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TPSolver.py
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import numpy as np
import cupy as cp
import cupyx.scipy.sparse
import cupyx.scipy.sparse.linalg as cpl
import scipy.sparse as sp
import scipy.sparse.linalg as spl
import matplotlib.pyplot as plt
import warnings
import time
from numba import cuda
from progress.bar import Bar # (pip install progress)
from cpuinfo import get_cpu_info
import os
def clearConsole(): return os.system(
'cls' if os.name in ('nt', 'dos') else 'clear')
class TPSolver:
nu = 0.001 # Kinematic Viscosity
rho = 1.225 # Fluid Density
nx = 10 # Number of Grid Points in x
ny = 10 # Number of Grid Points in y
Lx = 1 # Domain Length in x
Ly = 1 # Domain Length in y
dt = 0.001 # Time Step Size
tf = 1 # Simulation Time
nsteps = 0 # Number of Time Steps
t = 0 # Current Simulation Time
# INDICES
imin = imax = jmin = jmax = 0
# Miscellaneous
__type = np.float64
flagGPU = False
flagSparseL = False
linelenght = 70
plot_frequency = 100
flag_saveplot = False
sig_figs = 3
TPBX = 8
TPBY = 8
CFL = 0.75
# Matrices
x = y = xm = ym = p = us = vs = R = u = v = L = L_sp = []
data_sp = []
row_sp = []
col_sp = []
# Initial Velocities
u_bot = u_top = v_left = v_right = 0
# Mesh size
dx = dy = dxi = dxy = 0
debug = flagTimeStatistics = flagPlot = False
verbose = True
def __init__(self, license=True):
if license:
self.licenseDisclaimer()
def savePlots(self, mode):
self.flag_saveplot = mode
def enableGPU(self, mode):
self.flagGPU = mode
def enableSparseL(self, mode):
self.flagSparseL = mode
def setFloatType(self, val):
val = int(val)
if val == 32:
self.__type = np.float32
elif val == 64:
self.__type = np.float64
else:
raise ValueError('Values can only be: 32(single)/64(double)')
def setTPBX(self, val):
self.TPBX = val
def setTPBY(self, val):
self.TPBY = val
def setTPB(self,x,y):
self.TPBX = x
self.TPBY = y
def setCFL(self, val):
self.CFL = val
def setVerbose(self, val):
self.verbose = val
def plotEveryNTimeSteps(self, val):
self.plot_frequency = val
self.flagPlot = True
def setDebug(self, val):
self.debug = val
def printLine(self, char='-'):
s = char
print(s * self.linelenght)
def printTextOnLine(self, text, char='-'):
L = len(text)
LP = (self.linelenght - L)//2
if LP % 2 == 0:
print(char*LP, text, char*LP)
else:
print(char*(LP - 1), text, char*(LP))
def licenseDisclaimer(self):
self.printTextOnLine('License Disclaimer', '=')
print('TPSolver: 2D Navier-Stokes Solver for GPU')
print('This program is free software: you can redistribute it and/or modify')
print('it under the terms of the GNU Affero General Public License as published')
print('by the Free Software Foundation, either version 3 of the License.')
print('This program is distributed in the hope that it will be useful,')
print('but WITHOUT ANY WARRANTY; without even the implied warranty of')
print('MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the')
print('GNU Affero General Public License for more details.')
self.printLine('=')
print('')
def printHeaderAndOptions(self):
self.printTextOnLine('TPSolver', '=')
# print('Options selected:')
device = 'GPU' if self.flagGPU else 'CPU'
print('Device Mode: ', device)
if device == 'GPU':
cc_cores_per_SM_dict = {
(2, 0): 32,
(2, 1): 48,
(3, 0): 192,
(3, 5): 192,
(3, 7): 192,
(5, 0): 128,
(5, 2): 128,
(6, 0): 64,
(6, 1): 128,
(7, 0): 64,
(7, 5): 64,
(8, 0): 64,
(8, 6): 128}
gpu = cuda.get_current_device()
str = getattr(gpu, 'name')
print('GPU Model: ', str.decode("utf-8"))
my_sms = getattr(gpu, 'MULTIPROCESSOR_COUNT')
my_cc = gpu.compute_capability
cores_per_sm = cc_cores_per_SM_dict.get(my_cc)
total_cores = cores_per_sm*my_sms
print("GPU Compute Capability: ", my_cc)
print("GPU Total Number of SMs: ", my_sms)
print("GPU Total Cores: ", total_cores)
cpu = get_cpu_info()
print('CPU Model: ', cpu['brand_raw'])
print('CPU Total Cores: ', cpu['count'])
print('Debug Mode: ', self.debug)
self.printLine()
print('Density: ', self.rho)
print('Kinematics Viscosity: ', self.nu)
print('Grid size: ', self.nx, ' x ', self.ny)
print('Domain size: ', self.Lx, ' x ', self.Ly)
print('Time Step: ', round(self.dt, self.sig_figs))
print('Simulation Time: ', self.tf)
print('Float format: ', self.__type)
self.printLine()
print('Top Wall BC: ', self.u_top)
print('Bottom Wall BC: ', self.u_bot)
print('Left Wall BC: ', self.v_left)
print('Right Wall BC: ', self.v_right)
self.printLine()
if self.flagPlot:
print('Plotting every ', self.plot_frequency, ' steps.')
