + self.v[i] = ti.Vector([0,0,0]) + self.f[i] = self.F[i] + for s in ti.static(range(19)): + self.f[i][s] = self.f[i][s]*self.rho_fl[i]+self.w[s]*(1.0-self.rho_fl[i]) + #density for fluid + self.rho[i] += self.f[i].sum() + + for s in ti.static(range(19)): + self.v[i] += self.e_f[s]*self.f[i][s] + + f = self.cal_local_force(i.x, i.y, i.z) + #velocity for fluid + self.v[i] /= self.rho[i] + self.v[i] += (f/2)/self.rho[i] + + else: + #density and velocity for solid + self.rho[i] = 1.0 + self.v[i] = ti.Vector([0,0,0]) + +``streaming3()`` calculate enthalpy + +.. code-block:: python + + @ti.kernel + def streaming3_g(self): + for i in ti.grouped(self.rho_T): + self.rho_H[i] = 0.0 + #enthalpy here + self.rho_H[i] = self.Fg[i].sum() + #for s in ti.static(range(19)): + # self.rho_H[i] += self.Fg[i][s] + self.fg[i] = self.Fg[i] + +``update_T_fl()`` calculate volumn fraction and temperature + +.. code-block:: python + + @ti.kernel + def update_T_fl(self): + for I in ti.grouped(self.rho_T): + self.rho_T[I] = self.convert_H_T(self.rho_H[I]) + self.rho_fl[I] = self.convert_H_fl(self.rho_H[I]) + if (self.solid[I]>0): + self.rho_fl[I] = 0.0 + +``init_solute_simulation()`` initialize the solute simulation + +.. code-block:: python + + def init_solute_simulation(self): + + self.init_simulation() + self.update_H_sl() + #ethalpy + self.init_H() + #volumn fraction + self.init_fl() + #thermal distribution function + self.init_fg() + +``init_concentration(filename)`` import concentration data from file + +.. code-block:: python + + def init_concentration(self,filename): + in_dat = np.loadtxt(filename) + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + self.rho_T.from_numpy(in_dat) + +this + +.. code-block:: python + + def step(self): + self.colission() + self.colission_g() + + self.streaming1() + self.streaming1_g() + + self.Boundary_condition() + self.BC_concentration() + + self.streaming3_g() + self.streaming3() + self.streaming3_g() + + self.update_T_fl() + +this + +.. code-block:: python + + def export_VTK(self, n): + gridToVTK( + "./LB_SingelPhase_"+str(n), + self.x, + self.y, + self.z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()), + "rho": np.ascontiguousarray(self.rho.to_numpy()), + "Solid_Liquid": np.ascontiguousarray(self.rho_fl.to_numpy()), + "Tempreture": np.ascontiguousarray(self.rho_T.to_numpy()), + "Entropy": np.ascontiguousarray(self.rho_H.to_numpy()), + "velocity": ( np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])), + "Force": ( np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])) + } + ) + +this \ No newline at end of file diff --git a/docs/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt b/docs/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt new file mode 100644 index 0000000..4a6528d --- /dev/null +++ b/docs/_sources/phasechange/LBM_3D_SinglePhase_Solver.rst.txt @@ -0,0 +1,4 @@ +LBM_3D_SinglePhase_Solver +=========================== + +This file is the same as LBM_3D_SinglePhase_Solver in Single_phase folder \ No newline at end of file diff --git a/docs/_sources/phasechange/example_cavity_melting.rst.txt b/docs/_sources/phasechange/example_cavity_melting.rst.txt new file mode 100644 index 0000000..eb279eb --- /dev/null +++ b/docs/_sources/phasechange/example_cavity_melting.rst.txt @@ -0,0 +1,2 @@ +example_cavity_melting +============================= \ No newline at end of file diff --git a/docs/_sources/phasechange/example_phase_change.rst.txt b/docs/_sources/phasechange/example_phase_change.rst.txt new file mode 100644 index 0000000..7e2842c --- /dev/null +++ b/docs/_sources/phasechange/example_phase_change.rst.txt @@ -0,0 +1,2 @@ +example_phase_change +==================== \ No newline at end of file diff --git a/docs/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt b/docs/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt new file mode 100644 index 0000000..6ab6dde --- /dev/null +++ b/docs/_sources/phasechange/read_img_solute_psi_generation_2D.rst.txt @@ -0,0 +1,2 @@ +read_img_solute_psi_generation_2D +================================== \ No newline at end of file diff --git a/docs/_sources/phasechange/solute_psi_generation_2D.rst.txt b/docs/_sources/phasechange/solute_psi_generation_2D.rst.txt new file mode 100644 index 0000000..c8c1119 --- /dev/null +++ b/docs/_sources/phasechange/solute_psi_generation_2D.rst.txt @@ -0,0 +1,2 @@ +solute_psi_generation_2D +============================ \ No newline at end of file diff --git a/docs/_sources/phasechange/test1.rst.txt b/docs/_sources/phasechange/test1.rst.txt new file mode 100644 index 0000000..0b1d2a0 --- /dev/null +++ b/docs/_sources/phasechange/test1.rst.txt @@ -0,0 +1,2 @@ +test1 +=================== \ No newline at end of file diff --git a/docs/_sources/twophase/lbm_solver_3d_2phase.rst.txt b/docs/_sources/twophase/lbm_solver_3d_2phase.rst.txt new file mode 100644 index 0000000..1c42671 --- /dev/null +++ b/docs/_sources/twophase/lbm_solver_3d_2phase.rst.txt @@ -0,0 +1,734 @@ +lbm_solver_3d_2phase +======================================== + +This solver is the multiphase model based on color gradient model +Firstly, it defines some parameters + +.. code-block:: python + + # NOTE: THIS CODE NEED taichi_glsl, so please use taichi version <=0.8.5 + #import taichi, numpy, pyevtk and time package + import taichi as ti + import numpy as np + #import taichi_glsl as ts + from pyevtk.hl import gridToVTK + import time + #from taichi_glsl import scalar + + #from taichi_glsl.scalar import isinf, isnan + #from taichi_glsl.vector import vecFill + #intialize taichi + ti.init(arch=ti.cpu) + #ti.init(arch=ti.gpu, dynamic_index=True,offline_cache=True) + + #enable projection + enable_projection = True + # 131*131*131 + nx,ny,nz = 131,131,131 + #nx,ny,nz = 131,131,131 + #external force in x,y,z direction + fx,fy,fz = 5.0e-5,-2e-5,0.0 + #niu = 0.1 + #liquid viscosity + niu_l = 0.1 #psi>0 + #gas viscosity + niu_g = 0.1 #psi<0 + #psi in color gradient calculation + psi_solid = 0.7 + #surface tension + CapA = 0.005 + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 0, 0.995, 0.0, 0.0, 0.0 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + + bc_psi_x_left, psi_x_left = 1, -1.0 # boundary condition for phase-field: 0 = periodic, + bc_psi_x_right, psi_x_right = 0, 1.0 # 1 = constant value on the boundary, value = -1.0 phase1 or 1.0 = phase 2 + bc_psi_y_left, psi_y_left = 0, 1.0 + bc_psi_y_right, psi_y_right = 0, 1.0 + bc_psi_z_left, psi_z_left = 0, 1.0 + bc_psi_z_right, psi_z_right = 0, 1.0 + + # Non Sparse memory allocation + #density distribution function nx*ny*nz*19 + f = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density distribution function nx*ny*nz*19 + F = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density nx*ny*nz + rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #velocity nx*ny*nz vector + v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + #psi nx*ny*nz + psi = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rho_r = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rho_b = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rhor = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rhob = ti.field(ti.f32, shape=(nx,ny,nz)) + #lattice speed 19 dimensional vector + e = ti.Vector.field(3,ti.i32, shape=(19)) + #S_dig = ti.field(ti.f32,shape=(19)) + #lattice speed 19 dimensional vector + e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #weight parameter 19 dimensional vector + w = ti.field(ti.f32, shape=(19)) + #solid flag nx*ny*nz + solid = ti.field(ti.i32,shape=(nx,ny,nz)) + #streaming vector 19 dimensional vector + LR = ti.field(ti.i32,shape=(19)) + + #external force 3 dimensional vector + ext_f = ti.Vector.field(3,ti.f32,shape=()) + # x-left velocity 3 dimensional vector + bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=()) + # x-right velocity 3 dimensional vector + bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=()) + # y-left velocity 3 dimensional vector + bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=()) + # y-right velocity 3 dimensional vector + bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=()) + # z-left velocity 3 dimensional vector + bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=()) + # z-right velocity 3 dimensional vector + bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=()) + #transforming matrix 19*19 + M = ti.field(ti.f32, shape=(19,19)) + #inverse transforming matrix 19*19 + inv_M = ti.field(ti.f32, shape=(19,19)) + #parameters for calculating the parameter of s diagonal + #=======================================# + lg0, wl, wg = 0.0, 0.0, 0.0 + l1, l2, g1, g2 = 0.0, 0.0, 0.0, 0.0 + wl = 1.0/(niu_l/(1.0/3.0)+0.5) + wg = 1.0/(niu_g/(1.0/3.0)+0.5) + lg0 = 2*wl*wg/(wl+wg) + l1=2*(wl-lg0)*10 + l2=-l1/0.2 + g1=2*(lg0-wg)*10 + g2=g1/0.2 + #=======================================# + + #transformation matrix + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #inverde of transforming matrix + inv_M_np = np.linalg.inv(M_np) + #streaming array + LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]) + #M matrix from the numpy + M.from_numpy(M_np) + #inverse matrix from numpy + inv_M.from_numpy(inv_M_np) + + #steaming array from numpy + LR.from_numpy(LR_np) + #external force with vector three dimensional + ext_f[None] = ti.Vector([fx,fy,fz]) + #set transforming matrix, inverse matrix and streaming vector non-modified + ti.static(inv_M) + ti.static(M) + ti.static(LR) + + #set x,y,z array with nx*ny*nz + x = np.linspace(0, nx, nx) + y = np.linspace(0, ny, ny) + z = np.linspace(0, nz, nz) + #set meshgrid and return three meshgrid matrix X,Y,Z with non-cartesian indexing + X, Y, Z = np.meshgrid(x, y, z, indexing='ij') + +``feq(k,rho_local, u)`` calculate the equilibrium denisty distribution function + +.. code-block:: python + + @ti.func + def feq(k,rho_local, u): + # eu=ts.vector.dot(e[k],u) + # uv=ts.vector.dot(u,u) + eu = e[k].dot(u) + uv = u.dot(u) + #same as single phase equilibrium density distribution function + feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, w[k]) + return feqout + +``init()`` intialize some variable + +.. code-block:: python + + @ti.kernel + def init(): + for i,j,k in solid: + if (solid[i,j,k] == 0): + #if it is fluid intialize the density and velocity be one and zero + rho[i,j,k] = 1.0 + v[i,j,k] = ti.Vector([0,0,0]) + # set density r and density b based on psi + rho_r[i,j,k] = (psi[i,j,k]+1.0)/2.0 + rho_b[i,j,k] = 1.0 - rho_r[i,j,k] + #set another density r and density b + rhor[i,j,k] = 0.0 + rhob[i,j,k] = 0.0 + #set density distribution equals to equilibrium density distribution function + for s in ti.static(range(19)): + f[i,j,k,s] = feq(s,1.0,v[i,j,k]) + F[i,j,k,s] = feq(s,1.0,v[i,j,k]) + +``init_geo(filename, filename2)`` import the geometry data + +.. code-block:: python + + def init_geo(filename, filename2): + #read the solid flag data and set it as an column major array + in_dat = np.loadtxt(filename) + in_dat[in_dat>0] = 1 + in_dat = np.reshape(in_dat, (nx,ny,nz),order='F') + + #read the phase data from file + phase_in_dat = np.loadtxt(filename2) + #set the array from the file with colum major + phase_in_dat = np.reshape(phase_in_dat, (nx,ny,nz), order='F') + + return in_dat, phase_in_dat + +``static_init()`` initialize non-modified variable + +.. code-block:: python + + @ti.kernel + def static_init(): + if ti.static(enable_projection): # No runtime overhead + #define lattice speed + e[0] = ti.Vector([0,0,0]) + e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1]) + e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0]) + e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1]) + e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1]) + #define another lattice speed + e_f[0] = ti.Vector([0,0,0]) + e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1]) + e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0]) + e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1]) + e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1]) + #define a weight parameter + w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0; + w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0; + w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0; + #define the boundary velocity + bc_vel_x_left = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl]) + bc_vel_x_right = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr]) + bc_vel_y_left = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl]) + bc_vel_y_right = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr]) + bc_vel_z_left = ti.Vector([vx_bczl, vy_bczl, vz_bczl]) + bc_vel_z_right = ti.Vector([vx_bczr, vy_bczr, vz_bczr]) + +``multiply_M()`` calculate the density distribution function in momentum space + +.. code-block:: python + + @ti.func + def multiply_M(i,j,k): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + for index in ti.static(range(19)): + for s in ti.static(range(19)): + #calculate here + out[index] += M[index,s]*F[i,j,k,s] + #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s]) + return out + +``GuoF(i,j,k,s,u)`` calculate Guo's force term + +.. code-block:: python + + @ti.func + def GuoF(i,j,k,s,u): + out=0.0 + for l in ti.static(range(19)): + out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l] + + return out + +``meq_vec(rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``Compute_C()`` calculate the color gradient + +.. code-block:: python + + @ti.func + def Compute_C(i): + C = ti.Vector([0.0,0.0,0.0]) + ind_S = 0 + for s in ti.static(range(19)): + ip = periodic_index_for_psi(i+e[s]) + if (solid[ip] == 0): + #if it's fluid calculate the color gradient based on psi + C += 3.0*w[s]*e_f[s]*psi[ip] + else: + #if it is solid and abs(density r-density b) is less than 0.9 + ind_S = 1 + #calculate the color gradient based on psi_solid and set ind_s=1 + C += 3.0*w[s]*e_f[s]*psi_solid + + if (abs(rho_r[i]-rho_b[i]) > 0.9) and (ind_S == 1): + #if abs(density r-density b) is very large and it's solid set color gradient to be zero + C = ti.Vector([0.0,0.0,0.0]) + + return C + +``Compute_S_local`` calculate parameter of s diagonal + +.. code-block:: python + + @ti.func + def Compute_S_local(id): + sv=0.0; sother=0.0 + if (psi[id]>0): + if (psi[id]>0.1): + #if psi>0.1 + #sv=1.0/(niu_l/(1.0/3.0)+0.5) + sv=wl + else: + #if 0-0.1 + sv=lg0+g1*psi[id]+g2*psi[id]*psi[id] + #calculate s other + sother = 8.0*(2.0-sv)/(8.0-sv) + + #set s diagonal to be zero and set certain element to be relatie local parameter + S = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + S[1]=sv;S[2]=sv;S[4]=sother;S[6]=sother;S[8]=sother;S[9]=sv; + S[10]=sv;S[11]=sv;S[12]=sv;S[13]=sv;S[14]=sv;S[15]=sv;S[16]=sother; + S[17]=sother;S[18]=sother; + + + return S; + + +``collision()`` define the collision and recoloring process + +.. code-block:: python + + @ti.kernel + def colission(): + for i,j,k in rho: + #if it is inner fluid, calculate color gradient divided by norm of color gradient + if (i0 : + normal = C/cc + #calculate the M + m_temp = multiply_M(i,j,k) + meq = meq_vec(rho[i,j,k],v[i,j,k]) + #calculate surface tension term + meq[1] += CapA*cc + meq[9] += 0.5*CapA*cc*(2*normal.x*normal.x-normal.y*normal.y-normal.z*normal.z) + meq[11] += 0.5*CapA*cc*(normal.y*normal.y-normal.z*normal.z) + meq[13] += 0.5*CapA*cc*(normal.x*normal.y) + meq[14] += 0.5*CapA*cc*(normal.y*normal.z) + meq[15] += 0.5*CapA*cc*(normal.x*normal.z) + #calculate s local + S_local = Compute_S_local(ti.Vector([i,j,k])) + #calculate s*(m-meq) + for s in ti.static(range(19)): + m_temp[s] -= S_local[s]*(m_temp[s]-meq[s]) + m_temp[s] += (1-0.5*S_local[s])*GuoF(i,j,k,s,v[i,j,k]) + #calculte convection of density filed + g_r = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + g_b = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + + for s in ti.static(range(19)): + f[i,j,k,s] = 0 + for l in ti.static(range(19)): + # 1.single phase collision + f[i,j,k,s] += inv_M[s,l]*m_temp[l] + + g_r[s] = feq(s,rho_r[i,j,k],v[i,j,k]) + g_b[s] = feq(s,rho_b[i,j,k],v[i,j,k]) + + if (cc>0): + for kk in ti.static([1,3,5,7,9,11,13,15,17]): + # ef=ts.vector.dot(e[kk],C) + ef=e[kk].dot(C) + cospsi= g_r[kk] if (g_r[kk]nx-1: iout[0] = 0 + if i[1]<0: iout[1] = ny-1 + if i[1]>ny-1: iout[1] = 0 + if i[2]<0: iout[2] = nz-1 + if i[2]>nz-1: iout[2] = 0 + + return iout + +``periodic_index_for_psi(i)`` defines the index of boundary for psi if using periodic boundary condition + +.. code-block:: python + + @ti.func + def periodic_index_for_psi(i): + iout = i + if i[0]<0: + #if periodic boundary condition set index based on periodic boundary condition + if bc_psi_x_left == 0: + iout[0] = nx-1 + else: + #otherwise set neighbouring index, + #similar for other sides + iout[0] = 0 + + if i[0]>nx-1: + if bc_psi_x_right==0: + iout[0] = 0 + else: + iout[0] = nx-1 + + if i[1]<0: + if bc_psi_y_left == 0: + iout[1] = ny-1 + else: + iout[1] = 0 + + if i[1]>ny-1: + if bc_psi_y_right==0: + iout[1] = 0 + else: + iout[1] = ny-1 + + if i[2]<0: + if bc_psi_z_left==0: + iout[2] = nz-1 + else: + iout[2] = 0 + + if i[2]>nz-1: + if bc_psi_z_right==0: + iout[2] = 0 + else: + iout[2] = nz-1 + + return iout + + +``streaming1()`` defines steaming process of denisty distribution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i,j,k in rho: + #if (solid[i,j,k] == 0): + if (i0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) + + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) + + + # Direction Y + if ti.static(bc_y_left==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + if (solid[i,1,k]>0): + F[i,0,k,s]=feq(s, rho_bcyl, v[i,1,k]) + else: + F[i,0,k,s]=feq(s, rho_bcyl, v[i,0,k]) + + if ti.static(bc_y_left==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + F[i,0,k,s]=feq(LR[s], 1.0, bc_vel_y_left[None])-F[i,0,k,LR[s]]+feq(s,1.0,bc_vel_y_left[None]) + + if ti.static(bc_y_right==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + if (solid[i,ny-2,k]>0): + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-2,k]) + else: + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-1,k]) + + if ti.static(bc_y_right==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + F[i,ny-1,k,s]=feq(LR[s], 1.0, bc_vel_y_right[None])-F[i,ny-1,k,LR[s]]+feq(s,1.0,bc_vel_y_right[None]) + + # Z direction + if ti.static(bc_z_left==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + if (solid[i,j,1]>0): + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,1]) + else: + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,0]) + + if ti.static(bc_z_left==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + F[i,j,0,s]=feq(LR[s], 1.0, bc_vel_z_left[None])-F[i,j,0,LR[s]]+feq(s,1.0,bc_vel_z_left[None]) + + if ti.static(bc_z_right==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + if (solid[i,j,nz-2]>0): + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-2]) + else: + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-1]) + + if ti.static(bc_z_right==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + F[i,j,nz-1,s]=feq(LR[s], 1.0, bc_vel_z_right[None])-F[i,j,nz-1,LR[s]]+feq(s,1.0,bc_vel_z_right[None]) + +``Boundary_condition_psi()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i,j,k, in rho: + #if (solid[i,j,k] == 0): + if (i tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, 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---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, 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--------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} 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// [C]VC[V] is m=1 + var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1 + var s_v = "^(" + C + ")?" + v; // vowel in stem + + this.stemWord = function (w) { + var stem; + var suffix; + var firstch; + var origword = w; + + if (w.length < 3) + return w; + + var re; + var re2; + var re3; + var re4; + + firstch = w.substr(0,1); + if (firstch == "y") + w = firstch.toUpperCase() + w.substr(1); + + // Step 1a + re = /^(.+?)(ss|i)es$/; + re2 = /^(.+?)([^s])s$/; + + if (re.test(w)) + w = w.replace(re,"$1$2"); + else if (re2.test(w)) + w = w.replace(re2,"$1$2"); + + // Step 1b + re = /^(.+?)eed$/; + re2 = /^(.+?)(ed|ing)$/; + if (re.test(w)) { + var fp = re.exec(w); + re = new RegExp(mgr0); + if (re.test(fp[1])) { + re = /.$/; + w = w.replace(re,""); + } + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1]; + re2 = new RegExp(s_v); + if (re2.test(stem)) { + w = stem; + re2 = /(at|bl|iz)$/; + re3 = new RegExp("([^aeiouylsz])\\1$"); + re4 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re2.test(w)) + w = w + "e"; + else if (re3.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + else if (re4.test(w)) + w = w + "e"; + } + } + + // Step 1c + re = /^(.+?)y$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(s_v); + if (re.test(stem)) + w = stem + "i"; + } + + // Step 2 + re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step2list[suffix]; + } + + // Step 3 + re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + suffix = fp[2]; + re = new RegExp(mgr0); + if (re.test(stem)) + w = stem + step3list[suffix]; + } + + // Step 4 + re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/; + re2 = /^(.+?)(s|t)(ion)$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + if (re.test(stem)) + w = stem; + } + else if (re2.test(w)) { + var fp = re2.exec(w); + stem = fp[1] + fp[2]; + re2 = new RegExp(mgr1); + if (re2.test(stem)) + w = stem; + } + + // Step 5 + re = /^(.+?)e$/; + if (re.test(w)) { + var fp = re.exec(w); + stem = fp[1]; + re = new RegExp(mgr1); + re2 = new RegExp(meq1); + re3 = new RegExp("^" + C + v + "[^aeiouwxy]$"); + if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) + w = stem; + } + re = /ll$/; + re2 = new RegExp(mgr1); + if (re.test(w) && re2.test(w)) { + re = /.$/; + w = w.replace(re,""); + } + + // and turn initial Y back to y + if (firstch == "y") + w = firstch.toLowerCase() + w.substr(1); + return w; + } +} + diff --git a/docs/_static/minus.png b/docs/_static/minus.png new file mode 100644 index 0000000..d96755f Binary files /dev/null and b/docs/_static/minus.png differ diff --git a/docs/_static/plus.png b/docs/_static/plus.png new file mode 100644 index 0000000..7107cec Binary files /dev/null and b/docs/_static/plus.png differ diff --git a/docs/_static/pygments.css b/docs/_static/pygments.css new file mode 100644 index 0000000..08bec68 --- /dev/null +++ b/docs/_static/pygments.css @@ -0,0 +1,74 @@ +pre { line-height: 125%; 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = docUrlRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = docUrlRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + /** + * execute search (requires search index to be loaded) + */ + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // lookup as object + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); + + // now sort the results by score (in opposite order of appearance, since the + // display function below uses pop() to retrieve items) and then + // alphabetically + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; + }); + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/docs/_static/sphinx_highlight.js b/docs/_static/sphinx_highlight.js new file mode 100644 index 0000000..aae669d --- /dev/null +++ b/docs/_static/sphinx_highlight.js @@ -0,0 +1,144 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + parent.insertBefore( + span, + parent.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(SphinxHighlight.highlightSearchWords); +_ready(SphinxHighlight.initEscapeListener); diff --git a/docs/aaa.html b/docs/aaa.html new file mode 100644 index 0000000..2a18f1c --- /dev/null +++ b/docs/aaa.html @@ -0,0 +1,644 @@ + + + + + + + Single_phase.LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Single_phase.LBM_3D_SinglePhase_Solver

+

This is a D3Q19 MRT(multi-relaxation-time) solver for single phase. It defines a class called LB3D_Solver_Single_Phase. The Class has a default function +__init__() as normal python class.

+
class LB3D_Solver_Single_Phase:
+    def __init__(self, nx, ny, nz, sparse_storage = False):
+    #enable projection, define a sparse_storage flag
+    self.enable_projection = True
+    self.sparse_storage = sparse_storage
+    #the grid of the simulation in three direction
+    self.nx,self.ny,self.nz = nx,ny,nz
+    #nx,ny,nz = 120,120,120
+    #density distribution function in three direction
+    self.fx,self.fy,self.fz = 0.0e-6,0.0,0.0
+    #kinematic viscosity in lattice unit
+    self.niu = 0.16667
+    #define a taichi field of float scalar which is the maximum velocity
+    self.max_v=ti.field(ti.f32,shape=())
+    #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+    self.bc_x_left, self.rho_bcxl, self.vx_bcxl, self.vy_bcxl, self.vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+    self.bc_x_right, self.rho_bcxr, self.vx_bcxr, self.vy_bcxr, self.vz_bcxr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary x-axis right side
+    self.bc_y_left, self.rho_bcyl, self.vx_bcyl, self.vy_bcyl, self.vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+    self.bc_y_right, self.rho_bcyr, self.vx_bcyr, self.vy_bcyr, self.vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+    self.bc_z_left, self.rho_bczl, self.vx_bczl, self.vy_bczl, self.vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+    self.bc_z_right, self.rho_bczr, self.vx_bczr, self.vy_bczr, self.vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+    if sparse_storage == False:
+        #define old density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.f = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define new density distribution function with taichi field which has nx*ny*nz element and each element is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define density with taichi field which has nx*ny*nz element and each element is a scalar
+        self.rho = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define velocity with taichi field which has nx*ny*nz element and each element is a three dimensional vector
+        self.v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+    else:
+        #sparse storage the variable
+        #define old density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.f = ti.Vector.field(19, ti.f32)
+        #define new density distribution function by taichi field with one element and which is a 19 dimensional vector
+        self.F = ti.Vector.field(19,ti.f32)
+        #define density by taichi field with one element which is a scalar
+        self.rho = ti.field(ti.f32)
+        #define velocity by taichi field with one element which is a scalar
+        self.v = ti.Vector.field(3, ti.f32)
+        #define partition equals 3
+        n_mem_partition = 3
+        #every index has four variable rho, v, f, F
+        cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+        cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(self.rho, self.v, self.f, self.F)
+    #define lattice speed 3x19
+    self.e = ti.Vector.field(3,ti.i32, shape=(19))
+    #define s diagnol vector
+    self.S_dig = ti.Vector.field(19,ti.f32,shape=())
+    #define another lattice speed 3x19
+    self.e_f = ti.Vector.field(3,ti.f32, shape=(19))
+    #define weight parameter
+    self.w = ti.field(ti.f32, shape=(19))
+    #define solid which is a flag when equals 0 it is fluid, when it is 1 it is solid
+    self.solid = ti.field(ti.i8,shape=(nx,ny,nz))
+    #define external force which is a three dimensional vector
+    self.ext_f = ti.Vector.field(3,ti.f32,shape=())
+    #define transforming matrix M which is a 19x19 dimension matrix
+    self.M = ti.Matrix.field(19, 19, ti.f32, shape=())
+    #define the inverse transforming matrix M^-1
+    self.inv_M = ti.Matrix.field(19,19,ti.f32, shape=())
+    #define the numpy version of M.
+    M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define the numpy version of M^-1
+    inv_M_np = np.linalg.inv(M_np)
+    #define the index of 19 lattice node for bounce back
+    self.LR = [0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]
+    #define taichi field version of M
+    self.M[None] = ti.Matrix([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+    [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+    [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+    [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+    [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+    [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+    [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+    [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+    [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+    [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+    #define taichi field version of M^-1
+    self.inv_M[None] = ti.Matrix(inv_M_np)
+    #define coordinate nx*ny*nz
+    self.x = np.linspace(0, nx, nx)
+    self.y = np.linspace(0, ny, ny)
+    self.z = np.linspace(0, nz, nz)
+    #X, Y, Z = np.meshgrid(self.x, self.y, self.z, indexing='ij')
+
+
+

Following is the init_simulation() function which initialize some simulation parameter

+
def init_simulation(self):
+#x,y,z velocity vector from vx_bcxl,vy_bcxl and vz_bcxl
+self.bc_vel_x_left = [self.vx_bcxl, self.vy_bcxl, self.vz_bcxl]
+self.bc_vel_x_right = [self.vx_bcxr, self.vy_bcxr, self.vz_bcxr]
+self.bc_vel_y_left = [self.vx_bcyl, self.vy_bcyl, self.vz_bcyl]
+self.bc_vel_y_right = [self.vx_bcyr, self.vy_bcyr, self.vz_bcyr]
+self.bc_vel_z_left = [self.vx_bczl, self.vy_bczl, self.vz_bczl]
+self.bc_vel_z_right = [self.vx_bczr, self.vy_bczr, self.vz_bczr]
+#define single relaxation time tau
+self.tau_f=3.0*self.niu+0.5
+#define single relaxation frequency
+self.s_v=1.0/self.tau_f
+#define other parameter in the s diagonal
+self.s_other=8.0*(2.0-self.s_v)/(8.0-self.s_v)
+#define the s diagonal
+self.S_dig[None] = ti.Vector([0,self.s_v,self.s_v,0,self.s_other,0,self.s_other,0,self.s_other, self.s_v, self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_v,self.s_other,self.s_other,self.s_other])
+#define external force
+#self.ext_f[None] = ti.Vector([self.fx,self.fy,self.fz])
+self.ext_f[None][0] = self.fx
+self.ext_f[None][1] = self.fy
+self.ext_f[None][2] = self.fz
+#if external force greater than zero define force_flag equals 1
+#other wise force_flag equals 0
+if ((abs(self.fx)>0) or (abs(self.fy)>0) or (abs(self.fz)>0)):
+    self.force_flag = 1
+else:
+    self.force_flag = 0
+
+#define M M^-1 S diagonal not been modified.
+ti.static(self.inv_M)
+ti.static(self.M)
+#ti.static(LR)
+ti.static(self.S_dig)
+#statically initialize
+self.static_init()
+self.init()
+
+
+

feq() calculate the equilibrium density distribution function in velocity space

+
#taichi function
+@ti.func
+    def feq(self, k,rho_local, u):
+        eu = self.e[k].dot(u)
+        uv = u.dot(u)
+        #calculate the equilibrium density distribution function
+        feqout = self.w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+        #print(k, rho_local, self.w[k])
+        return feqout
+
+
+

init() initialize density velocity and density distribution function

+
@ti.kernel
+def init(self):
+    for i,j,k in self.solid:
+        #print(i,j,k)
+        if (self.sparse_storage==False or self.solid[i,j,k]==0):
+            #if it is fluid then initialize density equals one
+            self.rho[i,j,k] = 1.0
+            #initialize the velocity to be zero in all the direction
+            self.v[i,j,k] = ti.Vector([0,0,0])
+            for s in ti.static(range(19)):
+                #initialize 19 denisty distribution function equals the equilibrium density distribution function
+                self.f[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                self.F[i,j,k][s] = self.feq(s,1.0,self.v[i,j,k])
+                #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() import data from a file

+
def init_geo(self,filename):
+    #load data from a file
+    in_dat = np.loadtxt(filename)
+    #set any positive value to be one
+    in_dat[in_dat>0] = 1
+    #reshape it as a nx*ny*nz vector with column major
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    #assign it to solid varible
+    self.solid.from_numpy(in_dat)
+
+
+

static_init() initialize lattice speeed and weight parameter. These parameter is not modified during the simulation

+
#taichi kernel for parallization
+@ti.kernel
+def static_init(self):
+    if ti.static(self.enable_projection): # No runtime overhead
+        #initialize the lattice speed
+        self.e[0] = ti.Vector([0,0,0])
+        self.e[1] = ti.Vector([1,0,0]); self.e[2] = ti.Vector([-1,0,0]); self.e[3] = ti.Vector([0,1,0]); self.e[4] = ti.Vector([0,-1,0]);self.e[5] = ti.Vector([0,0,1]); self.e[6] = ti.Vector([0,0,-1])
+        self.e[7] = ti.Vector([1,1,0]); self.e[8] = ti.Vector([-1,-1,0]); self.e[9] = ti.Vector([1,-1,0]); self.e[10] = ti.Vector([-1,1,0])
+        self.e[11] = ti.Vector([1,0,1]); self.e[12] = ti.Vector([-1,0,-1]); self.e[13] = ti.Vector([1,0,-1]); self.e[14] = ti.Vector([-1,0,1])
+        self.e[15] = ti.Vector([0,1,1]); self.e[16] = ti.Vector([0,-1,-1]); self.e[17] = ti.Vector([0,1,-1]); self.e[18] = ti.Vector([0,-1,1])
+
+        self.e_f[0] = ti.Vector([0,0,0])
+        self.e_f[1] = ti.Vector([1,0,0]); self.e_f[2] = ti.Vector([-1,0,0]); self.e_f[3] = ti.Vector([0,1,0]); self.e_f[4] = ti.Vector([0,-1,0]);self.e_f[5] = ti.Vector([0,0,1]); self.e_f[6] = ti.Vector([0,0,-1])
+        self.e_f[7] = ti.Vector([1,1,0]); self.e_f[8] = ti.Vector([-1,-1,0]); self.e_f[9] = ti.Vector([1,-1,0]); self.e_f[10] = ti.Vector([-1,1,0])
+        self.e_f[11] = ti.Vector([1,0,1]); self.e_f[12] = ti.Vector([-1,0,-1]); self.e_f[13] = ti.Vector([1,0,-1]); self.e_f[14] = ti.Vector([-1,0,1])
+        self.e_f[15] = ti.Vector([0,1,1]); self.e_f[16] = ti.Vector([0,-1,-1]); self.e_f[17] = ti.Vector([0,1,-1]); self.e_f[18] = ti.Vector([0,-1,1])
+        #initialize the weight parameter
+        self.w[0] = 1.0/3.0; self.w[1] = 1.0/18.0; self.w[2] = 1.0/18.0; self.w[3] = 1.0/18.0; self.w[4] = 1.0/18.0; self.w[5] = 1.0/18.0; self.w[6] = 1.0/18.0;
+        self.w[7] = 1.0/36.0; self.w[8] = 1.0/36.0; self.w[9] = 1.0/36.0; self.w[10] = 1.0/36.0; self.w[11] = 1.0/36.0; self.w[12] = 1.0/36.0;
+        self.w[13] = 1.0/36.0; self.w[14] = 1.0/36.0; self.w[15] = 1.0/36.0; self.w[16] = 1.0/36.0; self.w[17] = 1.0/36.0; self.w[18] = 1.0/36.0;
+
+
+

meq_vec(self, rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(self, rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

cal_local_force(self,i,j,k) transfer the external force to a vector

+
@ti.func
+def cal_local_force(self,i,j,k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    return f
+
+
+

collision() defines the collision of LBM process

+
#taichi kernel for parallization
+@ti.kernel
+def colission(self):
+    #outer loop for every index in rho field
+    for i,j,k in self.rho:
+        #if is not solid and it is not on the boundary
+        if (self.solid[i,j,k] == 0 and i<self.nx and j<self.ny and k<self.nz):
+            #calculate S*(m-meq)
+            m_temp = self.M[None]@self.F[i,j,k]
+            meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+            m_temp -= self.S_dig[None]*(m_temp-meq)
+            #add force if there is force, here use Guo's force scheme
+            f = self.cal_local_force(i,j,k)
+            if (ti.static(self.force_flag==1)):
+                for s in ti.static(range(19)):
+                #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                    #f = self.cal_local_force()
+                    f_guo=0.0
+                    for l in ti.static(range(19)):
+                        f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                    #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                    m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+            #calculate density distribution function after collision f=M^-1*S*(m-meq)
+            self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            self.f[i,j,k] += self.inv_M[None]@m_temp
+
+
+

periodic_index(self,i) defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(self,i):
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = self.nx-1
+    #x-right
+    if i[0]>self.nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = self.ny-1
+    #y-right
+    if i[1]>self.ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = self.nz-1
+    #z-right
+    if i[2]>self.nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming prcoess of denisty distribution function

+
#taichi kernel for parallization
+@ti.kernel
+def streaming1(self):
+    #grouped index which loop the index of rho
+    for i in ti.grouped(self.rho):
+    # streaming for fluid and non-boundary
+        if (self.solid[i] == 0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            for s in ti.static(range(19)):
+            # streaming according to the lattice speed and on boundary with periodic index
+                ip = self.periodic_index(i+self.e[s])
+                if (self.solid[ip]==0):
+                # fluid new density distribution function equals the streaming of old density distribution fuction
+                    self.F[ip][s] = self.f[i][s]
+                else:
+                #solid bounce back scheme
+                    self.F[i][self.LR[s]] = self.f[i][s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition() define three direction fixed pressure or fixed velocity bounary condition

+
@ti.kernel
+def Boundary_condition(self):
+#fixed pressure boundary condition
+    if ti.static(self.bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[1,j,k]>0):
+                    # if the boundary is fluid but the neighbour is solid then the density distribution
+                    #function equals to the solid velcity equilibrium density distribution fucntion
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[1,j,k])
+                    else:
+                    # if the boundary is fluid and the neighbour is fluid then the density distribution
+                    #function equals to equilibrium density distribution fucntion on the boundary
+                        self.F[0,j,k][s]=self.feq(s, self.rho_bcxl, self.v[0,j,k])
+    #fixed velocity boundary condition
+    if ti.static(self.bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+        # if the boundary is fluid new density distribution fucntion equals to equilibrium density
+        #distibution function with fixed velocity
+            if (self.solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    self.F[0,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_left))
+    # fixed pressure boundary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[self.nx-2,j,k]>0):
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-2,j,k])
+                    else:
+                        self.F[self.nx-1,j,k][s]=self.feq(s, self.rho_bcxr, self.v[self.nx-1,j,k])
+    # fixed velocity boubndary condition on x-right similar for x-left
+    if ti.static(self.bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            if (self.solid[self.nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[nx-1,j,k][s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+                    self.F[self.nx-1,j,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_x_right))
+
+     # Direction Y
+     #fixed pressure boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,1,k]>0):
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,1,k])
+                    else:
+                        self.F[i,0,k][s]=self.feq(s, self.rho_bcyl, self.v[i,0,k])
+    #fixed velocity boundary condition on y-left similar for x direction
+    if ti.static(self.bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,0,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_left[None])-self.F[i,0,k][LR[s]]+self.feq(s,1.0,self.bc_vel_y_left[None])
+                    self.F[i,0,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_left))
+    #fixed pressure boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,self.ny-2,k]>0):
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-2,k])
+                    else:
+                        self.F[i,self.ny-1,k][s]=self.feq(s, self.rho_bcyr, self.v[i,self.ny-1,k])
+    #fixed velocity boundary condition on y-right similar for x direction
+    if ti.static(self.bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            if (self.solid[i,self.ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,self.ny-1,k][s]=self.feq(self.LR[s], 1.0, self.bc_vel_y_right[None])-self.F[i,self.ny-1,k][self.LR[s]]+self.feq(s,1.0,self.bc_vel_y_right[None])
+                    self.F[i,self.ny-1,k][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_y_right))
+
+    # Z direction
+    #fixed pressure boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,1]>0):
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,1])
+                    else:
+                        self.F[i,j,0][s]=self.feq(s, self.rho_bczl, self.v[i,j,0])
+    #fixed velocity boundary condition on z-left similar for x direction
+    if ti.static(self.bc_z_left==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,0][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_left[None])-self.F[i,j,0][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_left[None])
+                    self.F[i,j,0][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_left))
+    #fixed pressure boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (self.solid[i,j,self.nz-2]>0):
+                        self.F[i,j,self.nz-1,s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-2])
+                    else:
+                        self.F[i,j,self.nz-1][s]=self.feq(s, self.rho_bczr, self.v[i,j,self.nz-1])
+    #fixed velocity boundary condition on z-right similar for x direction
+    if ti.static(self.bc_z_right==2):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            if (self.solid[i,j,self.nz-1]==0):
+                for s in ti.static(range(19)):
+                    #self.F[i,j,self.nz-1][s]=self.feq(self.LR[s], 1.0, self.bc_vel_z_right[None])-self.F[i,j,self.nz-1][self.LR[s]]+self.feq(s,1.0,self.bc_vel_z_right[None])
+                    self.F[i,j,self.nz-1][s]=self.feq(s,1.0,ti.Vector(self.bc_vel_z_right))
+
+
+

streaming3() calculatet the macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        #print(i.x, i.y, i.z)
+        #if it is fluid and not on the boundary
+        if (self.solid[i]==0 and i.x<self.nx and i.y<self.ny and i.z<self.nz):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            #calculate density
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+
+            self.v[i] /= self.rho[i]
+            #calculate velocity
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        # if it is solid the velocity is zero and the density equals one
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

these function set bnoundary velocity, set viscosity,force and get and calculate maximum velocity