self.printLine()
def printTimeStatistics(self, val):
self.flagTimeStatistics = val
def printDebug(self, str, val):
# self.printLine('-')
self.printTextOnLine(str, '-')
print(val)
def setKinematicViscosity(self, val):
self.nu = val
def setDensity(self, val):
self.rho = val
def setGridPoints(self, nx, ny):
self.nx = nx
self.ny = ny
self.x = np.zeros(shape=nx + 2, dtype=self.__type)
self.y = np.zeros(shape=ny + 2, dtype=self.__type)
self.xm = np.zeros(shape=nx + 1, dtype=self.__type)
self.ym = np.zeros(shape=ny + 1, dtype=self.__type)
def setDomainSize(self, Lx, Ly):
self.Lx = Lx
self.Ly = Ly
def setTimeStep(self):
# Convective time step restriction
uMax = (max([abs(self.u_top), abs(self.u_bot)])**2.0
+ max([abs(self.v_left), abs(self.v_right)])**2.0)**0.5
dt_c = self.CFL*self.dx/uMax
# Diffusitve time step restriction
dt_d = self.CFL*self.dx**2.0/(4.0*self.nu)
self.dt = min([dt_c, dt_d])
if self.debug:
self.printDebug('Time Step', self.dt)
def setSimulationTime(self, tf):
self.tf = tf
if self.debug:
self.printDebug('Simulation Time', self.tf)
def calculateNumberOfTimeSteps(self):
if self.dt == 0:
self.setTimeStep()
self.nsteps = int(self.tf/self.dt)
if self.debug:
self.printDebug('Total Number of Steps', self.nsteps)
def createComputationalMesh(self):
self.imin = 1
self.imax = self.imin + self.nx - 1
self.jmin = 1
self.jmax = self.jmin + self.ny - 1
self.x[self.imin:self.imax +
2] = np.linspace(0, self.Lx, self.nx + 1, dtype=self.__type)
self.y[self.jmin:self.jmax +
2] = np.linspace(0, self.Ly, self.ny + 1, dtype=self.__type)
self.xm[self.imin:self.imax+1] = 0.5 * \
(self.x[self.imin:self.imax+1] + self.x[self.imin+1:self.imax+2])
self.ym[self.jmin:self.jmax+1] = 0.5 * \
(self.y[self.jmin:self.jmax+1] + self.y[self.jmin+1:self.jmax+2])
# Preallocate Matrices
self.p = np.zeros((self.imax+2, self.jmax+2), dtype=self.__type)
self.us = np.zeros((self.imax+2, self.jmax+2), dtype=self.__type)
self.vs = np.zeros((self.imax+2, self.jmax+2), dtype=self.__type)
if not self.flagSparseL:
self.L = np.zeros(
(self.nx*self.ny, self.nx*self.ny), dtype=self.__type)
self.u = np.zeros((self.imax+2, self.jmax+2), dtype=self.__type)
self.v = np.zeros((self.imax+2, self.jmax+2), dtype=self.__type)
# Preallocate Arrays
self.R = np.zeros(self.nx*self.ny, dtype=self.__type)
self.t = 0
self.dx = self.x[self.imin+1] - self.x[self.imin]
self.dy = self.y[self.jmin+1] - self.y[self.jmin]
self.dxi = 1/self.dx
self.dyi = 1/self.dy
self.calculateNumberOfTimeSteps()
def setWallVelocity(self, loc, val):
loc = str.lower(loc)
if loc == 'top':
self.u_top = val
elif loc == 'bottom':
self.u_bot = val
elif loc == 'left':
self.v_left = val
elif loc == 'right':
self.v_right = val
else:
raise ValueError('Values can only be: top/bottom/left/right')
self.setTimeStep()
def createLaplacianSparse(self):
ind = self.imax//2+(self.jmax//2)*self.nx
self.data_sp.append(1.0)
self.row_sp.append(ind)
self.col_sp.append(ind)
for j in range(self.ny):
for i in range(self.nx):
row = i+(j)*self.nx
if row == ind: continue
self.row_sp.append(row)
col = i+(j)*self.nx
self.col_sp.append(col)
data = 2*self.dxi*self.dxi + 2*self.dyi*self.dyi
self.data_sp.append(data)
end_ind = len(self.data_sp) - 1
for ii in range(i-1, i+2, 2):
if ii+1 > 0 and ii+1 <= self.nx:
data = -self.dxi*self.dxi
self.data_sp.append(data)
self.row_sp.append(row)
col = ii+(j)*self.nx
self.col_sp.append(col)
else:
self.data_sp[end_ind] = self.data_sp[end_ind]-self.dxi*self.dxi
for jj in range(j-1, j+2, 2):
if jj+1 > 0 and jj+1 <= self.ny:
data = -self.dxi*self.dxi
self.data_sp.append(data)
self.row_sp.append(row)
col = i+(jj)*self.nx
self.col_sp.append(col)
else:
self.data_sp[end_ind] = self.data_sp[end_ind]-self.dyi*self.dyi
self.data_sp = np.array(self.data_sp)
self.row_sp = np.array(self.row_sp)
self.col_sp = np.array(self.col_sp)
self.L_sp = sp.csr_matrix((self.data_sp, (self.row_sp, self.col_sp)), shape=(
self.nx*self.ny, self.nx*self.ny),dtype=self.__type)
def createLaplacian(self):
for j in range(self.ny):
for i in range(self.nx):
self.L[i+(j)*self.nx, i+(j)*self.nx] = 2*self.dxi*self.dxi + 2*self.dyi*self.dyi
for ii in range(i-1,i+2,2):
if ii +1> 0 and ii +1<= self.nx:
self.L[i+(j)*self.nx,ii+(j)*self.nx] = -self.dxi*self.dxi
else:
self.L[i+(j)*self.nx,i+(j)*self.nx] += -self.dxi*self.dxi
for jj in range(j-1,j+2,2):
if jj +1> 0 and jj +1<= self.ny:
self.L[i+(j)*self.nx,i+(jj)*self.nx] = -self.dyi*self.dyi
else:
self.L[i+(j)*self.nx,i+(j)*self.nx] += -self.dyi*self.dyi
ind = self.imax//2+(self.jmax//2)*self.nx
self.L[ind,:] = 0
self.L[ind,ind] = 1
if self.debug:
np.set_printoptions(edgeitems=30, linewidth=100000,formatter=dict(float=lambda x: " %.3g " % x))
self.printDebug('Laplacian Matrix',self.L)
def MomentumPredictor(self):
for j in range(self.jmin, self.jmax+1):
for i in range(self.imin, self.imax+1):
A = (self.nu*(self.u[i-1, j]-2*self.u[i, j]+self.u[i+1, j])*self.dxi**2 +
self.nu*(self.u[i, j-1]-2*self.u[i, j]+self.u[i, j+1])*self.dyi**2 -
self.u[i, j]*(self.u[i+1, j]-self.u[i-1, j])*0.5*self.dxi -
(0.25*(self.v[i-1, j]+self.v[i-1, j+1]+self.v[i, j]+self.v[i, j+1])) *
(self.u[i, j+1]-self.u[i, j-1])*0.5*self.dyi)
B = (self.nu*(self.v[i-1, j]-2*self.v[i, j]+self.v[i+1, j])*self.dxi**2 +
self.nu*(self.v[i, j-1]-2*self.v[i, j]+self.v[i, j+1])*self.dyi**2 -
(0.25*(self.u[i, j-1]+self.u[i+1, j-1]+self.u[i, j]+self.u[i+1, j])) *
(self.v[i+1, j]-self.v[i-1, j])*0.5*self.dxi -
self.v[i, j]*(self.v[i, j+1]-self.v[i, j-1])*0.5*self.dyi)
self.us[i, j] = self.u[i, j] + self.dt*A
self.vs[i, j] = self.v[i, j] + self.dt*B
if self.debug:
self.printDebug('us', self.us)
def computeRHS(self):
n = 0
for j in range(self.jmin, self.jmax+1):
for i in range(self.imin, self.imax+1):
# print(n, (i-self.imin+1)+(j - self.jmin+1)*(self.jmax-1))
# print(i,j,n,(j-1)*(self.imax-self.imin + 1) + i - 1)
self.R[n] = -self.rho/self.dt * (
(self.us[i+1, j] - self.us[i, j]) * self.dxi +
(self.vs[i, j+1] - self.vs[i, j]) * self.dyi)
n += 1
if self.debug:
self.printDebug('RHS', self.R)
def calculatePressure(self):
if self.flagSparseL:
pv = spl.spsolve(self.L_sp, self.R)
else:
pv = np.linalg.solve(self.L, self.R)
n = 0
for j in range(self.jmin, self.jmax+1):
for i in range(self.imin, self.imax+1):
self.p[i, j] = pv[n]
n += 1
if self.debug:
self.printDebug('Pressure', self.p)
def correctVelocities(self):