+
#get maxium velocity
+def get_max_v(self):
+    self.max_v[None] = -1e10
+    self.cal_max_v()
+    return self.max_v[None]
+
+#calculate maximum velocity with taichi kernel
+@ti.kernel
+def cal_max_v(self):
+    for I in ti.grouped(self.rho):
+        ti.atomic_max(self.max_v[None], self.v[I].norm())
+
+#set x-right velocity
+def set_bc_vel_x1(self, vel):
+    self.bc_x_right = 2
+    self.vx_bcxr = vel[0]; self.vy_bcxr = vel[1]; self.vz_bcxr = vel[2];
+#set x-left velocity
+def set_bc_vel_x0(self, vel):
+    self.bc_x_left = 2
+    self.vx_bcxl = vel[0]; self.vy_bcxl = vel[1]; self.vz_bcxl = vel[2];
+#set y-right velocity
+def set_bc_vel_y1(self, vel):
+    self.bc_y_right = 2
+    self.vx_bcyr = vel[0]; self.vy_bcyr = vel[1]; self.vz_bcyr = vel[2];
+#set y-left velocity
+def set_bc_vel_y0(self, vel):
+    self.bc_y_left = 2
+    self.vx_bcyl = vel[0]; self.vy_bcyl = vel[1]; self.vz_bcyl = vel[2];
+#set z-right velocity
+def set_bc_vel_z1(self, vel):
+    self.bc_z_right = 2
+    self.vx_bczr = vel[0]; self.vy_bczr = vel[1]; self.vz_bczr = vel[2];
+#set z-left velocity
+def set_bc_vel_z0(self, vel):
+    self.bc_z_left = 2
+    self.vx_bczl = vel[0]; self.vy_bczl = vel[1]; self.vz_bczl = vel[2];
+#set x-left density
+def set_bc_rho_x0(self, rho):
+    self.bc_x_left = 1
+    self.rho_bcxl = rho
+#set x-right density
+def set_bc_rho_x1(self, rho):
+    self.bc_x_right = 1
+    self.rho_bcxr = rho
+#set y-left density
+def set_bc_rho_y0(self, rho):
+    self.bc_y_left = 1
+    self.rho_bcyl = rho
+#set y-right density
+def set_bc_rho_y1(self, rho):
+    self.bc_y_right = 1
+    self.rho_bcyr = rho
+#set z-left density
+def set_bc_rho_z0(self, rho):
+    self.bc_z_left = 1
+    self.rho_bczl = rho
+#set z-right density
+def set_bc_rho_z1(self, rho):
+    self.bc_z_right = 1
+    self.rho_bczr = rho
+
+#set viscosity
+def set_viscosity(self,niu):
+    self.niu = niu
+#set external force
+def set_force(self,force):
+    self.fx = force[0]; self.fy = force[1]; self.fz = force[2];
+
+
+

export_VTK(self, n) function export results to vtk file use the package pyevtk

+
def export_VTK(self, n):
+#the function takes three arguments: the filename,coordinate system and the dictionary for reuslts
+    gridToVTK(
+        #file name
+            "./LB_SingelPhase_"+str(n),
+        #coordinate
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+        #the three dictionary which the key is solid,rho,velocity and it will be output to the vtk file
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

step() function define the simulation process of this solver

+
def step(self):
+    self.colission()
+    self.streaming1()
+    self.Boundary_condition()
+    self.streaming3()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/conf.py b/docs/conf.py new file mode 100644 index 0000000..aec4621 --- /dev/null +++ b/docs/conf.py @@ -0,0 +1,35 @@ +# Configuration file for the Sphinx documentation builder. +# +# For the full list of built-in configuration values, see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# -- Project information ----------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information +import os +import sys +sys.path.insert(0, os.path.abspath('..')) +project = 'taichi-LBM3D' +copyright = '2023, xiongxin' +author = 'xiongxin' +release = '0.0.1' + +# -- General configuration --------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration + +extensions = [ + # 'sphinx.ext.autodoc', + # 'sphinx.ext.napoleon', + # 'sphinx.ext.viewcode', + +] + +templates_path = ['_templates'] +exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store'] + + + +# -- Options for HTML output ------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#options-for-html-output + +html_theme = 'sphinx_rtd_theme' +html_static_path = ['_static'] diff --git a/docs/example_cavity.html b/docs/example_cavity.html new file mode 100644 index 0000000..c2e4989 --- /dev/null +++ b/docs/example_cavity.html @@ -0,0 +1,173 @@ + + + + + + + example_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_cavity

+

This file use the LBM_3D_SinglePhase_Solver to simulate the cavity flow

+
#import certain packages
+import time
+import taichi as ti
+
+ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#set 50*50*50 cavity based on LB3D_Solver_Single_Phase solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=50,ny=50,nz=50, sparse_storage=False)
+
+#import geometry data
+lb3d.init_geo('./geo_cavity.dat')
+#set the x-right velocity
+lb3d.set_bc_vel_x1([0.0,0.0,0.1])
+#initialize
+lb3d.init_simulation()
+
+#simulation step
+for iter in range(2000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #get the maximum velocity
+        max_v = lb3d.get_max_v()
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the number of time steps, maxiumum force and the force scale=0
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, max_v,  0.0))
+        #every 1000 time steps export the vtk file
+        if (iter%1000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/example_porous_medium.html b/docs/example_porous_medium.html new file mode 100644 index 0000000..844419e --- /dev/null +++ b/docs/example_porous_medium.html @@ -0,0 +1,170 @@ + + + + + + + example_porous_medium — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

example_porous_medium

+

This file simulate the porous medium based on the LBM_3D_SinglePhase_Solver

+
#import time and taichi package
+import time
+import taichi as ti
+#taichi intialization
+ti.init(arch=ti.cpu)
+#import the LBM_3D_SinglePhase_Solver
+import LBM_3D_SinglePhase_Solver as lb3dsp
+#set the time
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+
+#create the 131*131*131 gird LBM_3D_SinglePhase_Solver
+lb3d = lb3dsp.LB3D_Solver_Single_Phase(nx=131,ny=131,nz=131)
+#import the porous medium geometry
+lb3d.init_geo('./img_ftb131.txt')
+#set x-left and x-right density
+lb3d.set_bc_rho_x1(0.99)
+lb3d.set_bc_rho_x0(1.0)
+#initialize the simulation
+lb3d.init_simulation()
+#simulation loop
+for iter in range(50000+1):
+    lb3d.step()
+
+    if (iter%500==0):
+        #calculate the time
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+        #print the time
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        #print the time step, max force=10, force_scale=10
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+        #export VTK every 2000 time step
+        if (iter%2000==0):
+            lb3d.export_VTK(iter)
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/flow_domain_geo_generation_2D.html b/docs/flow_domain_geo_generation_2D.html new file mode 100644 index 0000000..526eb37 --- /dev/null +++ b/docs/flow_domain_geo_generation_2D.html @@ -0,0 +1,163 @@ + + + + + + + flow_domain_geo_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

flow_domain_geo_generation_2D

+

This file generate geometry file for solver to read

+
#import certain module
+import numpy as np
+import math
+
+
+#define the input file name
+# INPUT STL FILE NAME
+output_name = 'geo_cavity.dat'
+
+#define the grid resolution
+dnx, dny, dnz = 50, 50, 50
+
+#==========================================================
+#           DO NOT CHANGE BELOW
+#==========================================================
+
+#define an matrix dnx*dny*dnz with zero values
+out_dat = np.zeros((dnx,dny,dnz))
+
+#=======Can define some geometry here to out_dat=========
+#define the boundary to be solid
+out_dat[0,:,:] = 1
+#cout_dat[:,:,0] = 1
+out_dat[:,0,:] = 1
+out_dat[:,-1,:] = 1
+out_dat[:,:,0] = 1
+out_dat[:,:,-1] = 1
+
+#=========================================================
+#reshape the data to be column major
+out_dat = out_dat.reshape(out_dat.size, order = 'F')
+
+
+#output the transfer of out_dat to the file with integer type
+np.savetxt(output_name,out_dat.T,fmt='%d')
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/genindex.html b/docs/genindex.html new file mode 100644 index 0000000..08506b6 --- /dev/null +++ b/docs/genindex.html @@ -0,0 +1,103 @@ + + + + + + Index — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Index
    • +
  • +
    • +
+
+
+
+
+ + +

Index

+ +
+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/geo.dat b/docs/geo.dat new file mode 100644 index 0000000..1de297f --- /dev/null +++ b/docs/geo.dat @@ -0,0 +1,110592 @@ +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 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+ + + + \ No newline at end of file diff --git a/docs/index.rst b/docs/index.rst new file mode 100644 index 0000000..ce297ea --- /dev/null +++ b/docs/index.rst @@ -0,0 +1,19 @@ +.. taichi-LBM3D documentation master file, created by + sphinx-quickstart on Tue Apr 11 17:00:17 2023. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Welcome to taichi-LBM3D's documentation! +======================================== + +.. toctree:: + :maxdepth: 4 + :caption: Contents: + + modules + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`search` diff --git a/docs/lbm_solver_3d.html b/docs/lbm_solver_3d.html new file mode 100644 index 0000000..77ad6e0 --- /dev/null +++ b/docs/lbm_solver_3d.html @@ -0,0 +1,530 @@ + + + + + + + Single_phase.lbm_solver_3d — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

Single_phase.lbm_solver_3d

+

This file is the non-objective oriented version of singlephase solver without using class. +At the begining of the this file it define some variable first.

+
#import some package
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+#initialize taichi with cpu, dunamic index, disable profiler and disables printing the intermediate representation
+ti.init(arch=ti.cpu, dynamic_index=True, kernel_profiler=False, print_ir=False)
+#enable projection
+enable_projection = True
+#nx,ny,nz = 100,50,5
+#define 131x131x131 and zero external force
+nx,ny,nz = 131,131,131
+fx,fy,fz = 0.0e-6,0.0,0.0
+#viscosity=0.1
+niu = 0.1
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 1, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 1, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+#define old density distribution funciton nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define new density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#define density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#define velocity nx*ny*nz
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#define lattice speed 3*19
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#define s diagonal 19 dimension vector
+S_dig = ti.field(ti.f32,shape=(19))
+#define another lattice speed 3*19
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#define weight parameter 19 dimesnion vector
+w = ti.field(ti.f32, shape=(19))
+#define solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#define vector for streaming 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+#define external force with a 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+#define velocity in x,y,z direction with 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#define transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#define inverse of transforming matrix
+inv_M = ti.field(ti.f32, shape=(19,19))
+#define single relaxation parameter
+tau_f=3.0*niu+0.5
+#define single relaxation frequency
+s_v=1.0/tau_f
+#define other parameter in the s diagonal
+s_other=8.0*(2.0-s_v)/(8.0-s_v)
+#define s matrix but not used
+S_np = np.zeros((19,19))
+S_np[0,0]=0;        S_np[1,1]=s_v;          S_np[2,2]=s_v;          S_np[3,3]=0;        S_np[4,4]=s_other;      S_np[5,5]=0;
+S_np[6,6]=s_other;  S_np[7,7]=0;            S_np[8,8]=s_other;      S_np[9,9]=s_v;      S_np[10,10]=s_v;        S_np[11,11]=s_v;
+S_np[12,12]=s_v;    S_np[13,13]=s_v;        S_np[14,14]=s_v;        S_np[15,15]=s_v;    S_np[16,16]=s_other;    S_np[17,17]=s_other;
+S_np[18,18]=s_other
+#define numpy array version of s diagonal.
+S_dig_np = np.array([0,s_v,s_v,0,s_other,0,s_other,0,s_other, s_v, s_v,s_v,s_v,s_v,s_v,s_v,s_other,s_other,s_other])
+#define numpy version of transforming matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#define inverse of transforming matrix using inv function in linalg package
+inv_M_np = np.linalg.inv(M_np)
+#define index for streaming
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#assign numpy version to M.np to M
+M.from_numpy(M_np)
+#assign numpy version of inverser matrix inv_M_np to inv_M
+inv_M.from_numpy(inv_M_np)
+#assign numpy versio of LR array  to LR
+LR.from_numpy(LR_np)
+#assign fx,fy,fz to vector external force
+ext_f[None] = ti.Vector([fx,fy,fz])
+#assign numpy version of S diagnal S_dig_np to S_dig
+S_dig.from_numpy(S_dig_np)
+#make inv_M,M,LR,S_dig not modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+ti.static(S_dig)
+
+#create mesh nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#numpy meshgrid from x,y,z 1d array to 3d array X,Y,Z here use ij indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local,u) calculate the equilibrium density distribution function in velocity space

+
# taichi funciton
+@ti.func
+def feq(k,rho_local, u):
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #calculate the equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() initialize velocity=0, density=1 and denisty distribution function= equilibrium density distribution function

+
@ti.kernel
+def init():
+    for i,j,k in rho:
+        rho[i,j,k] = 1.0
+        v[i,j,k] = ti.Vector([0,0,0])
+        for s in range(19):
+            f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+            #print(F[i,j,k,s], feq(s,1.0,v[i,j,k]))
+
+
+

init_geo() load geometry file

+
def init_geo(filename):
+    #load data
+    in_dat = np.loadtxt(filename)
+    #reshape it with column major
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+    return in_dat
+
+
+

static_init() initialize lattixe speed weight parameter and boundary velocity

+
@ti.kernel
+def static_init():
+if ti.static(enable_projection): # No runtime overhead
+    #initialize lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #initialize lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #intialize weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #intialize boundary velocity
+    bc_vel_x_left[None] = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right[None] = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left[None] = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right[None] = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left[None] = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right[None] = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M calculate denisty distribution function in momentum space M*f=m

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in range(19):
+        for s in range(19):
+            #calculte m=M*f here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s Force scheme

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in range(19):
+    #calculate Guo's force here
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) calculate equilibrium density distribution function in momentum space

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

collison() define the prcoess of collision

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is fluid
+        if (solid[i,j,k] == 0):
+            #calculate m
+            m_temp = multiply_M(i,j,k)
+            #calculate meq
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            for s in range(19):
+                #calculate -s*(m-meq)
+                m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #add Guo's force
+                m_temp[s] += (1-0.5*S_dig[s])*GuoF(i,j,k,s,v[i,j,k])
+
+            for s in range(19):
+                f[i,j,k,s] = 0
+                for l in range(19):
+                    #f=-M^-1*S(m-meq)
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+
+

periodic_index(i) set the bounary index with periodic bounary condition

+
@ti.func
+def periodic_index(i):
+    #inner index
+    iout = i
+    #x-left
+    if i[0]<0:     iout[0] = nx-1
+    #x-right
+    if i[0]>nx-1:  iout[0] = 0
+    #y-left
+    if i[1]<0:     iout[1] = ny-1
+    #y-right
+    if i[1]>ny-1:  iout[1] = 0
+    #z-left
+    if i[2]<0:     iout[2] = nz-1
+    #z-right
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

streaming1() defines the streaming process of denisty distibution function

+
@ti.kernel
+def streaming1():
+    for i in ti.grouped(rho):
+        #if it is fluid
+        if (solid[i] == 0):
+            for s in range(19):
+                #the neighbour index
+                ip = periodic_index(i+e[s])
+                #if neighbour index is fluid just streaming
+                if (solid[ip]==0):
+                    F[ip,s] = f[i,s]
+                #if neighbour index is solid just bounce back
+                else:
+                    F[i,LR[s]] = f[i,s]
+                    #print(i, ip, "@@@")
+
+
+

streaming2() a simple streaming process without consideration of solid and boundary

+
@ti.kernel
+def streaming2():
+    for i in ti.grouped(rho):
+        for s in range(19):
+            f[i,s] = F[i,s]
+
+
+

Boudary_condition() define the bounary condition of fixed pressure and fixed velocity

+
@ti.kernel
+def Boundary_condition():
+    #pressure-boundary condtion x-left
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #if boundary is fluid but the neighbour is solid
+                #equilibrium density distribution function is calculated based on the neighbour velocity
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                #if boundary is fluid and the neighbour is also fluid
+                #equilibrium density distribution function is calculated based on the boundary velocity
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    #velocity-boundary conditon x-left
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in range(19):
+                #calculate density distribution fucntion based on equilibrium part and non-equilibrium part
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+
+    #pressure boundary condition x-right similar to x-left
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    #velocity booundary condition x-right similar to x-left
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in range(19):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])  #!!!!!!change velocity in feq into vector
+
+
+

streaming3() calculate the macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i in ti.grouped(rho):
+        #if it is fluid calculate density and velocity based on density distribution function
+        if (solid[i]==0):
+            rho[i] = 0
+            v[i] = ti.Vector([0,0,0])
+            for s in range(19):
+                f[i,s] = F[i,s]
+                rho[i] += f[i,s]
+                v[i] += e_f[s]*f[i,s]
+
+            v[i] /= rho[i]
+            v[i] += (ext_f[None]/2)/rho[i]
+        # if it is solid set denisty equals one and velocity equals zero
+        else:
+            rho[i] = 1.0
+            v[i] = ti.Vector([0,0,0])
+
+
+

At the end of the file do the actual simulation and export the data

+
#define some time varible
+time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+#import the solid flag data
+#solid_np = init_geo('./BC.dat')
+solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+
+# do the initialization
+static_init()
+init()
+
+# do the actual simulation
+for iter in range(50000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    # calculate every 1000 time step
+    if (iter%1000==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        #calculate the time difference between now and previous time step
+        diff_time = int(time_now-time_pre)
+        #calculate the time difference between now and the initial time
+        elap_time = int(time_now-time_init)
+        #divmod function return the quotient and the remainder
+        #so that h_diff,m_diff and s_diff represent the hour, minute and second. the same as the h_elap,m_elap and s_elap
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        #export every 1000 timestep to vtk with x,y,z coordinate and solid,density and velocity variable
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[:,:,:,0]), np.ascontiguousarray(v.to_numpy()[:,:,:,1]),np.ascontiguousarray(v.to_numpy()[:,:,:,2]))
+                            }
+            )
+# ti.sync()
+# ti.profiler.print_kernel_profiler_info()
+#print the profiler information of every kernel and task of taichi in this file
+ti.profiler.print_scoped_profiler_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/lbm_solver_3d_cavity.html b/docs/lbm_solver_3d_cavity.html new file mode 100644 index 0000000..7e051cd --- /dev/null +++ b/docs/lbm_solver_3d_cavity.html @@ -0,0 +1,156 @@ + + + + + + + lbm_solver_3d_cavity — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_cavity

+

This solver is almost similar to lbm_solver_3d expect several difference as follows: +.. number:: lbm_solver_3d_cavity

+
    +

  1. The Grid resolution in this solver is 50x50x50

    2. +

  2. The viscosity in this solver is 0.16667

    3. +

  3. The boundary condition in this solver is velocity solver on x-right as follows

    4. +
+

boundary condition of this solver

+
#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 2, 1.0, 0.0, 0.0, 0.1  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+
+

x-right is implementated with velocity boundary condition

+

4. The boundary condition implementation is different from lbm_solver_3d, in this solver, the density distribution +function is calculated based on velocity on the boundary.

+
if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    #F[0,j,k][s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])  #!!!!!!change velocity in feq into vector
+                    F[0,j,k][s]=feq(s,1.0,ti.Vector(bc_vel_x_left))
+
+
+
    +

  1. Finally, the definition of the varible is slightly different from lbm_solver_3d

    2. +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/lbm_solver_3d_sparse.html b/docs/lbm_solver_3d_sparse.html new file mode 100644 index 0000000..58c9363 --- /dev/null +++ b/docs/lbm_solver_3d_sparse.html @@ -0,0 +1,143 @@ + + + + + + + lbm_solver_3d_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_sparse

+

This solver is almost similar to lbm_solver_3d expect the sparse definition of some varible:

+
f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

It use a pointer and certain block to divide the region and then place different varible on the block which make the storage +sparse.