for j in range(self.jmin, self.jmax+1):
for i in range(self.imin, self.imax+1):
self.u[i, j] = self.us[i, j] - self.dt/self.rho * \
(self.p[i, j] - self.p[i-1, j])*self.dxi
self.v[i, j] = self.vs[i, j] - self.dt/self.rho * \
(self.p[i, j] - self.p[i, j-1])*self.dyi
if self.debug:
self.printDebug('Corrected u (Before BC)', self.u)
self.printDebug('Corrected v (Before BC)', self.v)
def setBoundaryConditions(self, val):
val = str.lower(val)
if val == "corrected":
self.u[:, self.jmin-1] = (self.u[:, self.jmin] -
2*(self.u[:, self.jmin] - self.u_bot))
self.u[:, self.jmax+1] = (self.u[:, self.jmax] -
2*(self.u[:, self.jmax] - self.u_top))
self.v[self.imin-1, :] = (self.v[self.imin, :] -
2 * (self.v[self.imin, :] - self.v_left))
self.v[self.imax+1, :] = (self.v[self.imax, :] -
2 * (self.v[self.imax, :] - self.v_right))
# Set corners to zero
self.v[0, self.jmax+1] = 0.0
self.u[self.imax+1,0] = 0.0
# Set wall velocity to zero
self.u[1, :] = 0.0
self.v[:, 1] = 0.0
elif val == "pressure":
self.p[:, self.jmin-1] = self.p[:, self.jmin]
self.p[:, self.jmax+1] = self.p[:, self.jmax]
self.p[self.imin-1, :] = self.p[self.imin, :]
self.p[self.imax+1, :] = self.p[self.imax, :]
elif val == "star":
self.us[:, self.jmin-1] = (self.us[:, self.jmin] -
2*(self.us[:, self.jmin] - self.u_bot))
self.us[:, self.jmax+1] = (self.us[:, self.jmax] -
2*(self.us[:, self.jmax] - self.u_top))
self.vs[self.imin-1, :] = (self.vs[self.imin, :] -
2 * (self.vs[self.imin, :] - self.v_left))
self.vs[self.imax+1, :] = (self.vs[self.imax, :] -
2 * (self.vs[self.imax, :] - self.v_right))
# Set corners to zero
self.vs[0, self.jmax+1] = 0.0
self.us[self.imax+1,0] = 0.0
# Set wall velocity to zero
self.us[1, :] = 0.0
self.vs[:, 1] = 0.0
if self.debug:
self.printDebug('Corrected u (After BC)', self.u)
self.printDebug('Corrected v (After BC)', self.v)
def plotContour(self):
self.checkNaN()
figure, ax = plt.subplots(figsize=(5, 5))
XX, YY = np.meshgrid(
self.x[self.imin:self.imax+1], self.y[self.jmin:self.jmax+1])
ax.contourf(XX, YY,
np.transpose(
self.p[self.imin:self.imax+1, self.jmin:self.jmax+1]),
10, cmap=plt.cm.bone, origin='lower')
plt.xlim([0, self.Lx - self.dx])
plt.ylim([0, self.Ly - self.dy])
plt.show()
def plotQuiver(self):
figure, ax = plt.subplots(figsize=(5, 5))
XX, YY = np.meshgrid(
self.x[self.imin:self.imax+1], self.y[self.jmin:self.jmax+1])
UU = np.transpose(self.u[self.imin:self.imax+1, self.jmin:self.jmax+1])
VV = np.transpose(self.v[self.imin:self.imax+1, self.jmin:self.jmax+1])
plt.quiver(XX, YY, UU, VV)
plt.xlim([0, self.Lx - self.dx])
plt.ylim([0, self.Ly - self.dy])
plt.show()
def initializeFigure(self, show = True):
fig, (ax1, ax2) = plt.subplots(
1, 2, figsize=(16, 8))
fig.suptitle('Results')
XX, YY = np.meshgrid(
self.x[self.imin:self.imax+1], self.y[self.jmin:self.jmax+1])
PP = np.transpose(self.p[self.imin:self.imax+1, self.jmin:self.jmax+1])
UU = np.transpose(
self.u[self.imin:self.imax+1, self.jmin:self.jmax+1]) + 1
VV = np.transpose(self.v[self.imin:self.imax+1, self.jmin:self.jmax+1])
# ax1.contourf(XX, YY, PP)
# ax1.set_xlabel('test')
ax1.quiver(XX, YY, UU, VV)
ax2.streamplot(XX, YY, UU, VV, density=2, linewidth=0.5, color='white')
plt.xlim([0, self.Lx - self.dx])
plt.ylim([0, self.Ly - self.dy])
if show:
fig.canvas.draw()
fig.canvas.flush_events()
plt.show(block=False)
return fig, (ax1, ax2)
def updatePlot(self, figure, axes, show = True):
try:
XX, YY = np.meshgrid(
self.x[self.imin:self.imax+1], self.y[self.jmin:self.jmax+1])
PP = np.transpose(
self.p[self.imin:self.imax+1, self.jmin:self.jmax+1])
UU = np.transpose(
self.u[self.imin:self.imax+1, self.jmin:self.jmax+1])
VV = np.transpose(
self.v[self.imin:self.imax+1, self.jmin:self.jmax+1])
# color = np.sqrt(UU**2 - VV**2)
axes[0].clear()
axes[1].clear()
ABSUV = np.sqrt(np.add(np.square(UU), np.square(VV)))
# axes[0].contourf(XX, YY, PP, levels=30)
axes[0].quiver(XX, YY, UU, VV)
axes[0].set_xlabel('X-Domain')
axes[0].set_ylabel('Y-Domain')
axes[0].set_title('Quiver Plot')
axes[1].contourf(XX, YY, ABSUV, levels=100)
# axes[1].quiver(XX,YY,UU,VV)
axes[1].streamplot(XX, YY, UU, VV, density=2,
linewidth=0.5, color='white')
axes[1].set_xlabel('X-Domain')
axes[1].set_ylabel('Y-Domain')
axes[1].set_title('Velocity Isolines and Contours')
axes[0].set_aspect('equal')
axes[1].set_aspect('equal')
axes[0].set_xlim([0, self.Lx - self.dx])
axes[0].set_ylim([0, self.Ly - self.dy])
axes[1].set_xlim([0, self.Lx - self.dx])
axes[1].set_ylim([0, self.Ly - self.dy])
if show:
figure.canvas.draw()
figure.canvas.flush_events()
# plt.show(block=False)
except:
raise ValueError(
'ERROR: Model went probably UNSTABLE! Check for NaN!')
return figure, axes
@cuda.jit()
def momentumPredictor_kernel(vec, bds, u, v, us, vs):
i, j = cuda.grid(2)
nu, dxi, dyi, dt, rho = vec
imin, imax, jmin, jmax = bds
if i < imin or i > imax or j < jmin or j > jmax:
return
vs[i, j] = v[i, j] + dt*(nu*(v[i-1, j]-2*v[i, j]+v[i+1, j])*dxi**2 +
nu*(v[i, j-1]-2*v[i, j]+v[i, j+1])*dyi**2 -
(0.25*(u[i, j-1]+u[i+1, j-1]+u[i, j]+u[i+1, j])) *
(v[i+1, j]-v[i-1, j])*0.5*dxi -
v[i, j]*(v[i, j+1]-v[i, j-1])*0.5*dyi)
us[i, j] = u[i, j] + dt*(nu*(u[i-1, j]-2*u[i, j]+u[i+1, j])*dxi*dxi +
nu*(u[i, j-1]-2*u[i, j]+u[i, j+1])*dyi*dyi -
u[i, j]*(u[i+1, j]-u[i-1, j])*0.5*dxi -
(0.25*(v[i-1, j]+v[i-1, j+1]+v[i, j]+v[i, j+1])) *
(u[i, j+1]-u[i, j-1])*0.5*dyi)
@cuda.jit()
def computeRHS_kernel(vec, bds, R, us, vs):
i, j = cuda.grid(2)
nu, dxi, dyi, dt, rho = vec
imin, imax, jmin, jmax = bds
if i < imin or i > imax or j < jmin or j > jmax:
return
n = (j-1)*imax + (i-1)
R[n] = -rho/dt * ((us[i+1, j] - us[i, j]) * dxi +
(vs[i, j+1] - vs[i, j]) * dyi)
@cuda.jit()
def calculatePressure_kernel(bds, p, pv):
i, j = cuda.grid(2)
imin, imax, jmin, jmax = bds
if i < imin or i > imax or j < jmin or j > jmax:
return
n = (j-1)*imax + (i-1)
p[i, j] = pv[n]
@cuda.jit()
def correct_vel_kernel(vec, bds, u, v, us, vs, p):
i, j = cuda.grid(2)
nu, dxi, dyi, dt, rho = vec
imin, imax, jmin, jmax = bds
if i < imin or i > imax or j < jmin or j > jmax:
return
u[i, j] = us[i, j] - dt/rho * (p[i, j] - p[i-1, j]) * dxi
v[i, j] = vs[i, j] - dt/rho * (p[i, j] - p[i, j-1]) * dyi
@cuda.jit()
def apply_vel_bc_kernel(bds, u, v, vel_bc):
i, j = cuda.grid(2)
imin, imax, jmin, jmax = bds
u_bot, u_top, v_left, v_right = vel_bc
if i > imax+1 or j > jmax+1:
return
#Tangential BCs