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/make.bat b/docs/make.bat new file mode 100644 index 0000000..32bb245 --- /dev/null +++ b/docs/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=. +set BUILDDIR=_build + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.https://www.sphinx-doc.org/ + exit /b 1 +) + +if "%1" == "" goto help + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/docs/modules.html b/docs/modules.html new file mode 100644 index 0000000..139c882 --- /dev/null +++ b/docs/modules.html @@ -0,0 +1,148 @@ + + + + + + + taichi_LBM3D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+ +
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/modules.rst b/docs/modules.rst new file mode 100644 index 0000000..b9bfd06 --- /dev/null +++ b/docs/modules.rst @@ -0,0 +1,10 @@ +taichi_LBM3D +============ + +.. toctree:: + :maxdepth: 4 + + Single_phase + Grey_Scale + 2phase + Phase_change diff --git a/docs/objects.inv b/docs/objects.inv new file mode 100644 index 0000000..8b79ea0 Binary files /dev/null and b/docs/objects.inv differ diff --git a/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.html b/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.html new file mode 100644 index 0000000..cae5168 --- /dev/null +++ b/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.html @@ -0,0 +1,699 @@ + + + + + + + LBM_3D_SinglePhase_Solute_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

LBM_3D_SinglePhase_Solute_Solver

+

This file is the solver for solute transportation

+

First import the certain package and define the class of LB3D_Solver_Single_Phase_Solute which inheritant from +LB3D_Solver_Single_Phase_Solute

+
from sympy import inverse_mellin_transform
+import taichi as ti
+import numpy as np
+from pyevtk.hl import gridToVTK
+import time
+
+#ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False)
+import LBM_3D_SinglePhase_Solver as lb3d
+
+@ti.data_oriented
+class LB3D_Solver_Single_Phase_Solute(lb3d.LB3D_Solver_Single_Phase):
+    def __init__(self, nx, ny, nz):
+        super(LB3D_Solver_Single_Phase_Solute, self).__init__(nx, ny, nz, sparse_storage = False)
+        #define solute boundary condition
+        self.solute_bc_x_left, self.solute_bcxl = 0, 0.0
+        self.solute_bc_x_right, self.solute_bcxr = 0, 0.0
+        self.solute_bc_y_left, self.solute_bcyl = 0, 0.0
+        self.solute_bc_y_right, self.solute_bcyr = 0, 0.0
+        self.solute_bc_z_left, self.solute_bczl = 0, 0.0
+        self.solute_bc_z_right, self.solute_bczr = 0, 0.0
+
+        #define parameters for bouyancy force
+        self.buoyancy_parameter = 20.0   #Buoyancy Parameter (0= no buoyancy)
+        self.ref_T = 20.0              #reference_psi F=/rho*g+Bouyancy*(/psi-reference_psi)*g)
+        #define gravity
+        self.gravity = 5e-7
+
+        #define concentration distribution function
+        self.fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define another concentration distribution function
+        self.Fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz))
+        #define external force
+        self.forcexyz = ti.Vector.field(3,ti.f32,shape=(nx,ny,nz))
+        #define entropy
+        self.rho_H = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define temperature
+        self.rho_T = ti.field(ti.f32, shape=(nx,ny,nz))
+        #define liquid volumn fraction
+        self.rho_fl = ti.field(ti.f32, shape=(nx,ny,nz))
+
+        #define specific heat of liquid
+        self.Cp_l= 1.0
+        #define specific heat of solid
+        self.Cp_s = 1.0
+        #define latent heat
+        self.Lt = 1.0
+        #define solid temperature
+        self.T_s = -10.0
+        #define liquid temperature
+        self.T_l = -10.0
+        #define viscosity of solid
+        self.niu_s = 0.002
+        #define viscosity of liquid
+        self.niu_l = 0.002
+
+        #define energy of solid
+        self.H_s = None
+        #define energy of liquid
+        self.H_l = None
+
+        #define rock thermal diffusivity
+        self.niu_solid = 0.001
+        #define specific heat of rock
+        self.Cp_solid = 1.0
+
+
+

An then it sets these parameters with functions

+
#set gravity
+def set_gravity(self, gravity):
+self.gravity = gravity
+#set buoyancy force parameter
+def set_buoyancy_parameter(self, buoyancy_param):
+    self.buoyancy_parameter = buoyancy_param
+#set reference temperature
+def set_ref_T(self, ref_t):
+    self.ref_T = ref_t
+#set specific heat of solid
+def set_specific_heat_solid(self, cps):
+    self.Cp_s = cps
+#set specfic heat of liquid
+def set_specific_heat_liquid(self, cpl):
+    self.Cp_l = cpl
+#set specfic heat of rock
+def set_specific_heat_rock(self, cprock):
+    self.Cp_solid = cprock
+#set latent heat
+def set_latent_heat(self, ltheat):
+    self.Lt = ltheat
+#set solidus temperature
+def set_solidus_temperature(self, ts):
+    self.T_s = ts
+#set liquidus temperature
+def set_liquidus_temperature(self, tl):
+    self.T_l = tl
+#set solid thermal diffusivity
+def set_solid_thermal_diffusivity(self, nius):
+    self.niu_s = nius
+#set liquid thermal diffusivity
+def set_liquid_thermal_diffusivity(self, niul):
+    self.niu_l = niul
+#set rock thermal diffusivity
+def set_rock_thermal_diffusivity(self, niurock):
+    self.niu_solid = niurock
+#set adiabatic boundary on x-left
+def set_bc_adiabatic_x_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_x_left = 2
+#set adiabatic boundary on x-right
+def set_bc_adiabatic_x_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_x_right = 2
+#set adiabatic boundary on y-left
+def set_bc_adiabatic_y_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_y_left = 2
+#set adiabatic boundary on y-right
+def set_bc_adiabatic_y_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_y_right = 2
+#set adiabatic boundary on z-left
+def set_bc_adiabatic_z_left(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_z_left = 2
+#set adiabatic boundary on z-right
+def set_bc_adiabatic_z_right(self, bc_ad):
+    if (bc_ad==True):
+        self.solute_bc_z_right = 2
+#set constant temperature on x-left
+def set_bc_constant_temperature_x_left(self,xl):
+    self.solute_bc_x_left = 1
+    self.solute_bcxl = xl
+#set constant temperature on x-right
+def set_bc_constant_temperature_x_right(self,xr):
+    self.solute_bc_x_right = 1
+    self.solute_bcxr = xr
+#set constant temperature on y-left
+def set_bc_constant_temperature_y_left(self,yl):
+    self.solute_bc_y_left = 1
+    self.solute_bcyl = yl
+#set constant temperature on y-right
+def set_bc_constant_temperature_y_right(self,yr):
+    self.solute_bc_y_right = 1
+    self.solute_bcyr = yr
+#set constant temperature on z-left
+def set_bc_constant_temperature_z_left(self,zl):
+    self.solute_bc_z_left = 1
+    self.solute_bczl = zl
+#set constant temperature on z-right
+def set_bc_constant_temperature_z_right(self,zr):
+    self.solute_bc_y_right = 1
+    self.solute_bczr = zr
+
+# update energy of solid and liquid
+def update_H_sl(self):
+    #energy of solid
+    self.H_s = self.Cp_s*self.T_s
+    #energy of liquid
+    self.H_l = self.H_s+self.Lt
+    print('H_s',self.H_s)
+    print('H_l',self.H_l)
+
+
+

Then it initialize some variable or function

+
#intialize the energy
+@ti.kernel
+def init_H(self):
+    for I in ti.grouped(self.rho_T):
+        #calculate the energy, convert_T_H() define later
+        self.rho_H[I] = self.convert_T_H(self.rho_T[I])
+
+#intialize the density distribiution function for solute concentration
+@ti.kernel
+def init_fg(self):
+    for I in ti.grouped(self.fg):
+        #calculate the overall specific heat
+        Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s
+        #intialize the density distribiution function for solute concentration equals equilibrium density distribiution function for solute concentration
+        for s in ti.static(range(19)):
+            self.fg[I][s] = self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])
+            self.Fg[I][s] = self.fg[I][s]
+
+#intialize the volumn fraction of liquid
+@ti.kernel
+def init_fl(self):
+    for I in ti.grouped(self.rho_T):
+        #convert_T_fl define later
+        self.rho_fl[I] = self.convert_T_fl(self.rho_T[I])
+
+
+

g_feq(self, k,local_T,local_H, Cp, u) calculate the equilibrium density distribiution function for thermal energy

+
@ti.func
+def g_feq(self, k,local_T,local_H, Cp, u):
+    eu = self.e[k].dot(u)
+    uv = u.dot(u)
+    feqout = 0.0
+    #calculating the zero-velocity equilibrium thermal distribution function
+    if (k==0):
+        feqout = local_H-Cp*local_T+self.w[k]*Cp*local_T*(1-1.5*uv)
+    else:
+    #calculating other directions equilibrium thermal distribution function
+        feqout = self.w[k]*Cp*local_T*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, self.w[k], feqout, Cp, local_T)
+    return feqout
+
+
+

cal_local_force(i, j, k) calculates buoyancy force

+
#density is the function of temperture delat(rho)=-rho*beta*delta(T)
+@ti.func
+def cal_local_force(self, i, j, k):
+    f = ti.Vector([self.fx, self.fy, self.fz])
+    f[1] += self.gravity*self.buoyancy_parameter*(self.rho_T[i,j,k]-self.ref_T)
+    #f= delta(rho)*delta(v)*g
+    f *= self.rho_fl[i,j,k]
+    return f
+
+
+

collision_g() defines the the collision of thermal distribution function

+
@ti.kernel
+def colission_g(self):
+    for I in ti.grouped(self.rho_T):
+        #overall relaxation time
+        tau_s = 3*(self.niu_s*(1.0-self.rho_fl[I])+self.niu_l*self.rho_fl[I])+0.5
+        #overall specific heat
+        Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s
+
+        #ROCK overall relaxation time and specific heat
+        if (self.solid[I] >0):
+            tau_s = 3.0*self.niu_solid+0.5
+            Cp = self.Cp_solid
+
+        #f=f-1/tau*(f-feq)
+        for s in ti.static(range(19)):
+            tmp_fg = -1.0/tau_s*(self.fg[I][s]-self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]))
+            #print(self.fg[I][s],tmp_fg,I,s,self.rho_H[I],self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]))
+            self.fg[I][s] += tmp_fg
+
+
+

collision() defines the the collision of density distribution function

+
@ti.kernel
+def colission(self):
+    for i,j,k in self.rho:
+        #if (self.solid[i,j,k] == 0):
+        m_temp = self.M[None]@self.F[i,j,k]
+        meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k])
+        m_temp -= self.S_dig[None]*(m_temp-meq)
+        f = self.cal_local_force(i,j,k)
+        if (ti.static(self.force_flag==1)):
+            for s in ti.static(range(19)):
+            #    m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s])
+                #f = self.cal_local_force()
+                f_guo=0.0
+                for l in ti.static(range(19)):
+                    f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l]
+                #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force)
+                m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo
+
+        self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+        #calculate the denisty distribution function in momentum space here
+        self.f[i,j,k] += self.inv_M[None]@m_temp
+        #calculate the fluid density distribution function here
+        for s in ti.static(range(19)):
+            self.f[i,j,k][s] = self.f[i,j,k][s]*(self.rho_fl[i,j,k]) + self.w[s]*(1.0-self.rho_fl[i,j,k])
+
+
+

streaming1() and streaming1_g() defines the fluid denisty distribiution function and +thermal density distribiution function

+
@ti.kernel
+def streaming1(self):
+    for i in ti.grouped(self.rho):
+        #if (self.solid[i] == 0):
+        for s in ti.static(range(19)):
+            ip = self.periodic_index(i+self.e[s])
+            self.F[ip][s] = self.f[i][s]
+
+@ti.kernel
+def streaming1_g(self):
+    for i in ti.grouped(self.rho_T):
+        for s in ti.static(range(19)):
+            ip = self.periodic_index(i+self.e[s])
+            self.Fg[ip][s] = self.fg[i][s]
+
+
+

this

+
@ti.kernel
+def BC_concentration(self):
+    #constant temperature boundary condition
+    if ti.static(self.solute_bc_x_left==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            local_T = self.solute_bcxl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[0,j,k]*self.Cp_l + (1-self.rho_fl[0,j,k])*self.Cp_s
+            #the boundary's thermal distribution function equals the equilibrium thermal distribution function on the boundary
+            for s in ti.static(range(19)):
+                self.fg[0,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[0,j,k])
+                self.Fg[0,j,k][s] = self.fg[0,j,k][s]
+    #adiabatic boundary condition
+    elif ti.static(self.solute_bc_x_left==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            for s in ti.static(range(19)):
+            #there is no thermal transfer between the boundaty and neighbouring cell
+                self.fg[0,j,k][s] = self.fg[1,j,k][s]
+                self.Fg[0,j,k][s] = self.fg[1,j,k][s]
+
+    #x-right
+    if ti.static(self.solute_bc_x_right==1):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            local_T = self.solute_bcxr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[self.nx-1,j,k]*self.Cp_l + (1-self.rho_fl[self.nx-1,j,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[self.nx-1,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[self.nx-1,j,k])
+                self.Fg[self.nx-1,j,k][s]= self.fg[self.nx-1,j,k][s]
+    elif ti.static(self.solute_bc_x_right==2):
+        for j,k in ti.ndrange((0,self.ny),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s]
+                self.Fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s]
+
+    #y-left
+    if ti.static(self.solute_bc_y_left==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            local_T = self.solute_bcyl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,0,k]*self.Cp_l + (1-self.rho_fl[i,0,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,0,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,0,k])
+                self.Fg[i,0,k][s] = self.fg[i,0,k][s]
+    elif ti.static(self.solute_bc_y_left==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[i,0,k][s] = self.fg[i,1,k][s]
+                self.Fg[i,0,k][s] = self.fg[i,1,k][s]
+
+    #y-right
+    if ti.static(self.solute_bc_y_right==1):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            local_T = self.solute_bcyr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,self.ny-1,k]*self.Cp_l + (1-self.rho_fl[i,self.ny-1,k])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,self.ny-1,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,self.ny-1,k])
+                self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-1,k][s]
+    elif ti.static(self.solute_bc_y_right==2):
+        for i,k in ti.ndrange((0,self.nx),(0,self.nz)):
+            for s in ti.static(range(19)):
+                self.fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s]
+                self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s]
+
+    #z-left
+    if ti.static(self.solute_bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            local_T = self.solute_bczl
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,j,0]*self.Cp_l + (1-self.rho_fl[i,j,0])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,j,0][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,0])
+                self.Fg[i,j,0][s] = self.fg[i,j,0][s]
+    elif ti.static(self.solute_bc_z_left==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            for s in ti.static(range(19)):
+                self.fg[i,j,0][s] = self.fg[i,j,1][s]
+                self.Fg[i,j,0][s] = self.fg[i,j,1][s]
+
+    #z-right
+    if ti.static(self.solute_bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            local_T = self.solute_bczr
+            local_H = self.convert_T_H(local_T)
+            Cp = self.rho_fl[i,j,self.nz-1]*self.Cp_l + (1-self.rho_fl[i,j,self.nz-1])*self.Cp_s
+
+            for s in ti.static(range(19)):
+                self.fg[i,j,self.nz-1][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,self.nz-1])
+                self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-1][s]
+    elif ti.static(self.solute_bc_z_right==1):
+        for i,j in ti.ndrange((0,self.nx),(0,self.ny)):
+            for s in ti.static(range(19)):
+                self.fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s]
+                self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s]
+
+
+

convert_H_T() calculate the temperature

+
@ti.func
+def convert_H_T(self,local_H):
+    new_T=0.0
+    #if local enthalpy is less than solid enthalpy
+    #T= enthalpy/specific heat
+    if (local_H<self.H_s):
+        new_T = local_H/self.Cp_s
+    #if if local enthalpy is greater than liquid enthalpy
+    #T= Tliquid+(enthalpy-liquid enthalpy)/speific heat of liquid
+    elif (local_H>self.H_l):
+        new_T = self.T_l+(local_H-self.H_l)/self.Cp_l
+    #if if temperature is greater than solid temperature
+    #T= Tsolid+(enthalpy-solid enthalpy)/(enthalpy of liquid-enthalpy of solid)*(temperature of liquid- temperature of solid)
+    elif (self.T_l>self.T_s):
+        new_T = self.T_s+(local_H-self.H_s)/(self.H_l-self.H_s)*(self.T_l-self.T_s)
+    else:
+    #else T= temperature of solid
+        new_T = self.T_s
+
+    return new_T
+
+
+

convert_H_fl() calculate the volumn fraction of liquid

+
@ti.func
+def convert_H_fl(self,local_H):
+    new_fl=0.0
+    #if enthalpy is less than solid enthalpy
+    #it is zero
+    if (local_H<self.H_s):
+        new_fl = 0.0
+    #if it is greater than liquid enthalpy
+    #it is one
+    elif (local_H>self.H_l):
+        new_fl = 1.0
+    #else
+    #it equals to (enthaply- soid enthaply)/(enthaply of liquid- enthalpy of solid)
+    else:
+        new_fl = (local_H-self.H_s)/(self.H_l-self.H_s)
+
+    return new_fl
+
+
+

convert_T_H() calculate the enthaply from temperature

+
@ti.func
+def convert_T_H(self,local_T):
+    new_H = 0.0
+    # calculate enthaply for three different conditions
+    if (local_T<=self.T_s):
+        new_H = self.Cp_s*local_T
+    elif (local_T>self.T_l):
+        new_H = (local_T-self.T_l)*self.Cp_l+self.H_l
+    else:
+        fluid_frc = (local_T-self.T_s)/(self.T_l-self.T_s)
+        new_H = self.H_s*(1-fluid_frc) + self.H_l*fluid_frc
+    return new_H
+
+
+

convert_T_fl() calculate volumn fraction from temperature

+
@ti.func
+def convert_T_fl(self,local_T):
+    new_fl = 0.0
+    # calculate volumn fraction for three different conditions
+    if (local_T<=self.T_s):
+        new_fl = 0.0
+    elif (local_T>=self.T_l):
+        new_fl = 1.0
+    elif (self.T_l>self.T_s):
+        new_fl = (local_T-self.T_s)/(self.T_l-self.T_s)
+    else:
+        new_fl = 1.0
+
+    return new_fl
+
+
+

streaming3() calculate macroscopic variable

+
@ti.kernel
+def streaming3(self):
+    for i in ti.grouped(self.rho):
+        self.forcexyz[i] = self.cal_local_force(i.x, i.y, i.z)
+        #print(i.x, i.y, i.z)
+        if ((self.solid[i]==0) or (self.rho_fl[i]>0.0)):
+            self.rho[i] = 0
+            self.v[i] = ti.Vector([0,0,0])
+            self.f[i] = self.F[i]
+            for s in ti.static(range(19)):
+                self.f[i][s] = self.f[i][s]*self.rho_fl[i]+self.w[s]*(1.0-self.rho_fl[i])
+            #density for fluid
+            self.rho[i] += self.f[i].sum()
+
+            for s in ti.static(range(19)):
+                self.v[i] += self.e_f[s]*self.f[i][s]
+
+            f = self.cal_local_force(i.x, i.y, i.z)
+            #velocity for fluid
+            self.v[i] /= self.rho[i]
+            self.v[i] += (f/2)/self.rho[i]
+
+        else:
+        #density and velocity for solid
+            self.rho[i] = 1.0
+            self.v[i] = ti.Vector([0,0,0])
+
+
+

streaming3() calculate enthalpy

+
@ti.kernel
+def streaming3_g(self):
+    for i in ti.grouped(self.rho_T):
+        self.rho_H[i] = 0.0
+        #enthalpy here
+        self.rho_H[i] = self.Fg[i].sum()
+        #for s in ti.static(range(19)):
+        #    self.rho_H[i] += self.Fg[i][s]
+        self.fg[i] = self.Fg[i]
+
+
+

update_T_fl() calculate volumn fraction and temperature

+
@ti.kernel
+def update_T_fl(self):
+    for I in ti.grouped(self.rho_T):
+        self.rho_T[I] = self.convert_H_T(self.rho_H[I])
+        self.rho_fl[I] = self.convert_H_fl(self.rho_H[I])
+        if (self.solid[I]>0):
+            self.rho_fl[I] = 0.0
+
+
+