if i == imin-1:
v[i, j] = v[i+1, j] - 2 * (v[i+1, j] - v_left)
if i == imax+1:
v[i, j] = v[i-1, j] - 2 * (v[i-1, j] - v_right)
if j == jmin-1:
u[i, j] = u[i, j+1] - 2 * (u[i, j+1] - u_bot)
if j == jmax+1:
u[i, j] = u[i, j-1] - 2 * (u[i, j-1] - u_top)
# Perpendicular BCs
if i == imin:
u[i, j] = 0.0
if j == jmin:
v[i, j] = 0.0
# Corner BCs
if i == imin-1 and j == jmax+1:
v[i, j] = 0.0
if i == imax+1 and j == jmin-1:
u[i, j] = 0.0
@cuda.jit()
def apply_pres_bc_kernel(bds, p):
i, j = cuda.grid(2)
imin, imax, jmin, jmax = bds
if i > imax+1 or j > jmax+1:
return
if i == imin-1:
p[i, j] = p[i+1, j]
if i == imax+1:
p[i, j] = p[i-1, j]
if j == jmin-1:
p[i, j] = p[i, j+1]
if j == jmax+1:
p[i, j] = p[i, j-1]
def debugGPUmode(self):
self.createComputationalMesh()
self.setBoundaryConditions('corrected')
if self.flagSparseL:
self.createLaplacianSparse()
else:
self.createLaplacian()
gridDims = [(self.imax+2+self.TPBX-1)//self.TPBX, (self.jmax+2+self.TPBY-1)//self.TPBY]
blockDims = [self.TPBX, self.TPBY]
# Send some quantities over
bds = np.array([self.imin, self.imax, self.jmin,
self.jmax], dtype=np.uint32)
vec = np.array([self.nu,
self.dxi,
self.dyi,
self.dt,
self.rho],
dtype=self.__type)
vel_bc = np.array([self.u_bot, self.u_top, self.v_left, self.v_right])
d_vec = cp.asarray(vec)
d_bds = cp.asarray(bds)
d_u = cp.asarray(self.u)
d_v = cp.asarray(self.v)
d_us = cp.asarray(self.us)
d_vs = cp.asarray(self.vs)
d_R = cp.asarray(self.R)
d_p = cp.asarray(self.p)
d_pv = cp.zeros_like(d_R)
if self.flagSparseL:
d_L_sp = cupyx.scipy.sparse.csr_matrix(self.L_sp)
else:
d_L = cp.asarray(self.L)
d_vel_bc = cp.asarray(vel_bc)
self.debug = True
np.set_printoptions(edgeitems=30, linewidth=100000,
formatter=dict(float=lambda x: " %.3g " % x))
self.debug = False
while self.t <= self.tf:
self.t += self.dt
if self.debug:
print('\n')
self.printDebug('Time', self.t)
print('\n')
# # (1) momentum Predictor
self.MomentumPredictor()
self.setBoundaryConditions('star')
self.momentumPredictor_kernel[gridDims, blockDims](
d_vec, d_bds, d_u, d_v, d_us, d_vs)
self.apply_vel_bc_kernel[gridDims, blockDims](
d_bds, d_us, d_vs, d_vel_bc)
us_gpu = cp.asnumpy(d_us)
self.printDebug('us - CPU', self.us)
self.printDebug('us - GPU', us_gpu)
np.testing.assert_allclose(self.us, us_gpu, atol=1e-3, err_msg='us')
vs_gpu = cp.asnumpy(d_vs)
self.printDebug('vs - GPU', vs_gpu)
np.testing.assert_allclose(self.vs, vs_gpu, atol=1e-3, err_msg='vs')
# (2) RHS
self.computeRHS()
self.computeRHS_kernel[gridDims, blockDims](
d_vec, d_bds, d_R, d_us, d_vs)
# RHS_gpu = d_R.copy_to_host()
RHS_gpu = cp.asnumpy(d_R)
self.printDebug('RHS - GPU', RHS_gpu)
np.testing.assert_allclose(self.R, RHS_gpu, atol=1e-3, err_msg='RHS')
# (2bis) Poisson Step
if self.flagSparseL:
d_pv = cpl.spsolve(d_L_sp, d_R)
else:
d_pv = cp.linalg.solve(d_L, d_R)
# (3) Calculate Pressure
self.calculatePressure()
self.setBoundaryConditions('pressure')
self.calculatePressure_kernel[gridDims, blockDims](
d_bds, d_p, d_pv)
self.apply_pres_bc_kernel[gridDims, blockDims](d_bds, d_p)
# p_gpu = d_p.copy_to_host()
p_gpu = cp.asnumpy(d_p)
self.printDebug('Pressure - CPU', self.p)
self.printDebug('Pressure - GPU', p_gpu)
np.testing.assert_allclose(self.p, p_gpu, atol=1e-3, err_msg='P')
# (4) u,v corrected
self.debug = False
self.correctVelocities()
self.debug = True
self.correct_vel_kernel[gridDims, blockDims](
d_vec, d_bds, d_u, d_v, d_us, d_vs, d_p)
u_gpu = cp.asnumpy(d_u)
v_gpu = cp.asnumpy(d_v)
self.printDebug('Corrected u (Before BC)', self.u)
self.printDebug('Corrected u (Before BC) - GPU', u_gpu)
self.printDebug('Corrected v (Before BC)', self.v)
self.printDebug('Corrected v (Before BC) - GPU', v_gpu)
np.testing.assert_allclose(self.u, u_gpu, atol=1e-3, err_msg='u')
np.testing.assert_allclose(self.v, v_gpu, atol=1e-3, err_msg='v')
# (5) Apply BC
self.setBoundaryConditions('corrected')
self.apply_vel_bc_kernel[gridDims, blockDims](
d_bds, d_u, d_v, d_vel_bc)
# u_gpu = d_u.copy_to_host()
# v_gpu = d_v.copy_to_host()
u_gpu = cp.asnumpy(d_u)
v_gpu = cp.asnumpy(d_v)
self.printDebug('Corrected u (After BC) - GPU', u_gpu)
self.printDebug('Corrected v (After BC) - GPU', v_gpu)
np.testing.assert_allclose(self.u, u_gpu, atol=1e-3, err_msg='u')
np.testing.assert_allclose(self.v, v_gpu, atol=1e-3, err_msg='v')
def checkNaN(self):
pass
def solve_parallel(self):
# cuda.profile_start()
gridDims = [(self.imax+2+self.TPBX-1)//self.TPBX, (self.jmax+2+self.TPBY-1)//self.TPBY]
blockDims = [self.TPBX, self.TPBY]
bds = np.array([self.imin, self.imax, self.jmin,
self.jmax], dtype=np.uint32)
vec = np.array([self.nu,
self.dxi,
self.dyi,
self.dt,
self.rho],
dtype=self.__type)
vel_bc = np.array([self.u_bot, self.u_top, self.v_left, self.v_right])
d_vec = cp.asarray(vec)
d_bds = cp.asarray(bds)
d_u = cp.asarray(self.u)
d_v = cp.asarray(self.v)
d_us = cp.asarray(self.us)
d_vs = cp.asarray(self.vs)
d_R = cp.asarray(self.R)
d_p = cp.asarray(self.p)
d_pv = cp.zeros_like(d_R)
if self.flagSparseL:
d_L_sp = cupyx.scipy.sparse.csr_matrix(self.L_sp)
else:
d_L = cp.asarray(self.L)
d_vel_bc = cp.asarray(vel_bc)
# stream1 = cuda.stream()
# stream2 = cuda.stream()
bar = Bar('Computing', max=self.nsteps)
it = 1
first_plot = True
start = time.time()
while self.t <= self.tf:
self.t += self.dt
self.momentumPredictor_kernel[gridDims, blockDims](
d_vec, d_bds, d_u, d_v, d_us, d_vs)
self.apply_vel_bc_kernel[gridDims, blockDims](
d_bds, d_us, d_vs, d_vel_bc)
self.computeRHS_kernel[gridDims, blockDims](
d_vec, d_bds, d_R, d_us, d_vs)
if self.flagSparseL:
d_pv = cpl.spsolve(d_L_sp, d_R)
else:
d_pv = cp.linalg.solve(d_L, d_R)
self.calculatePressure_kernel[gridDims, blockDims](
d_bds, d_p, d_pv)
self.apply_pres_bc_kernel[gridDims, blockDims](d_bds, d_p)
self.correct_vel_kernel[gridDims, blockDims](
d_vec, d_bds, d_u, d_v, d_us, d_vs, d_p)
self.apply_vel_bc_kernel[gridDims, blockDims](
d_bds, d_u, d_v, d_vel_bc)
if first_plot and self.flagPlot:
fig, axes = self.initializeFigure()
first_plot = False
if it % self.plot_frequency == 0 and self.flagPlot:
self.p = cp.asnumpy(d_p)
self.u = cp.asnumpy(d_u)
self.v = cp.asnumpy(d_v)
fig, axes = self.updatePlot(fig, axes)
bar.next()
it += 1
# cuda.profile_stop()
bar.finish()
end = time.time()
self.p = cp.asnumpy(d_p)
self.u = cp.asnumpy(d_u)
self.v = cp.asnumpy(d_v)
return float(end-start)
def solve(self):