init_solute_simulation() initialize the solute simulation

+
def init_solute_simulation(self):
+
+    self.init_simulation()
+    self.update_H_sl()
+    #ethalpy
+    self.init_H()
+    #volumn fraction
+    self.init_fl()
+    #thermal distribution function
+    self.init_fg()
+
+
+

init_concentration(filename) import concentration data from file

+
def init_concentration(self,filename):
+    in_dat = np.loadtxt(filename)
+    in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F')
+    self.rho_T.from_numpy(in_dat)
+
+
+

this

+
def step(self):
+    self.colission()
+    self.colission_g()
+
+    self.streaming1()
+    self.streaming1_g()
+
+    self.Boundary_condition()
+    self.BC_concentration()
+
+    self.streaming3_g()
+    self.streaming3()
+    self.streaming3_g()
+
+    self.update_T_fl()
+
+
+

this

+
def export_VTK(self, n):
+    gridToVTK(
+            "./LB_SingelPhase_"+str(n),
+            self.x,
+            self.y,
+            self.z,
+            #cellData={"pressure": pressure},
+            pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()),
+                        "rho": np.ascontiguousarray(self.rho.to_numpy()),
+                        "Solid_Liquid": np.ascontiguousarray(self.rho_fl.to_numpy()),
+                        "Tempreture": np.ascontiguousarray(self.rho_T.to_numpy()),
+                        "Entropy": np.ascontiguousarray(self.rho_H.to_numpy()),
+                        "velocity": (   np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])),
+                        "Force": (      np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]),
+                                        np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]),
+                                        np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2]))
+                        }
+        )
+
+
+

this

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst b/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst new file mode 100644 index 0000000..04dbf54 --- /dev/null +++ b/docs/phasechange/LBM_3D_SinglePhase_Solute_Solver.rst @@ -0,0 +1,619 @@ +LBM_3D_SinglePhase_Solute_Solver +====================================== + +This file is the solver for solute transportation + +First import the certain package and define the class of ``LB3D_Solver_Single_Phase_Solute`` which inheritant from +``LB3D_Solver_Single_Phase_Solute`` + +.. code-block:: python + + from sympy import inverse_mellin_transform + import taichi as ti + import numpy as np + from pyevtk.hl import gridToVTK + import time + + #ti.init(arch=ti.cpu, dynamic_index=False, kernel_profiler=False, print_ir=False) + import LBM_3D_SinglePhase_Solver as lb3d + + @ti.data_oriented + class LB3D_Solver_Single_Phase_Solute(lb3d.LB3D_Solver_Single_Phase): + def __init__(self, nx, ny, nz): + super(LB3D_Solver_Single_Phase_Solute, self).__init__(nx, ny, nz, sparse_storage = False) + #define solute boundary condition + self.solute_bc_x_left, self.solute_bcxl = 0, 0.0 + self.solute_bc_x_right, self.solute_bcxr = 0, 0.0 + self.solute_bc_y_left, self.solute_bcyl = 0, 0.0 + self.solute_bc_y_right, self.solute_bcyr = 0, 0.0 + self.solute_bc_z_left, self.solute_bczl = 0, 0.0 + self.solute_bc_z_right, self.solute_bczr = 0, 0.0 + + #define parameters for bouyancy force + self.buoyancy_parameter = 20.0 #Buoyancy Parameter (0= no buoyancy) + self.ref_T = 20.0 #reference_psi F=/rho*g+Bouyancy*(/psi-reference_psi)*g) + #define gravity + self.gravity = 5e-7 + + #define concentration distribution function + self.fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define another concentration distribution function + self.Fg = ti.Vector.field(19,ti.f32,shape=(nx,ny,nz)) + #define external force + self.forcexyz = ti.Vector.field(3,ti.f32,shape=(nx,ny,nz)) + #define entropy + self.rho_H = ti.field(ti.f32, shape=(nx,ny,nz)) + #define temperature + self.rho_T = ti.field(ti.f32, shape=(nx,ny,nz)) + #define liquid volumn fraction + self.rho_fl = ti.field(ti.f32, shape=(nx,ny,nz)) + + #define specific heat of liquid + self.Cp_l= 1.0 + #define specific heat of solid + self.Cp_s = 1.0 + #define latent heat + self.Lt = 1.0 + #define solid temperature + self.T_s = -10.0 + #define liquid temperature + self.T_l = -10.0 + #define viscosity of solid + self.niu_s = 0.002 + #define viscosity of liquid + self.niu_l = 0.002 + + #define energy of solid + self.H_s = None + #define energy of liquid + self.H_l = None + + #define rock thermal diffusivity + self.niu_solid = 0.001 + #define specific heat of rock + self.Cp_solid = 1.0 + +An then it sets these parameters with functions + +.. code-block:: python + + #set gravity + def set_gravity(self, gravity): + self.gravity = gravity + #set buoyancy force parameter + def set_buoyancy_parameter(self, buoyancy_param): + self.buoyancy_parameter = buoyancy_param + #set reference temperature + def set_ref_T(self, ref_t): + self.ref_T = ref_t + #set specific heat of solid + def set_specific_heat_solid(self, cps): + self.Cp_s = cps + #set specfic heat of liquid + def set_specific_heat_liquid(self, cpl): + self.Cp_l = cpl + #set specfic heat of rock + def set_specific_heat_rock(self, cprock): + self.Cp_solid = cprock + #set latent heat + def set_latent_heat(self, ltheat): + self.Lt = ltheat + #set solidus temperature + def set_solidus_temperature(self, ts): + self.T_s = ts + #set liquidus temperature + def set_liquidus_temperature(self, tl): + self.T_l = tl + #set solid thermal diffusivity + def set_solid_thermal_diffusivity(self, nius): + self.niu_s = nius + #set liquid thermal diffusivity + def set_liquid_thermal_diffusivity(self, niul): + self.niu_l = niul + #set rock thermal diffusivity + def set_rock_thermal_diffusivity(self, niurock): + self.niu_solid = niurock + #set adiabatic boundary on x-left + def set_bc_adiabatic_x_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_left = 2 + #set adiabatic boundary on x-right + def set_bc_adiabatic_x_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_x_right = 2 + #set adiabatic boundary on y-left + def set_bc_adiabatic_y_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_left = 2 + #set adiabatic boundary on y-right + def set_bc_adiabatic_y_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_y_right = 2 + #set adiabatic boundary on z-left + def set_bc_adiabatic_z_left(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_left = 2 + #set adiabatic boundary on z-right + def set_bc_adiabatic_z_right(self, bc_ad): + if (bc_ad==True): + self.solute_bc_z_right = 2 + #set constant temperature on x-left + def set_bc_constant_temperature_x_left(self,xl): + self.solute_bc_x_left = 1 + self.solute_bcxl = xl + #set constant temperature on x-right + def set_bc_constant_temperature_x_right(self,xr): + self.solute_bc_x_right = 1 + self.solute_bcxr = xr + #set constant temperature on y-left + def set_bc_constant_temperature_y_left(self,yl): + self.solute_bc_y_left = 1 + self.solute_bcyl = yl + #set constant temperature on y-right + def set_bc_constant_temperature_y_right(self,yr): + self.solute_bc_y_right = 1 + self.solute_bcyr = yr + #set constant temperature on z-left + def set_bc_constant_temperature_z_left(self,zl): + self.solute_bc_z_left = 1 + self.solute_bczl = zl + #set constant temperature on z-right + def set_bc_constant_temperature_z_right(self,zr): + self.solute_bc_y_right = 1 + self.solute_bczr = zr + + # update energy of solid and liquid + def update_H_sl(self): + #energy of solid + self.H_s = self.Cp_s*self.T_s + #energy of liquid + self.H_l = self.H_s+self.Lt + print('H_s',self.H_s) + print('H_l',self.H_l) + +Then it initialize some variable or function + +.. code-block:: python + + #intialize the energy + @ti.kernel + def init_H(self): + for I in ti.grouped(self.rho_T): + #calculate the energy, convert_T_H() define later + self.rho_H[I] = self.convert_T_H(self.rho_T[I]) + + #intialize the density distribiution function for solute concentration + @ti.kernel + def init_fg(self): + for I in ti.grouped(self.fg): + #calculate the overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + #intialize the density distribiution function for solute concentration equals equilibrium density distribiution function for solute concentration + for s in ti.static(range(19)): + self.fg[I][s] = self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I]) + self.Fg[I][s] = self.fg[I][s] + + #intialize the volumn fraction of liquid + @ti.kernel + def init_fl(self): + for I in ti.grouped(self.rho_T): + #convert_T_fl define later + self.rho_fl[I] = self.convert_T_fl(self.rho_T[I]) + +``g_feq(self, k,local_T,local_H, Cp, u)`` calculate the equilibrium density distribiution function for thermal energy + +.. code-block:: python + + @ti.func + def g_feq(self, k,local_T,local_H, Cp, u): + eu = self.e[k].dot(u) + uv = u.dot(u) + feqout = 0.0 + #calculating the zero-velocity equilibrium thermal distribution function + if (k==0): + feqout = local_H-Cp*local_T+self.w[k]*Cp*local_T*(1-1.5*uv) + else: + #calculating other directions equilibrium thermal distribution function + feqout = self.w[k]*Cp*local_T*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, self.w[k], feqout, Cp, local_T) + return feqout + +``cal_local_force(i, j, k)`` calculates buoyancy force + +.. code-block:: python + + #density is the function of temperture delat(rho)=-rho*beta*delta(T) + @ti.func + def cal_local_force(self, i, j, k): + f = ti.Vector([self.fx, self.fy, self.fz]) + f[1] += self.gravity*self.buoyancy_parameter*(self.rho_T[i,j,k]-self.ref_T) + #f= delta(rho)*delta(v)*g + f *= self.rho_fl[i,j,k] + return f + +``collision_g()`` defines the the collision of thermal distribution function + +.. code-block:: python + + @ti.kernel + def colission_g(self): + for I in ti.grouped(self.rho_T): + #overall relaxation time + tau_s = 3*(self.niu_s*(1.0-self.rho_fl[I])+self.niu_l*self.rho_fl[I])+0.5 + #overall specific heat + Cp = self.rho_fl[I]*self.Cp_l + (1-self.rho_fl[I])*self.Cp_s + + #ROCK overall relaxation time and specific heat + if (self.solid[I] >0): + tau_s = 3.0*self.niu_solid+0.5 + Cp = self.Cp_solid + + #f=f-1/tau*(f-feq) + for s in ti.static(range(19)): + tmp_fg = -1.0/tau_s*(self.fg[I][s]-self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + #print(self.fg[I][s],tmp_fg,I,s,self.rho_H[I],self.g_feq(s,self.rho_T[I],self.rho_H[I], Cp, self.v[I])) + self.fg[I][s] += tmp_fg + +``collision()`` defines the the collision of density distribution function + +.. code-block:: python + + @ti.kernel + def colission(self): + for i,j,k in self.rho: + #if (self.solid[i,j,k] == 0): + m_temp = self.M[None]@self.F[i,j,k] + meq = self.meq_vec(self.rho[i,j,k],self.v[i,j,k]) + m_temp -= self.S_dig[None]*(m_temp-meq) + f = self.cal_local_force(i,j,k) + if (ti.static(self.force_flag==1)): + for s in ti.static(range(19)): + # m_temp[s] -= S_dig[s]*(m_temp[s]-meq[s]) + #f = self.cal_local_force() + f_guo=0.0 + for l in ti.static(range(19)): + f_guo += self.w[l]*((self.e_f[l]-self.v[i,j,k]).dot(f)+(self.e_f[l].dot(self.v[i,j,k])*(self.e_f[l].dot(f))))*self.M[None][s,l] + #m_temp[s] += (1-0.5*self.S_dig[None][s])*self.GuoF(i,j,k,s,self.v[i,j,k],force) + m_temp[s] += (1-0.5*self.S_dig[None][s])*f_guo + + self.f[i,j,k] = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + #calculate the denisty distribution function in momentum space here + self.f[i,j,k] += self.inv_M[None]@m_temp + #calculate the fluid density distribution function here + for s in ti.static(range(19)): + self.f[i,j,k][s] = self.f[i,j,k][s]*(self.rho_fl[i,j,k]) + self.w[s]*(1.0-self.rho_fl[i,j,k]) + +``streaming1()`` and ``streaming1_g()`` defines the fluid denisty distribiution function and +thermal density distribiution function + +.. code-block:: python + + @ti.kernel + def streaming1(self): + for i in ti.grouped(self.rho): + #if (self.solid[i] == 0): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.F[ip][s] = self.f[i][s] + + @ti.kernel + def streaming1_g(self): + for i in ti.grouped(self.rho_T): + for s in ti.static(range(19)): + ip = self.periodic_index(i+self.e[s]) + self.Fg[ip][s] = self.fg[i][s] + +this + +.. code-block:: python + + @ti.kernel + def BC_concentration(self): + #constant temperature boundary condition + if ti.static(self.solute_bc_x_left==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[0,j,k]*self.Cp_l + (1-self.rho_fl[0,j,k])*self.Cp_s + #the boundary's thermal distribution function equals the equilibrium thermal distribution function on the boundary + for s in ti.static(range(19)): + self.fg[0,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[0,j,k]) + self.Fg[0,j,k][s] = self.fg[0,j,k][s] + #adiabatic boundary condition + elif ti.static(self.solute_bc_x_left==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + #there is no thermal transfer between the boundaty and neighbouring cell + self.fg[0,j,k][s] = self.fg[1,j,k][s] + self.Fg[0,j,k][s] = self.fg[1,j,k][s] + + #x-right + if ti.static(self.solute_bc_x_right==1): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + local_T = self.solute_bcxr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[self.nx-1,j,k]*self.Cp_l + (1-self.rho_fl[self.nx-1,j,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[self.nx-1,j,k]) + self.Fg[self.nx-1,j,k][s]= self.fg[self.nx-1,j,k][s] + elif ti.static(self.solute_bc_x_right==2): + for j,k in ti.ndrange((0,self.ny),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + self.Fg[self.nx-1,j,k][s] = self.fg[self.nx-2,j,k][s] + + #y-left + if ti.static(self.solute_bc_y_left==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,0,k]*self.Cp_l + (1-self.rho_fl[i,0,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,0,k]) + self.Fg[i,0,k][s] = self.fg[i,0,k][s] + elif ti.static(self.solute_bc_y_left==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,0,k][s] = self.fg[i,1,k][s] + self.Fg[i,0,k][s] = self.fg[i,1,k][s] + + #y-right + if ti.static(self.solute_bc_y_right==1): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + local_T = self.solute_bcyr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,self.ny-1,k]*self.Cp_l + (1-self.rho_fl[i,self.ny-1,k])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,self.ny-1,k]) + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-1,k][s] + elif ti.static(self.solute_bc_y_right==2): + for i,k in ti.ndrange((0,self.nx),(0,self.nz)): + for s in ti.static(range(19)): + self.fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + self.Fg[i,self.ny-1,k][s] = self.fg[i,self.ny-2,k][s] + + #z-left + if ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczl + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,0]*self.Cp_l + (1-self.rho_fl[i,j,0])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,0]) + self.Fg[i,j,0][s] = self.fg[i,j,0][s] + elif ti.static(self.solute_bc_z_left==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,0][s] = self.fg[i,j,1][s] + self.Fg[i,j,0][s] = self.fg[i,j,1][s] + + #z-right + if ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + local_T = self.solute_bczr + local_H = self.convert_T_H(local_T) + Cp = self.rho_fl[i,j,self.nz-1]*self.Cp_l + (1-self.rho_fl[i,j,self.nz-1])*self.Cp_s + + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.g_feq(s,local_T, local_H, Cp, self.v[i,j,self.nz-1]) + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-1][s] + elif ti.static(self.solute_bc_z_right==1): + for i,j in ti.ndrange((0,self.nx),(0,self.ny)): + for s in ti.static(range(19)): + self.fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + self.Fg[i,j,self.nz-1][s] = self.fg[i,j,self.nz-2][s] + +``convert_H_T()`` calculate the temperature + +.. code-block:: python + + @ti.func + def convert_H_T(self,local_H): + new_T=0.0 + #if local enthalpy is less than solid enthalpy + #T= enthalpy/specific heat + if (local_Hself.H_l): + new_T = self.T_l+(local_H-self.H_l)/self.Cp_l + #if if temperature is greater than solid temperature + #T= Tsolid+(enthalpy-solid enthalpy)/(enthalpy of liquid-enthalpy of solid)*(temperature of liquid- temperature of solid) + elif (self.T_l>self.T_s): + new_T = self.T_s+(local_H-self.H_s)/(self.H_l-self.H_s)*(self.T_l-self.T_s) + else: + #else T= temperature of solid + new_T = self.T_s + + return new_T + +``convert_H_fl()`` calculate the volumn fraction of liquid + +.. code-block:: python + + @ti.func + def convert_H_fl(self,local_H): + new_fl=0.0 + #if enthalpy is less than solid enthalpy + #it is zero + if (local_Hself.H_l): + new_fl = 1.0 + #else + #it equals to (enthaply- soid enthaply)/(enthaply of liquid- enthalpy of solid) + else: + new_fl = (local_H-self.H_s)/(self.H_l-self.H_s) + + return new_fl + +``convert_T_H()`` calculate the enthaply from temperature + +.. code-block:: python + + @ti.func + def convert_T_H(self,local_T): + new_H = 0.0 + # calculate enthaply for three different conditions + if (local_T<=self.T_s): + new_H = self.Cp_s*local_T + elif (local_T>self.T_l): + new_H = (local_T-self.T_l)*self.Cp_l+self.H_l + else: + fluid_frc = (local_T-self.T_s)/(self.T_l-self.T_s) + new_H = self.H_s*(1-fluid_frc) + self.H_l*fluid_frc + return new_H + +``convert_T_fl()`` calculate volumn fraction from temperature + +.. code-block:: python + + @ti.func + def convert_T_fl(self,local_T): + new_fl = 0.0 + # calculate volumn fraction for three different conditions + if (local_T<=self.T_s): + new_fl = 0.0 + elif (local_T>=self.T_l): + new_fl = 1.0 + elif (self.T_l>self.T_s): + new_fl = (local_T-self.T_s)/(self.T_l-self.T_s) + else: + new_fl = 1.0 + + return new_fl + +``streaming3()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(self): + for i in ti.grouped(self.rho): + self.forcexyz[i] = self.cal_local_force(i.x, i.y, i.z) + #print(i.x, i.y, i.z) + if ((self.solid[i]==0) or (self.rho_fl[i]>0.0)): + self.rho[i] = 0 + self.v[i] = ti.Vector([0,0,0]) + self.f[i] = self.F[i] + for s in ti.static(range(19)): + self.f[i][s] = self.f[i][s]*self.rho_fl[i]+self.w[s]*(1.0-self.rho_fl[i]) + #density for fluid + self.rho[i] += self.f[i].sum() + + for s in ti.static(range(19)): + self.v[i] += self.e_f[s]*self.f[i][s] + + f = self.cal_local_force(i.x, i.y, i.z) + #velocity for fluid + self.v[i] /= self.rho[i] + self.v[i] += (f/2)/self.rho[i] + + else: + #density and velocity for solid + self.rho[i] = 1.0 + self.v[i] = ti.Vector([0,0,0]) + +``streaming3()`` calculate enthalpy + +.. code-block:: python + + @ti.kernel + def streaming3_g(self): + for i in ti.grouped(self.rho_T): + self.rho_H[i] = 0.0 + #enthalpy here + self.rho_H[i] = self.Fg[i].sum() + #for s in ti.static(range(19)): + # self.rho_H[i] += self.Fg[i][s] + self.fg[i] = self.Fg[i] + +``update_T_fl()`` calculate volumn fraction and temperature + +.. code-block:: python + + @ti.kernel + def update_T_fl(self): + for I in ti.grouped(self.rho_T): + self.rho_T[I] = self.convert_H_T(self.rho_H[I]) + self.rho_fl[I] = self.convert_H_fl(self.rho_H[I]) + if (self.solid[I]>0): + self.rho_fl[I] = 0.0 + +``init_solute_simulation()`` initialize the solute simulation + +.. code-block:: python + + def init_solute_simulation(self): + + self.init_simulation() + self.update_H_sl() + #ethalpy + self.init_H() + #volumn fraction + self.init_fl() + #thermal distribution function + self.init_fg() + +``init_concentration(filename)`` import concentration data from file + +.. code-block:: python + + def init_concentration(self,filename): + in_dat = np.loadtxt(filename) + in_dat = np.reshape(in_dat, (self.nx,self.ny,self.nz),order='F') + self.rho_T.from_numpy(in_dat) + +this + +.. code-block:: python + + def step(self): + self.colission() + self.colission_g() + + self.streaming1() + self.streaming1_g() + + self.Boundary_condition() + self.BC_concentration() + + self.streaming3_g() + self.streaming3() + self.streaming3_g() + + self.update_T_fl() + +this + +.. code-block:: python + + def export_VTK(self, n): + gridToVTK( + "./LB_SingelPhase_"+str(n), + self.x, + self.y, + self.z, + #cellData={"pressure": pressure}, + pointData={ "Solid": np.ascontiguousarray(self.solid.to_numpy()), + "rho": np.ascontiguousarray(self.rho.to_numpy()), + "Solid_Liquid": np.ascontiguousarray(self.rho_fl.to_numpy()), + "Tempreture": np.ascontiguousarray(self.rho_T.to_numpy()), + "Entropy": np.ascontiguousarray(self.rho_H.to_numpy()), + "velocity": ( np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.v.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])), + "Force": ( np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,0]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,1]), + np.ascontiguousarray(self.forcexyz.to_numpy()[0:self.nx,0:self.ny,0:self.nz,2])) + } + ) + +this \ No newline at end of file diff --git a/docs/phasechange/LBM_3D_SinglePhase_Solver.html b/docs/phasechange/LBM_3D_SinglePhase_Solver.html new file mode 100644 index 0000000..2ee3a59 --- /dev/null +++ b/docs/phasechange/LBM_3D_SinglePhase_Solver.html @@ -0,0 +1,125 @@ + + + + + + + LBM_3D_SinglePhase_Solver — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

LBM_3D_SinglePhase_Solver

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This file is the same as LBM_3D_SinglePhase_Solver in Single_phase folder

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/LBM_3D_SinglePhase_Solver.rst b/docs/phasechange/LBM_3D_SinglePhase_Solver.rst new file mode 100644 index 0000000..4a6528d --- /dev/null +++ b/docs/phasechange/LBM_3D_SinglePhase_Solver.rst @@ -0,0 +1,4 @@ +LBM_3D_SinglePhase_Solver +=========================== + +This file is the same as LBM_3D_SinglePhase_Solver in Single_phase folder \ No newline at end of file diff --git a/docs/phasechange/example_cavity_melting.html b/docs/phasechange/example_cavity_melting.html new file mode 100644 index 0000000..ae9d24d --- /dev/null +++ b/docs/phasechange/example_cavity_melting.html @@ -0,0 +1,124 @@ + + + + + + + example_cavity_melting — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

example_cavity_melting

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/example_cavity_melting.rst b/docs/phasechange/example_cavity_melting.rst new file mode 100644 index 0000000..eb279eb --- /dev/null +++ b/docs/phasechange/example_cavity_melting.rst @@ -0,0 +1,2 @@ +example_cavity_melting +============================= \ No newline at end of file diff --git a/docs/phasechange/example_phase_change.html b/docs/phasechange/example_phase_change.html new file mode 100644 index 0000000..90da0ca --- /dev/null +++ b/docs/phasechange/example_phase_change.html @@ -0,0 +1,124 @@ + + + + + + + example_phase_change — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

example_phase_change

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/example_phase_change.rst b/docs/phasechange/example_phase_change.rst new file mode 100644 index 0000000..7e2842c --- /dev/null +++ b/docs/phasechange/example_phase_change.rst @@ -0,0 +1,2 @@ +example_phase_change +==================== \ No newline at end of file diff --git a/docs/phasechange/read_img_solute_psi_generation_2D.html b/docs/phasechange/read_img_solute_psi_generation_2D.html new file mode 100644 index 0000000..1bf9ec6 --- /dev/null +++ b/docs/phasechange/read_img_solute_psi_generation_2D.html @@ -0,0 +1,124 @@ + + + + + + + read_img_solute_psi_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

read_img_solute_psi_generation_2D

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/read_img_solute_psi_generation_2D.rst b/docs/phasechange/read_img_solute_psi_generation_2D.rst new file mode 100644 index 0000000..6ab6dde --- /dev/null +++ b/docs/phasechange/read_img_solute_psi_generation_2D.rst @@ -0,0 +1,2 @@ +read_img_solute_psi_generation_2D +================================== \ No newline at end of file diff --git a/docs/phasechange/solute_psi_generation_2D.html b/docs/phasechange/solute_psi_generation_2D.html new file mode 100644 index 0000000..7f736fb --- /dev/null +++ b/docs/phasechange/solute_psi_generation_2D.html @@ -0,0 +1,124 @@ + + + + + + + solute_psi_generation_2D — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
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+

solute_psi_generation_2D

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/solute_psi_generation_2D.rst b/docs/phasechange/solute_psi_generation_2D.rst new file mode 100644 index 0000000..c8c1119 --- /dev/null +++ b/docs/phasechange/solute_psi_generation_2D.rst @@ -0,0 +1,2 @@ +solute_psi_generation_2D +============================ \ No newline at end of file diff --git a/docs/phasechange/test1.html b/docs/phasechange/test1.html new file mode 100644 index 0000000..9141c6e --- /dev/null +++ b/docs/phasechange/test1.html @@ -0,0 +1,122 @@ + + + + + + + test1 — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + +
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+

test1

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+ + + + \ No newline at end of file diff --git a/docs/phasechange/test1.rst b/docs/phasechange/test1.rst new file mode 100644 index 0000000..0b1d2a0 --- /dev/null +++ b/docs/phasechange/test1.rst @@ -0,0 +1,2 @@ +test1 +=================== \ No newline at end of file diff --git a/docs/search.html b/docs/search.html new file mode 100644 index 0000000..1eb12ca --- /dev/null +++ b/docs/search.html @@ -0,0 +1,118 @@ + + + + + + Search — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + + +
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16, "solute_bc_x_left": 16, "solute_bcxl": 16, "solute_bc_x_right": 16, "solute_bcxr": 16, "solute_bc_y_left": 16, "solute_bcyl": 16, "solute_bc_y_right": 16, "solute_bcyr": 16, "solute_bc_z_left": 16, "solute_bczl": 16, "solute_bc_z_right": 16, "solute_bczr": 16, "bouyanc": 16, "buoyancy_paramet": 16, "20": 16, "buoyanc": 16, "ref_t": 16, "reference_psi": 16, "g": 16, "graviti": 16, "5e": 16, "concentr": 16, "fg": 16, "forcexyz": 16, "entropi": 16, "rho_h": 16, "temperatur": 16, "rho_t": 16, "volumn": 16, "fraction": 16, "rho_fl": 16, "cp_l": 16, "cp_": 16, "lt": 16, "t_": 16, "t_l": 16, "niu_": 16, "002": 16, "h_": 16, "h_l": 16, "niu_solid": 16, "001": 16, "cp_solid": 16, "specif": 16, "heat": 16, "latent": 16, "energi": 16, "rock": 16, "thermal": 16, "diffus": 16, "set_grav": 16, "set_buoyancy_paramet": 16, "buoyancy_param": 16, "refer": 16, "set_ref_t": 16, "set_specific_heat_solid": 16, "cp": 16, "specfic": 16, "set_specific_heat_liquid": 16, "cpl": 16, "set_specific_heat_rock": 16, "cprock": 16, "set_latent_heat": 16, "ltheat": 16, "solidu": 16, "set_solidus_temperatur": 16, "liquidu": 16, "set_liquidus_temperatur": 16, "tl": 16, "set_solid_thermal_diffus": 16, "set_liquid_thermal_diffus": 16, "niul": 16, "set_rock_thermal_diffus": 16, "niurock": 16, "adiabat": 16, "set_bc_adiabatic_x_left": 16, "bc_ad": 16, "set_bc_adiabatic_x_right": 16, "set_bc_adiabatic_y_left": 16, "set_bc_adiabatic_y_right": 16, "set_bc_adiabatic_z_left": 16, "set_bc_adiabatic_z_right": 16, "set_bc_constant_temperature_x_left": 16, "xl": 16, "set_bc_constant_temperature_x_right": 16, "xr": 16, "set_bc_constant_temperature_y_left": 16, "yl": 16, "set_bc_constant_temperature_y_right": 16, "yr": 16, "set_bc_constant_temperature_z_left": 16, "zl": 16, "set_bc_constant_temperature_z_right": 16, "zr": 16, "updat": 16, "update_h_sl": 16, "Then": 16, "init_h": 16, "convert_t_h": 16, "later": 16, "init_fg": 16, "g_feq": 16, "init_fl": 16, "convert_t_fl": 16, "distribiut": 16, "overal": 16, 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"indices-and-tables"]], "Grey_Scale": [[1, "grey-scale"]], "Single_phase": [[5, "single-phase"]], "Convert_stl_to_binary": [[6, "convert-stl-to-binary"]], "Single_phase.LBM_3D_SinglePhase_Solver": [[7, "single-phase-lbm-3d-singlephase-solver"]], "example_cavity": [[8, "example-cavity"]], "example_porous_medium": [[9, "example-porous-medium"]], "flow_domain_geo_generation_2D": [[10, "flow-domain-geo-generation-2d"]], "Single_phase.lbm_solver_3d": [[11, "single-phase-lbm-solver-3d"]], "lbm_solver_3d_sparse": [[13, "lbm-solver-3d-sparse"]], "flow_domain_geo_generation": [[2, "flow-domain-geo-generation"]], "lbm_solver_3d_cavity": [[12, "lbm-solver-3d-cavity"]], "lbm_solver_3d_Macro_Sukop": [[3, "lbm-solver-3d-macro-sukop"]], "2phase": [[0, "phase"]], "example_cavity_melting": [[18, "example-cavity-melting"]], "example_phase_change": [[19, "example-phase-change"]], "read_img_solute_psi_generation_2D": [[20, "read-img-solute-psi-generation-2d"]], "solute_psi_generation_2D": [[21, "solute-psi-generation-2d"]], "test1": [[22, "test1"]], "lbm_solver_3d_2phase": [[23, "lbm-solver-3d-2phase"]], "lbm_solver_3d_2phase_sparse": [[24, "lbm-solver-3d-2phase-sparse"]], "Phase_change": [[4, "phase-change"]], "LBM_3D_SinglePhase_Solver": [[17, "lbm-3d-singlephase-solver"]], "LBM_3D_SinglePhase_Solute_Solver": [[16, "lbm-3d-singlephase-solute-solver"]]}, "indexentries": {}}) \ No newline at end of file diff --git a/docs/twophase/lbm_solver_3d_2phase.html b/docs/twophase/lbm_solver_3d_2phase.html new file mode 100644 index 0000000..65b85a2 --- /dev/null +++ b/docs/twophase/lbm_solver_3d_2phase.html @@ -0,0 +1,813 @@ + + + + + + + lbm_solver_3d_2phase — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_2phase

+

This solver is the multiphase model based on color gradient model +Firstly, it defines some parameters

+
# NOTE: THIS CODE NEED taichi_glsl, so please use taichi version <=0.8.5
+#import taichi, numpy, pyevtk and time package
+import taichi as ti
+import numpy as np
+#import taichi_glsl as ts
+from pyevtk.hl import gridToVTK
+import time
+#from taichi_glsl import scalar
+
+#from taichi_glsl.scalar import isinf, isnan
+#from taichi_glsl.vector import vecFill
+#intialize taichi
+ti.init(arch=ti.cpu)
+#ti.init(arch=ti.gpu, dynamic_index=True,offline_cache=True)
+
+#enable projection
+enable_projection = True
+# 131*131*131
+nx,ny,nz = 131,131,131
+#nx,ny,nz = 131,131,131
+#external force in x,y,z direction
+fx,fy,fz = 5.0e-5,-2e-5,0.0
+#niu = 0.1
+#liquid viscosity
+niu_l = 0.1         #psi>0
+#gas viscosity
+niu_g = 0.1         #psi<0
+#psi in color gradient calculation
+psi_solid = 0.7
+#surface tension
+CapA = 0.005
+
+#Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz
+bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0  #Boundary x-axis left side
+bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 0, 0.995, 0.0, 0.0, 0.0  #Boundary x-axis right side
+bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis left side
+bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary y-axis right side
+bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis left side
+bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0  #Boundary z-axis right side
+
+bc_psi_x_left, psi_x_left = 1, -1.0          #   boundary condition for phase-field: 0 = periodic,
+bc_psi_x_right, psi_x_right = 0, 1.0        #   1 = constant value on the boundary, value = -1.0 phase1 or 1.0 = phase 2
+bc_psi_y_left, psi_y_left = 0, 1.0
+bc_psi_y_right, psi_y_right = 0, 1.0
+bc_psi_z_left, psi_z_left = 0, 1.0
+bc_psi_z_right, psi_z_right = 0, 1.0
+
+# Non Sparse memory allocation
+#density distribution function nx*ny*nz*19
+f = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#density distribution function nx*ny*nz*19
+F = ti.field(ti.f32,shape=(nx,ny,nz,19))
+#density nx*ny*nz
+rho = ti.field(ti.f32, shape=(nx,ny,nz))
+#velocity nx*ny*nz vector
+v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz))
+#psi nx*ny*nz
+psi = ti.field(ti.f32, shape=(nx,ny,nz))
+#density r nx*ny*nz
+rho_r = ti.field(ti.f32, shape=(nx,ny,nz))
+#density b nx*ny*nz
+rho_b = ti.field(ti.f32, shape=(nx,ny,nz))
+#density r nx*ny*nz
+rhor = ti.field(ti.f32, shape=(nx,ny,nz))
+#density b nx*ny*nz
+rhob = ti.field(ti.f32, shape=(nx,ny,nz))
+#lattice speed 19 dimensional vector
+e = ti.Vector.field(3,ti.i32, shape=(19))
+#S_dig = ti.field(ti.f32,shape=(19))
+#lattice speed 19 dimensional vector
+e_f = ti.Vector.field(3,ti.f32, shape=(19))
+#weight parameter 19 dimensional vector
+w = ti.field(ti.f32, shape=(19))
+#solid flag nx*ny*nz
+solid = ti.field(ti.i32,shape=(nx,ny,nz))
+#streaming vector 19 dimensional vector
+LR = ti.field(ti.i32,shape=(19))
+
+#external force 3 dimensional vector
+ext_f = ti.Vector.field(3,ti.f32,shape=())
+# x-left velocity 3 dimensional vector
+bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=())
+# x-right velocity 3 dimensional vector
+bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=())
+# y-left velocity 3 dimensional vector
+bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=())
+# y-right velocity 3 dimensional vector
+bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=())
+# z-left velocity 3 dimensional vector
+bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=())
+# z-right velocity 3 dimensional vector
+bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=())
+#transforming matrix 19*19
+M = ti.field(ti.f32, shape=(19,19))
+#inverse transforming matrix 19*19
+inv_M = ti.field(ti.f32, shape=(19,19))
+#parameters for calculating the parameter of s diagonal
+#=======================================#
+lg0, wl, wg = 0.0, 0.0, 0.0
+l1, l2, g1, g2 = 0.0, 0.0, 0.0, 0.0
+wl = 1.0/(niu_l/(1.0/3.0)+0.5)
+wg = 1.0/(niu_g/(1.0/3.0)+0.5)
+lg0 = 2*wl*wg/(wl+wg)
+l1=2*(wl-lg0)*10
+l2=-l1/0.2
+g1=2*(lg0-wg)*10
+g2=g1/0.2
+#=======================================#
+
+#transformation matrix
+M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
+[-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1],
+[1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1],
+[0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0],
+[0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1],
+[0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2],
+[0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0],
+[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0],
+[0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0],
+[0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1],
+[0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]])
+#inverde of transforming matrix
+inv_M_np = np.linalg.inv(M_np)
+#streaming array
+LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17])
+#M matrix from the numpy
+M.from_numpy(M_np)
+#inverse matrix from numpy
+inv_M.from_numpy(inv_M_np)
+
+#steaming array from numpy
+LR.from_numpy(LR_np)
+#external force with vector three dimensional
+ext_f[None] = ti.Vector([fx,fy,fz])
+#set transforming matrix, inverse matrix and streaming vector non-modified
+ti.static(inv_M)
+ti.static(M)
+ti.static(LR)
+
+#set x,y,z array with nx*ny*nz
+x = np.linspace(0, nx, nx)
+y = np.linspace(0, ny, ny)
+z = np.linspace(0, nz, nz)
+#set meshgrid and return three meshgrid matrix X,Y,Z with non-cartesian indexing
+X, Y, Z = np.meshgrid(x, y, z, indexing='ij')
+
+
+

feq(k,rho_local, u) calculate the equilibrium denisty distribution function

+
@ti.func
+def feq(k,rho_local, u):
+    # eu=ts.vector.dot(e[k],u)
+    # uv=ts.vector.dot(u,u)
+    eu = e[k].dot(u)
+    uv = u.dot(u)
+    #same as single phase equilibrium density distribution function
+    feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv)
+    #print(k, rho_local, w[k])
+    return feqout
+
+
+

init() intialize some variable

+
@ti.kernel
+def init():
+    for i,j,k in solid:
+        if (solid[i,j,k] == 0):
+        #if it is fluid intialize the density and velocity be one and zero
+            rho[i,j,k] = 1.0
+            v[i,j,k] = ti.Vector([0,0,0])
+            # set density r and density b based on psi
+            rho_r[i,j,k] = (psi[i,j,k]+1.0)/2.0
+            rho_b[i,j,k] = 1.0 - rho_r[i,j,k]
+            #set another density r and density b
+            rhor[i,j,k] = 0.0
+            rhob[i,j,k] = 0.0
+            #set density distribution equals to equilibrium density distribution function
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = feq(s,1.0,v[i,j,k])
+                F[i,j,k,s] = feq(s,1.0,v[i,j,k])
+
+
+

init_geo(filename, filename2) import the geometry data

+
def init_geo(filename, filename2):
+    #read the solid flag data and set it as an column major array
+    in_dat = np.loadtxt(filename)
+    in_dat[in_dat>0] = 1
+    in_dat = np.reshape(in_dat, (nx,ny,nz),order='F')
+
+    #read the phase data from file
+    phase_in_dat = np.loadtxt(filename2)
+    #set the array from the file with colum major
+    phase_in_dat = np.reshape(phase_in_dat, (nx,ny,nz), order='F')
+
+    return in_dat, phase_in_dat
+
+
+

static_init() initialize non-modified variable

+
@ti.kernel
+def static_init():
+    if ti.static(enable_projection): # No runtime overhead
+    #define lattice speed
+    e[0] = ti.Vector([0,0,0])
+    e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1])
+    e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0])
+    e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1])
+    e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1])
+    #define another lattice speed
+    e_f[0] = ti.Vector([0,0,0])
+    e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1])
+    e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0])
+    e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1])
+    e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1])
+    #define a weight parameter
+    w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0;
+    w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0;
+    w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0;
+    #define the boundary velocity
+    bc_vel_x_left = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl])
+    bc_vel_x_right = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr])
+    bc_vel_y_left = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl])
+    bc_vel_y_right = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr])
+    bc_vel_z_left = ti.Vector([vx_bczl, vy_bczl, vz_bczl])
+    bc_vel_z_right = ti.Vector([vx_bczr, vy_bczr, vz_bczr])
+
+
+

multiply_M() calculate the density distribution function in momentum space

+
@ti.func
+def multiply_M(i,j,k):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    for index in ti.static(range(19)):
+        for s in ti.static(range(19)):
+            #calculate here
+            out[index] += M[index,s]*F[i,j,k,s]
+            #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s])
+    return out
+
+
+

GuoF(i,j,k,s,u) calculate Guo’s force term

+
@ti.func
+def GuoF(i,j,k,s,u):
+    out=0.0
+    for l in ti.static(range(19)):
+        out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l]
+
+    return out
+
+
+

meq_vec(rho_local,u) defines the equilibrium momentum

+
@ti.func
+def meq_vec(rho_local,u):
+    out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    out[0] = rho_local;             out[3] = u[0];    out[5] = u[1];    out[7] = u[2];
+    out[1] = u.dot(u);    out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z;         out[11] = u.y*u.y-u.z*u.z
+    out[13] = u.x*u.y;    out[14] = u.y*u.z;                            out[15] = u.x*u.z
+    return out
+
+
+

Compute_C() calculate the color gradient

+
@ti.func
+def Compute_C(i):
+    C = ti.Vector([0.0,0.0,0.0])
+    ind_S = 0
+    for s in ti.static(range(19)):
+        ip = periodic_index_for_psi(i+e[s])
+        if (solid[ip] == 0):
+            #if it's fluid calculate the color gradient based on psi
+            C += 3.0*w[s]*e_f[s]*psi[ip]
+        else:
+            #if it is solid and abs(density r-density b) is less than 0.9
+            ind_S = 1
+            #calculate the color gradient based on psi_solid and set ind_s=1
+            C += 3.0*w[s]*e_f[s]*psi_solid
+
+    if (abs(rho_r[i]-rho_b[i]) > 0.9) and (ind_S == 1):
+        #if abs(density r-density b) is very large and it's solid set color gradient to be zero
+        C = ti.Vector([0.0,0.0,0.0])
+
+    return C
+
+
+

Compute_S_local calculate parameter of s diagonal

+
@ti.func
+def Compute_S_local(id):
+    sv=0.0; sother=0.0
+    if (psi[id]>0):
+        if (psi[id]>0.1):
+        #if psi>0.1
+        #sv=1.0/(niu_l/(1.0/3.0)+0.5)
+            sv=wl
+        else:
+        #if 0<psi<0.1   calculate sv
+            sv=lg0+l1*psi[id]+l2*psi[id]*psi[id]
+    else:
+        #if psi <-0.1
+        if (psi[id]<-0.1):
+        #calculate sv
+            sv=wg
+        else:
+        #if psi >-0.1
+            sv=lg0+g1*psi[id]+g2*psi[id]*psi[id]
+    #calculate s other
+    sother = 8.0*(2.0-sv)/(8.0-sv)
+
+    #set s diagonal to be zero and set certain element to be relatie local parameter
+    S = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+    S[1]=sv;S[2]=sv;S[4]=sother;S[6]=sother;S[8]=sother;S[9]=sv;
+    S[10]=sv;S[11]=sv;S[12]=sv;S[13]=sv;S[14]=sv;S[15]=sv;S[16]=sother;
+    S[17]=sother;S[18]=sother;
+
+
+    return S;
+
+
+

collision() define the collision and recoloring process

+
@ti.kernel
+def colission():
+    for i,j,k in rho:
+        #if it is inner fluid, calculate color gradient divided by norm of color gradient
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            uu = v[i,j,k].norm_sqr()
+            C = Compute_C(ti.Vector([i,j,k]))
+            cc = C.norm()
+            normal = ti.Vector([0.0,0.0,0.0])
+            if cc>0 :
+                normal = C/cc
+            #calculate the M
+            m_temp = multiply_M(i,j,k)
+            meq = meq_vec(rho[i,j,k],v[i,j,k])
+            #calculate surface tension term
+            meq[1] += CapA*cc
+            meq[9] += 0.5*CapA*cc*(2*normal.x*normal.x-normal.y*normal.y-normal.z*normal.z)
+            meq[11] += 0.5*CapA*cc*(normal.y*normal.y-normal.z*normal.z)
+            meq[13] += 0.5*CapA*cc*(normal.x*normal.y)
+            meq[14] += 0.5*CapA*cc*(normal.y*normal.z)
+            meq[15] += 0.5*CapA*cc*(normal.x*normal.z)
+            #calculate s local
+            S_local = Compute_S_local(ti.Vector([i,j,k]))
+            #calculate s*(m-meq)
+            for s in ti.static(range(19)):
+                m_temp[s] -= S_local[s]*(m_temp[s]-meq[s])
+                m_temp[s] += (1-0.5*S_local[s])*GuoF(i,j,k,s,v[i,j,k])
+            #calculte convection of density filed
+            g_r = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+            g_b = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])
+
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = 0
+                for l in ti.static(range(19)):
+                # 1.single phase collision
+                    f[i,j,k,s] += inv_M[s,l]*m_temp[l]
+
+                g_r[s] = feq(s,rho_r[i,j,k],v[i,j,k])
+                g_b[s] = feq(s,rho_b[i,j,k],v[i,j,k])
+
+            if (cc>0):
+                for kk in ti.static([1,3,5,7,9,11,13,15,17]):
+                    # ef=ts.vector.dot(e[kk],C)
+                    ef=e[kk].dot(C)
+                    cospsi= g_r[kk] if (g_r[kk]<g_r[kk+1]) else g_r[kk+1]
+                    cospsi= cospsi if (cospsi<g_b[kk]) else g_b[kk]
+                    cospsi=cospsi if (cospsi<g_b[kk+1]) else g_b[kk+1]
+                    cospsi*=ef/cc
+                    #2.surface tension perturbation
+                    g_r[kk]+=cospsi
+                    g_r[kk+1]-=cospsi
+                    g_b[kk]-=cospsi
+                    g_b[kk+1]+=cospsi
+            # recoloring
+            for s in ti.static(range(19)):
+                ip = periodic_index(ti.Vector([i,j,k])+e[s])
+                if (solid[ip]==0):
+                    rhor[ip] += g_r[s]
+                    rhob[ip] += g_b[s]
+                else:
+                    rhor[i,j,k] += g_r[s]
+                    rhob[i,j,k] += g_b[s]
+
+
+

periodic_index() defines the index of boundary if using periodic boundary condition

+
@ti.func
+def periodic_index(i):
+    iout = i
+    if i[0]<0:     iout[0] = nx-1
+    if i[0]>nx-1:  iout[0] = 0
+    if i[1]<0:     iout[1] = ny-1
+    if i[1]>ny-1:  iout[1] = 0
+    if i[2]<0:     iout[2] = nz-1
+    if i[2]>nz-1:  iout[2] = 0
+
+    return iout
+
+
+

periodic_index_for_psi(i) defines the index of boundary for psi if using periodic boundary condition

+
@ti.func
+def periodic_index_for_psi(i):
+    iout = i
+    if i[0]<0:
+    #if periodic boundary condition set index based on periodic boundary condition
+        if bc_psi_x_left == 0:
+            iout[0] = nx-1
+        else:
+    #otherwise set neighbouring index,
+    #similar for other sides
+            iout[0] = 0
+
+    if i[0]>nx-1:
+        if bc_psi_x_right==0:
+            iout[0] = 0
+        else:
+            iout[0] = nx-1
+
+    if i[1]<0:
+        if bc_psi_y_left == 0:
+            iout[1] = ny-1
+        else:
+            iout[1] = 0
+
+    if i[1]>ny-1:
+        if bc_psi_y_right==0:
+            iout[1] = 0
+        else:
+            iout[1] = ny-1
+
+    if i[2]<0:
+        if bc_psi_z_left==0:
+            iout[2] = nz-1
+        else:
+            iout[2] = 0
+
+    if i[2]>nz-1:
+        if bc_psi_z_right==0:
+            iout[2] = 0
+        else:
+            iout[2] = nz-1
+
+    return iout
+
+
+

streaming1() defines steaming process of denisty distribution function

+
@ti.kernel
+def streaming1():
+    for i,j,k in rho:
+        #if (solid[i,j,k] == 0):
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            ci = ti.Vector([i,j,k])
+            for s in ti.static(range(19)):
+                ip = periodic_index(ci+e[s])
+                if (solid[ip]==0):
+                #if it is fluid,streaming along certain direction
+                    F[ip,s] = f[ci,s]
+                else:
+                #if it is on the solid, bounce back to the opposite
+                    F[ci,LR[s]] = f[ci,s]
+                    #print(i, ip, "@@@")
+
+
+

Boundary_condition_psi() defines boundary condition for psi

+
@ti.kernel
+def Boundary_condition_psi():
+    if bc_psi_x_left == 1:
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+            #if it is fluid the value of psi equals to the psi_x_left
+                psi[0,j,k] = psi_x_left
+            #calculate density according to psi
+            #similar for other sides
+                rho_r[0,j,k] = (psi_x_left + 1.0)/2.0
+                rho_b[0,j,k] = 1.0 - rho_r[0,j,k]
+
+    if bc_psi_x_right == 1:
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                psi[nx-1,j,k] = psi_x_right
+                rho_r[nx-1,j,k] = (psi_x_right + 1.0)/2.0
+                rho_b[nx-1,j,k] = 1.0 - rho_r[nx-1,j,k]
+
+    if bc_psi_y_left == 1:
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                psi[i,0,k] = psi_y_left
+                rho_r[i,0,k] = (psi_y_left + 1.0)/2.0
+                rho_b[i,0,k] = 1.0 - rho_r[i,0,k]
+
+    if bc_psi_y_right == 1:
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                psi[i,ny-1,k] = psi_y_right
+                rho_r[i,ny-1,k] = (psi_y_right + 1.0)/2.0
+                rho_b[i,ny-1,k] = 1.0 - rho_r[i,ny-1,k]
+
+    if bc_psi_z_left == 1:
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                psi[i,j,0] = psi_z_left
+                rho_r[i,j,0] = (psi_z_left + 1.0)/2.0
+                rho_b[i,j,0] = 1.0 - rho_r[i,j,0]
+
+    if bc_psi_z_right == 1:
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                psi[i,j,nz-1] = psi_z_right
+                rho_r[i,j,nz-1] = (psi_z_right + 1.0)/2.0
+                rho_b[i,j,nz-1] = 1.0 - rho_r[i,j,nz-1]
+
+
+

Boundary_condition defines boundary condition and the same as single_phase solver

+
@ti.kernel
+def Boundary_condition():
+    if ti.static(bc_x_left==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[1,j,k]>0):
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k])
+                    else:
+                        F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k])
+
+    if ti.static(bc_x_left==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[0,j,k]==0):
+                for s in ti.static(range(19)):
+                    F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None])
+
+    if ti.static(bc_x_right==1):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[nx-2,j,k]>0):
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k])
+                    else:
+                        F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k])
+
+    if ti.static(bc_x_right==2):
+        for j,k in ti.ndrange((0,ny),(0,nz)):
+            if (solid[nx-1,j,k]==0):
+                for s in ti.static(range(19)):
+                    F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None])
+
+
+    # Direction Y
+    if ti.static(bc_y_left==1):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,1,k]>0):
+                        F[i,0,k,s]=feq(s, rho_bcyl, v[i,1,k])
+                    else:
+                        F[i,0,k,s]=feq(s, rho_bcyl, v[i,0,k])
+
+    if ti.static(bc_y_left==2):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,0,k]==0):
+                for s in ti.static(range(19)):
+                    F[i,0,k,s]=feq(LR[s], 1.0, bc_vel_y_left[None])-F[i,0,k,LR[s]]+feq(s,1.0,bc_vel_y_left[None])
+
+    if ti.static(bc_y_right==1):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,ny-2,k]>0):
+                        F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-2,k])
+                    else:
+                        F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-1,k])
+
+    if ti.static(bc_y_right==2):
+        for i,k in ti.ndrange((0,nx),(0,nz)):
+            if (solid[i,ny-1,k]==0):
+                for s in ti.static(range(19)):
+                    F[i,ny-1,k,s]=feq(LR[s], 1.0, bc_vel_y_right[None])-F[i,ny-1,k,LR[s]]+feq(s,1.0,bc_vel_y_right[None])
+
+    # Z direction
+    if ti.static(bc_z_left==1):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,j,1]>0):
+                        F[i,j,0,s]=feq(s, rho_bczl, v[i,j,1])
+                    else:
+                        F[i,j,0,s]=feq(s, rho_bczl, v[i,j,0])
+
+    if ti.static(bc_z_left==2):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,0]==0):
+                for s in ti.static(range(19)):
+                    F[i,j,0,s]=feq(LR[s], 1.0, bc_vel_z_left[None])-F[i,j,0,LR[s]]+feq(s,1.0,bc_vel_z_left[None])
+
+    if ti.static(bc_z_right==1):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                for s in ti.static(range(19)):
+                    if (solid[i,j,nz-2]>0):
+                        F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-2])
+                    else:
+                        F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-1])
+
+    if ti.static(bc_z_right==2):
+        for i,j in ti.ndrange((0,nx),(0,ny)):
+            if (solid[i,j,nz-1]==0):
+                for s in ti.static(range(19)):
+                    F[i,j,nz-1,s]=feq(LR[s], 1.0, bc_vel_z_right[None])-F[i,j,nz-1,LR[s]]+feq(s,1.0,bc_vel_z_right[None])
+
+
+

Boundary_condition_psi() calculate macroscopic variable

+
@ti.kernel
+def streaming3():
+    for i,j,k, in rho:
+        #if (solid[i,j,k] == 0):
+        if (i<nx and j<ny and k<nz and solid[i,j,k] == 0):
+            rho[i,j,k] = 0
+            v[i,j,k] = ti.Vector([0,0,0])
+            #define denisty r and density b
+            rho_r[i,j,k] = rhor[i,j,k]
+            rho_b[i,j,k] = rhob[i,j,k]
+            rhor[i,j,k] = 0.0; rhob[i,j,k] = 0.0
+
+            for s in ti.static(range(19)):
+                f[i,j,k,s] = F[i,j,k,s]
+                rho[i,j,k] += f[i,j,k,s]
+                v[i,j,k] += e_f[s]*f[i,j,k,s]
+            #calculate velocity and psi
+            v[i,j,k] /= rho[i,j,k]
+            v[i,j,k] += (ext_f[None]/2)/rho[i,j,k]
+            psi[i,j,k] = rho_r[i,j,k]-rho_b[i,j,k]/(rho_r[i,j,k] + rho_b[i,j,k])
+
+
+

The code snippts below define time, read file do the simulation and export results +It is almost the same as the single-phase solver except two input file and export phase variable

+
time_init = time.time()
+time_now = time.time()
+time_pre = time.time()
+dt_count = 0
+
+
+solid_np, phase_np = init_geo('./img_ftb131.txt','./phase_ftb131.dat')
+
+#solid_np = init_geo('./img_ftb131.txt')
+solid.from_numpy(solid_np)
+psi.from_numpy(phase_np)
+
+static_init()
+init()
+
+#print(wl,wg, lg0, l1, l2,'~@@@@@~@~@~@~@')
+
+for iter in range(80000+1):
+    colission()
+    streaming1()
+    Boundary_condition()
+    #streaming2()
+    streaming3()
+    Boundary_condition_psi()
+
+
+    if (iter%500==0):
+
+        time_pre = time_now
+        time_now = time.time()
+        diff_time = int(time_now-time_pre)
+        elap_time = int(time_now-time_init)
+        m_diff, s_diff = divmod(diff_time, 60)
+        h_diff, m_diff = divmod(m_diff, 60)
+        m_elap, s_elap = divmod(elap_time, 60)
+        h_elap, m_elap = divmod(m_elap, 60)
+
+        print('----------Time between two outputs is %dh %dm %ds; elapsed time is %dh %dm %ds----------------------' %(h_diff, m_diff, s_diff,h_elap,m_elap,s_elap))
+        print('The %dth iteration, Max Force = %f,  force_scale = %f\n\n ' %(iter, 10.0,  10.0))
+
+        if (iter%10000==0):
+            gridToVTK(
+                "./structured"+str(iter),
+                x,
+                y,
+                z,
+                #cellData={"pressure": pressure},
+                pointData={ "Solid": np.ascontiguousarray(solid.to_numpy()),
+                            "rho": np.ascontiguousarray(rho.to_numpy()[0:nx,0:ny,0:nz]),
+                            "phase": np.ascontiguousarray(psi.to_numpy()[0:nx,0:ny,0:nz]),
+                            "velocity": (np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,0]), np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,1]),np.ascontiguousarray(v.to_numpy()[0:nx,0:ny,0:nz,2]))
+                            }
+            )
+
+#ti.print_kernel_profile_info()
+#ti.print_profile_info()
+
+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/twophase/lbm_solver_3d_2phase.rst b/docs/twophase/lbm_solver_3d_2phase.rst new file mode 100644 index 0000000..1c42671 --- /dev/null +++ b/docs/twophase/lbm_solver_3d_2phase.rst @@ -0,0 +1,734 @@ +lbm_solver_3d_2phase +======================================== + +This solver is the multiphase model based on color gradient model +Firstly, it defines some parameters + +.. code-block:: python + + # NOTE: THIS CODE NEED taichi_glsl, so please use taichi version <=0.8.5 + #import taichi, numpy, pyevtk and time package + import taichi as ti + import numpy as np + #import taichi_glsl as ts + from pyevtk.hl import gridToVTK + import time + #from taichi_glsl import scalar + + #from taichi_glsl.scalar import isinf, isnan + #from taichi_glsl.vector import vecFill + #intialize taichi + ti.init(arch=ti.cpu) + #ti.init(arch=ti.gpu, dynamic_index=True,offline_cache=True) + + #enable projection + enable_projection = True + # 131*131*131 + nx,ny,nz = 131,131,131 + #nx,ny,nz = 131,131,131 + #external force in x,y,z direction + fx,fy,fz = 5.0e-5,-2e-5,0.0 + #niu = 0.1 + #liquid viscosity + niu_l = 0.1 #psi>0 + #gas viscosity + niu_g = 0.1 #psi<0 + #psi in color gradient calculation + psi_solid = 0.7 + #surface tension + CapA = 0.005 + + #Boundary condition mode: 0=periodic, 1= fix pressure, 2=fix velocity; boundary pressure value (rho); boundary velocity value for vx,vy,vz + bc_x_left, rho_bcxl, vx_bcxl, vy_bcxl, vz_bcxl = 0, 1.0, 0.0e-5, 0.0, 0.0 #Boundary x-axis left side + bc_x_right, rho_bcxr, vx_bcxr, vy_bcxr, vz_bcxr = 0, 0.995, 0.0, 0.0, 0.0 #Boundary x-axis right side + bc_y_left, rho_bcyl, vx_bcyl, vy_bcyl, vz_bcyl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis left side + bc_y_right, rho_bcyr, vx_bcyr, vy_bcyr, vz_bcyr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary y-axis right side + bc_z_left, rho_bczl, vx_bczl, vy_bczl, vz_bczl = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis left side + bc_z_right, rho_bczr, vx_bczr, vy_bczr, vz_bczr = 0, 1.0, 0.0, 0.0, 0.0 #Boundary z-axis right side + + bc_psi_x_left, psi_x_left = 1, -1.0 # boundary condition for phase-field: 0 = periodic, + bc_psi_x_right, psi_x_right = 0, 1.0 # 1 = constant value on the boundary, value = -1.0 phase1 or 1.0 = phase 2 + bc_psi_y_left, psi_y_left = 0, 1.0 + bc_psi_y_right, psi_y_right = 0, 1.0 + bc_psi_z_left, psi_z_left = 0, 1.0 + bc_psi_z_right, psi_z_right = 0, 1.0 + + # Non Sparse memory allocation + #density distribution function nx*ny*nz*19 + f = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density distribution function nx*ny*nz*19 + F = ti.field(ti.f32,shape=(nx,ny,nz,19)) + #density nx*ny*nz + rho = ti.field(ti.f32, shape=(nx,ny,nz)) + #velocity nx*ny*nz vector + v = ti.Vector.field(3,ti.f32, shape=(nx,ny,nz)) + #psi nx*ny*nz + psi = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rho_r = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rho_b = ti.field(ti.f32, shape=(nx,ny,nz)) + #density r nx*ny*nz + rhor = ti.field(ti.f32, shape=(nx,ny,nz)) + #density b nx*ny*nz + rhob = ti.field(ti.f32, shape=(nx,ny,nz)) + #lattice speed 19 dimensional vector + e = ti.Vector.field(3,ti.i32, shape=(19)) + #S_dig = ti.field(ti.f32,shape=(19)) + #lattice speed 19 dimensional vector + e_f = ti.Vector.field(3,ti.f32, shape=(19)) + #weight parameter 19 dimensional vector + w = ti.field(ti.f32, shape=(19)) + #solid flag nx*ny*nz + solid = ti.field(ti.i32,shape=(nx,ny,nz)) + #streaming vector 19 dimensional vector + LR = ti.field(ti.i32,shape=(19)) + + #external force 3 dimensional vector + ext_f = ti.Vector.field(3,ti.f32,shape=()) + # x-left velocity 3 dimensional vector + bc_vel_x_left = ti.Vector.field(3,ti.f32, shape=()) + # x-right velocity 3 dimensional vector + bc_vel_x_right = ti.Vector.field(3,ti.f32, shape=()) + # y-left velocity 3 dimensional vector + bc_vel_y_left = ti.Vector.field(3,ti.f32, shape=()) + # y-right velocity 3 dimensional vector + bc_vel_y_right = ti.Vector.field(3,ti.f32, shape=()) + # z-left velocity 3 dimensional vector + bc_vel_z_left = ti.Vector.field(3,ti.f32, shape=()) + # z-right velocity 3 dimensional vector + bc_vel_z_right = ti.Vector.field(3,ti.f32, shape=()) + #transforming matrix 19*19 + M = ti.field(ti.f32, shape=(19,19)) + #inverse transforming matrix 19*19 + inv_M = ti.field(ti.f32, shape=(19,19)) + #parameters for calculating the parameter of s diagonal + #=======================================# + lg0, wl, wg = 0.0, 0.0, 0.0 + l1, l2, g1, g2 = 0.0, 0.0, 0.0, 0.0 + wl = 1.0/(niu_l/(1.0/3.0)+0.5) + wg = 1.0/(niu_g/(1.0/3.0)+0.5) + lg0 = 2*wl*wg/(wl+wg) + l1=2*(wl-lg0)*10 + l2=-l1/0.2 + g1=2*(lg0-wg)*10 + g2=g1/0.2 + #=======================================# + + #transformation matrix + M_np = np.array([[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], + [-1,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1], + [1,-2,-2,-2,-2,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1], + [0,1,-1,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,-2,2,0,0,0,0,1,-1,1,-1,1,-1,1,-1,0,0,0,0], + [0,0,0,1,-1,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,-2,2,0,0,1,-1,-1,1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,1,-1,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,0,0,0,0,-2,2,0,0,0,0,1,-1,-1,1,1,-1,-1,1], + [0,2,2,-1,-1,-1,-1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,-2,-2,1,1,1,1,1,1,1,1,1,1,1,1,-2,-2,-2,-2], + [0,0,0,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,0,0], + [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0], + [0,0,0,0,0,0,0,1,-1,1,-1,-1,1,-1,1,0,0,0,0], + [0,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,1,-1,1,-1], + [0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,1,-1]]) + #inverde of transforming matrix + inv_M_np = np.linalg.inv(M_np) + #streaming array + LR_np = np.array([0,2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15,18,17]) + #M matrix from the numpy + M.from_numpy(M_np) + #inverse matrix from numpy + inv_M.from_numpy(inv_M_np) + + #steaming array from numpy + LR.from_numpy(LR_np) + #external force with vector three dimensional + ext_f[None] = ti.Vector([fx,fy,fz]) + #set transforming matrix, inverse matrix and streaming vector non-modified + ti.static(inv_M) + ti.static(M) + ti.static(LR) + + #set x,y,z array with nx*ny*nz + x = np.linspace(0, nx, nx) + y = np.linspace(0, ny, ny) + z = np.linspace(0, nz, nz) + #set meshgrid and return three meshgrid matrix X,Y,Z with non-cartesian indexing + X, Y, Z = np.meshgrid(x, y, z, indexing='ij') + +``feq(k,rho_local, u)`` calculate the equilibrium denisty distribution function + +.. code-block:: python + + @ti.func + def feq(k,rho_local, u): + # eu=ts.vector.dot(e[k],u) + # uv=ts.vector.dot(u,u) + eu = e[k].dot(u) + uv = u.dot(u) + #same as single phase equilibrium density distribution function + feqout = w[k]*rho_local*(1.0+3.0*eu+4.5*eu*eu-1.5*uv) + #print(k, rho_local, w[k]) + return feqout + +``init()`` intialize some variable + +.. code-block:: python + + @ti.kernel + def init(): + for i,j,k in solid: + if (solid[i,j,k] == 0): + #if it is fluid intialize the density and velocity be one and zero + rho[i,j,k] = 1.0 + v[i,j,k] = ti.Vector([0,0,0]) + # set density r and density b based on psi + rho_r[i,j,k] = (psi[i,j,k]+1.0)/2.0 + rho_b[i,j,k] = 1.0 - rho_r[i,j,k] + #set another density r and density b + rhor[i,j,k] = 0.0 + rhob[i,j,k] = 0.0 + #set density distribution equals to equilibrium density distribution function + for s in ti.static(range(19)): + f[i,j,k,s] = feq(s,1.0,v[i,j,k]) + F[i,j,k,s] = feq(s,1.0,v[i,j,k]) + +``init_geo(filename, filename2)`` import the geometry data + +.. code-block:: python + + def init_geo(filename, filename2): + #read the solid flag data and set it as an column major array + in_dat = np.loadtxt(filename) + in_dat[in_dat>0] = 1 + in_dat = np.reshape(in_dat, (nx,ny,nz),order='F') + + #read the phase data from file + phase_in_dat = np.loadtxt(filename2) + #set the array from the file with colum major + phase_in_dat = np.reshape(phase_in_dat, (nx,ny,nz), order='F') + + return in_dat, phase_in_dat + +``static_init()`` initialize non-modified variable + +.. code-block:: python + + @ti.kernel + def static_init(): + if ti.static(enable_projection): # No runtime overhead + #define lattice speed + e[0] = ti.Vector([0,0,0]) + e[1] = ti.Vector([1,0,0]); e[2] = ti.Vector([-1,0,0]); e[3] = ti.Vector([0,1,0]); e[4] = ti.Vector([0,-1,0]);e[5] = ti.Vector([0,0,1]); e[6] = ti.Vector([0,0,-1]) + e[7] = ti.Vector([1,1,0]); e[8] = ti.Vector([-1,-1,0]); e[9] = ti.Vector([1,-1,0]); e[10] = ti.Vector([-1,1,0]) + e[11] = ti.Vector([1,0,1]); e[12] = ti.Vector([-1,0,-1]); e[13] = ti.Vector([1,0,-1]); e[14] = ti.Vector([-1,0,1]) + e[15] = ti.Vector([0,1,1]); e[16] = ti.Vector([0,-1,-1]); e[17] = ti.Vector([0,1,-1]); e[18] = ti.Vector([0,-1,1]) + #define another lattice speed + e_f[0] = ti.Vector([0,0,0]) + e_f[1] = ti.Vector([1,0,0]); e_f[2] = ti.Vector([-1,0,0]); e_f[3] = ti.Vector([0,1,0]); e_f[4] = ti.Vector([0,-1,0]);e_f[5] = ti.Vector([0,0,1]); e_f[6] = ti.Vector([0,0,-1]) + e_f[7] = ti.Vector([1,1,0]); e_f[8] = ti.Vector([-1,-1,0]); e_f[9] = ti.Vector([1,-1,0]); e_f[10] = ti.Vector([-1,1,0]) + e_f[11] = ti.Vector([1,0,1]); e_f[12] = ti.Vector([-1,0,-1]); e_f[13] = ti.Vector([1,0,-1]); e_f[14] = ti.Vector([-1,0,1]) + e_f[15] = ti.Vector([0,1,1]); e_f[16] = ti.Vector([0,-1,-1]); e_f[17] = ti.Vector([0,1,-1]); e_f[18] = ti.Vector([0,-1,1]) + #define a weight parameter + w[0] = 1.0/3.0; w[1] = 1.0/18.0; w[2] = 1.0/18.0; w[3] = 1.0/18.0; w[4] = 1.0/18.0; w[5] = 1.0/18.0; w[6] = 1.0/18.0; + w[7] = 1.0/36.0; w[8] = 1.0/36.0; w[9] = 1.0/36.0; w[10] = 1.0/36.0; w[11] = 1.0/36.0; w[12] = 1.0/36.0; + w[13] = 1.0/36.0; w[14] = 1.0/36.0; w[15] = 1.0/36.0; w[16] = 1.0/36.0; w[17] = 1.0/36.0; w[18] = 1.0/36.0; + #define the boundary velocity + bc_vel_x_left = ti.Vector([vx_bcxl, vy_bcxl, vz_bcxl]) + bc_vel_x_right = ti.Vector([vx_bcxr, vy_bcxr, vz_bcxr]) + bc_vel_y_left = ti.Vector([vx_bcyl, vy_bcyl, vz_bcyl]) + bc_vel_y_right = ti.Vector([vx_bcyr, vy_bcyr, vz_bcyr]) + bc_vel_z_left = ti.Vector([vx_bczl, vy_bczl, vz_bczl]) + bc_vel_z_right = ti.Vector([vx_bczr, vy_bczr, vz_bczr]) + +``multiply_M()`` calculate the density distribution function in momentum space + +.. code-block:: python + + @ti.func + def multiply_M(i,j,k): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + for index in ti.static(range(19)): + for s in ti.static(range(19)): + #calculate here + out[index] += M[index,s]*F[i,j,k,s] + #print(i,j,k, index, s, out[index], M[index,s], F[i,j,k,s]) + return out + +``GuoF(i,j,k,s,u)`` calculate Guo's force term + +.. code-block:: python + + @ti.func + def GuoF(i,j,k,s,u): + out=0.0 + for l in ti.static(range(19)): + out += w[l]*((e_f[l]-u).dot(ext_f[None])+(e_f[l].dot(u)*(e_f[l].dot(ext_f[None]))))*M[s,l] + + return out + +``meq_vec(rho_local,u)`` defines the equilibrium momentum + +.. code-block:: python + + @ti.func + def meq_vec(rho_local,u): + out = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + out[0] = rho_local; out[3] = u[0]; out[5] = u[1]; out[7] = u[2]; + out[1] = u.dot(u); out[9] = 2*u.x*u.x-u.y*u.y-u.z*u.z; out[11] = u.y*u.y-u.z*u.z + out[13] = u.x*u.y; out[14] = u.y*u.z; out[15] = u.x*u.z + return out + +``Compute_C()`` calculate the color gradient + +.. code-block:: python + + @ti.func + def Compute_C(i): + C = ti.Vector([0.0,0.0,0.0]) + ind_S = 0 + for s in ti.static(range(19)): + ip = periodic_index_for_psi(i+e[s]) + if (solid[ip] == 0): + #if it's fluid calculate the color gradient based on psi + C += 3.0*w[s]*e_f[s]*psi[ip] + else: + #if it is solid and abs(density r-density b) is less than 0.9 + ind_S = 1 + #calculate the color gradient based on psi_solid and set ind_s=1 + C += 3.0*w[s]*e_f[s]*psi_solid + + if (abs(rho_r[i]-rho_b[i]) > 0.9) and (ind_S == 1): + #if abs(density r-density b) is very large and it's solid set color gradient to be zero + C = ti.Vector([0.0,0.0,0.0]) + + return C + +``Compute_S_local`` calculate parameter of s diagonal + +.. code-block:: python + + @ti.func + def Compute_S_local(id): + sv=0.0; sother=0.0 + if (psi[id]>0): + if (psi[id]>0.1): + #if psi>0.1 + #sv=1.0/(niu_l/(1.0/3.0)+0.5) + sv=wl + else: + #if 0-0.1 + sv=lg0+g1*psi[id]+g2*psi[id]*psi[id] + #calculate s other + sother = 8.0*(2.0-sv)/(8.0-sv) + + #set s diagonal to be zero and set certain element to be relatie local parameter + S = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + S[1]=sv;S[2]=sv;S[4]=sother;S[6]=sother;S[8]=sother;S[9]=sv; + S[10]=sv;S[11]=sv;S[12]=sv;S[13]=sv;S[14]=sv;S[15]=sv;S[16]=sother; + S[17]=sother;S[18]=sother; + + + return S; + + +``collision()`` define the collision and recoloring process + +.. code-block:: python + + @ti.kernel + def colission(): + for i,j,k in rho: + #if it is inner fluid, calculate color gradient divided by norm of color gradient + if (i0 : + normal = C/cc + #calculate the M + m_temp = multiply_M(i,j,k) + meq = meq_vec(rho[i,j,k],v[i,j,k]) + #calculate surface tension term + meq[1] += CapA*cc + meq[9] += 0.5*CapA*cc*(2*normal.x*normal.x-normal.y*normal.y-normal.z*normal.z) + meq[11] += 0.5*CapA*cc*(normal.y*normal.y-normal.z*normal.z) + meq[13] += 0.5*CapA*cc*(normal.x*normal.y) + meq[14] += 0.5*CapA*cc*(normal.y*normal.z) + meq[15] += 0.5*CapA*cc*(normal.x*normal.z) + #calculate s local + S_local = Compute_S_local(ti.Vector([i,j,k])) + #calculate s*(m-meq) + for s in ti.static(range(19)): + m_temp[s] -= S_local[s]*(m_temp[s]-meq[s]) + m_temp[s] += (1-0.5*S_local[s])*GuoF(i,j,k,s,v[i,j,k]) + #calculte convection of density filed + g_r = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + g_b = ti.Vector([0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]) + + for s in ti.static(range(19)): + f[i,j,k,s] = 0 + for l in ti.static(range(19)): + # 1.single phase collision + f[i,j,k,s] += inv_M[s,l]*m_temp[l] + + g_r[s] = feq(s,rho_r[i,j,k],v[i,j,k]) + g_b[s] = feq(s,rho_b[i,j,k],v[i,j,k]) + + if (cc>0): + for kk in ti.static([1,3,5,7,9,11,13,15,17]): + # ef=ts.vector.dot(e[kk],C) + ef=e[kk].dot(C) + cospsi= g_r[kk] if (g_r[kk]nx-1: iout[0] = 0 + if i[1]<0: iout[1] = ny-1 + if i[1]>ny-1: iout[1] = 0 + if i[2]<0: iout[2] = nz-1 + if i[2]>nz-1: iout[2] = 0 + + return iout + +``periodic_index_for_psi(i)`` defines the index of boundary for psi if using periodic boundary condition + +.. code-block:: python + + @ti.func + def periodic_index_for_psi(i): + iout = i + if i[0]<0: + #if periodic boundary condition set index based on periodic boundary condition + if bc_psi_x_left == 0: + iout[0] = nx-1 + else: + #otherwise set neighbouring index, + #similar for other sides + iout[0] = 0 + + if i[0]>nx-1: + if bc_psi_x_right==0: + iout[0] = 0 + else: + iout[0] = nx-1 + + if i[1]<0: + if bc_psi_y_left == 0: + iout[1] = ny-1 + else: + iout[1] = 0 + + if i[1]>ny-1: + if bc_psi_y_right==0: + iout[1] = 0 + else: + iout[1] = ny-1 + + if i[2]<0: + if bc_psi_z_left==0: + iout[2] = nz-1 + else: + iout[2] = 0 + + if i[2]>nz-1: + if bc_psi_z_right==0: + iout[2] = 0 + else: + iout[2] = nz-1 + + return iout + + +``streaming1()`` defines steaming process of denisty distribution function + +.. code-block:: python + + @ti.kernel + def streaming1(): + for i,j,k in rho: + #if (solid[i,j,k] == 0): + if (i0): + F[0,j,k,s]=feq(s, rho_bcxl, v[1,j,k]) + else: + F[0,j,k,s]=feq(s, rho_bcxl, v[0,j,k]) + + if ti.static(bc_x_left==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[0,j,k]==0): + for s in ti.static(range(19)): + F[0,j,k,s]=feq(LR[s], 1.0, bc_vel_x_left[None])-F[0,j,k,LR[s]]+feq(s,1.0,bc_vel_x_left[None]) + + if ti.static(bc_x_right==1): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + if (solid[nx-2,j,k]>0): + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-2,j,k]) + else: + F[nx-1,j,k,s]=feq(s, rho_bcxr, v[nx-1,j,k]) + + if ti.static(bc_x_right==2): + for j,k in ti.ndrange((0,ny),(0,nz)): + if (solid[nx-1,j,k]==0): + for s in ti.static(range(19)): + F[nx-1,j,k,s]=feq(LR[s], 1.0, bc_vel_x_right[None])-F[nx-1,j,k,LR[s]]+feq(s,1.0,bc_vel_x_right[None]) + + + # Direction Y + if ti.static(bc_y_left==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + if (solid[i,1,k]>0): + F[i,0,k,s]=feq(s, rho_bcyl, v[i,1,k]) + else: + F[i,0,k,s]=feq(s, rho_bcyl, v[i,0,k]) + + if ti.static(bc_y_left==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,0,k]==0): + for s in ti.static(range(19)): + F[i,0,k,s]=feq(LR[s], 1.0, bc_vel_y_left[None])-F[i,0,k,LR[s]]+feq(s,1.0,bc_vel_y_left[None]) + + if ti.static(bc_y_right==1): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + if (solid[i,ny-2,k]>0): + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-2,k]) + else: + F[i,ny-1,k,s]=feq(s, rho_bcyr, v[i,ny-1,k]) + + if ti.static(bc_y_right==2): + for i,k in ti.ndrange((0,nx),(0,nz)): + if (solid[i,ny-1,k]==0): + for s in ti.static(range(19)): + F[i,ny-1,k,s]=feq(LR[s], 1.0, bc_vel_y_right[None])-F[i,ny-1,k,LR[s]]+feq(s,1.0,bc_vel_y_right[None]) + + # Z direction + if ti.static(bc_z_left==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + if (solid[i,j,1]>0): + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,1]) + else: + F[i,j,0,s]=feq(s, rho_bczl, v[i,j,0]) + + if ti.static(bc_z_left==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,0]==0): + for s in ti.static(range(19)): + F[i,j,0,s]=feq(LR[s], 1.0, bc_vel_z_left[None])-F[i,j,0,LR[s]]+feq(s,1.0,bc_vel_z_left[None]) + + if ti.static(bc_z_right==1): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + if (solid[i,j,nz-2]>0): + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-2]) + else: + F[i,j,nz-1,s]=feq(s, rho_bczr, v[i,j,nz-1]) + + if ti.static(bc_z_right==2): + for i,j in ti.ndrange((0,nx),(0,ny)): + if (solid[i,j,nz-1]==0): + for s in ti.static(range(19)): + F[i,j,nz-1,s]=feq(LR[s], 1.0, bc_vel_z_right[None])-F[i,j,nz-1,LR[s]]+feq(s,1.0,bc_vel_z_right[None]) + +``Boundary_condition_psi()`` calculate macroscopic variable + +.. code-block:: python + + @ti.kernel + def streaming3(): + for i,j,k, in rho: + #if (solid[i,j,k] == 0): + if (i + + + + + + lbm_solver_3d_2phase_sparse — taichi-LBM3D 0.0.1 documentation + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

lbm_solver_3d_2phase_sparse

+

This file is almost the same as the lbm_solver_3d_2phase.py file execpt sparse storage definition of some varibles

+
# Sparse Storage memory allocation
+f = ti.field(ti.f32)
+F = ti.field(ti.f32)
+rho = ti.field(ti.f32)
+v = ti.Vector.field(3, ti.f32)
+rhor = ti.field(ti.f32)
+rhob = ti.field(ti.f32)
+rho_r = ti.field(ti.f32)
+rho_b = ti.field(ti.f32)
+n_mem_partition = 3
+
+cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1))
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhor)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhob)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_r)
+cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_b)
+
+
+cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1))
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f)
+cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F)
+
+
+

Above code snippts define the sparse storage of some varibles

+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/twophase/lbm_solver_3d_2phase_sparse.rst b/docs/twophase/lbm_solver_3d_2phase_sparse.rst new file mode 100644 index 0000000..0e10b26 --- /dev/null +++ b/docs/twophase/lbm_solver_3d_2phase_sparse.rst @@ -0,0 +1,32 @@ +lbm_solver_3d_2phase_sparse +======================================== + +This file is almost the same as the ``lbm_solver_3d_2phase.py`` file execpt sparse storage definition of some varibles + +.. code-block:: python + + # Sparse Storage memory allocation + f = ti.field(ti.f32) + F = ti.field(ti.f32) + rho = ti.field(ti.f32) + v = ti.Vector.field(3, ti.f32) + rhor = ti.field(ti.f32) + rhob = ti.field(ti.f32) + rho_r = ti.field(ti.f32) + rho_b = ti.field(ti.f32) + n_mem_partition = 3 + + cell1 = ti.root.pointer(ti.ijk, (nx//n_mem_partition+1,ny//n_mem_partition+1,nz//n_mem_partition+1)) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(v) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhor) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rhob) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_r) + cell1.dense(ti.ijk, (n_mem_partition,n_mem_partition,n_mem_partition)).place(rho_b) + + + cell2 = ti.root.pointer(ti.ijkl,(nx//3+1,ny//3+1,nz//3+1,1)) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(f) + cell2.dense(ti.ijkl,(n_mem_partition,n_mem_partition,n_mem_partition,19)).place(F) + +Above code snippts define the sparse storage of some varibles \ No newline at end of file