self.createComputationalMesh()
self.setBoundaryConditions('corrected')
if self.flagSparseL:
self.createLaplacianSparse()
else:
self.createLaplacian()
if self.verbose:
self.printHeaderAndOptions()
if self.flagGPU:
time_elapsed = self.solve_parallel()
else:
first_plot = True
it = 1
bar = Bar('Computing', max=self.nsteps)
start = time.time()
while self.t <= self.tf:
# Update Time
self.t += self.dt
if self.debug:
print('\n')
self.printDebug('Time', self.t)
print('\n')
self.MomentumPredictor()
self.setBoundaryConditions('star')
self.computeRHS()
self.calculatePressure()
self.setBoundaryConditions('pressure')
self.correctVelocities()
self.setBoundaryConditions('corrected')
if first_plot and self.flagPlot:
fig, axes = self.initializeFigure()
first_plot = False
if it % self.plot_frequency == 0 and self.flagPlot:
fig, axes = self.updatePlot(fig, axes)
bar.next()
it += 1
bar.finish()
time_elapsed = time.time() - start
self.updatePlot(fig, axes)
if self.flagTimeStatistics:
self.printTextOnLine('Time Statistics', '-')
if self.flagGPU:
print('GPU Mode: ', end='')
else:
print('CPU Mode: ', end='')
print(' ' + str(round(time_elapsed, self.sig_figs)) + ' seconds!')
if self.flag_saveplot:
plt.savefig('Results.pdf')
plt.show()
def runBenchmark(self, N=None):
# Run N iteration CPU vs GPU
if N is None:
N = self.nsteps
self.createComputationalMesh()
self.setBoundaryConditions('corrected')
if self.flagSparseL:
self.createLaplacianSparse()
else:
self.createLaplacian()
self.debug = False
self.flagPlot = False
self.flagGPU = True
if self.verbose:
self.printHeaderAndOptions()
self.printTextOnLine(
('CPU/GPU Benchmark for ' + str(N) + ' iterations'))
self.printLine()
# Run CPU First
bar = Bar('CPU Run ', max=N)
it = 1
start = time.time()
while it <= N:
# Update Time
self.t += self.dt
self.MomentumPredictor()
self.setBoundaryConditions('star')
self.computeRHS()
self.calculatePressure()
self.setBoundaryConditions('pressure')
self.correctVelocities()
self.setBoundaryConditions('corrected')
bar.next()
it += 1
end = time.time()
bar.finish()
cpu_time = float(end-start)
us_cpu = self.us
vs_cpu = self.vs
R_cpu = self.R
p_cpu = self.p
u_cpu = self.u
v_cpu = self.v
if self.flag_saveplot:
fig, axes = self.initializeFigure(False)
fig, axes = self.updatePlot(fig, axes, False)
plt.savefig('ResultsBenchmark-CPU.pdf')
# Reset Values
self.createComputationalMesh()
self.setBoundaryConditions('corrected')
if self.flagSparseL:
self.createLaplacianSparse()
else:
self.createLaplacian()
self.t = 0
# Run GPU
gridDims = [(self.imax+2+self.TPBX-1)//self.TPBX, (self.jmax+2+self.TPBY-1)//self.TPBY]
blockDims = [self.TPBX, self.TPBY]
bds = np.array([self.imin, self.imax, self.jmin,
self.jmax], dtype=np.uint32)
vec = np.array([self.nu,
self.dxi,
self.dyi,
self.dt,
self.rho],
dtype=self.__type)
vel_bc = np.array([self.u_bot, self.u_top, self.v_left, self.v_right])
d_vec = cp.asarray(vec)
d_bds = cp.asarray(bds)
d_u = cp.asarray(self.u)
d_v = cp.asarray(self.v)
d_us = cp.asarray(self.us)
d_vs = cp.asarray(self.vs)
d_R = cp.asarray(self.R)
d_p = cp.asarray(self.p)
d_pv = cp.zeros_like(d_R)
if self.flagSparseL:
d_L_sp = cupyx.scipy.sparse.csr_matrix(self.L_sp)
else: