Interactive mpm128.py based on the amazing keyboard system by @archibate

 on Windows and Linux

examples/mpm128.py

@@ -0,0 +1,128 @@
+import taichi as ti
+import numpy as np
+ti.init(arch=ti.cuda) # Try to run on GPU
+quality = 1 # Use a larger value for higher-res simulations
+n_particles, n_grid = 9000 * quality ** 2, 128 * quality
+dx, inv_dx = 1 / n_grid, float(n_grid)
+dt = 1e-4 / quality
+p_vol, p_rho = (dx * 0.5)**2, 1
+p_mass = p_vol * p_rho
+E, nu = 5e3, 0.2 # Young's modulus and Poisson's ratio
+mu_0, lambda_0 = E / (2 * (1 + nu)), E * nu / ((1+nu) * (1 - 2 * nu)) # Lame parameters
+
+x = ti.Vector(2, dt=ti.f32, shape=n_particles) # position
+v = ti.Vector(2, dt=ti.f32, shape=n_particles) # velocity
+C = ti.Matrix(2, 2, dt=ti.f32, shape=n_particles) # affine velocity field
+F = ti.Matrix(2, 2, dt=ti.f32, shape=n_particles) # deformation gradient
+material = ti.var(dt=ti.i32, shape=n_particles) # material id
+Jp = ti.var(dt=ti.f32, shape=n_particles) # plastic deformation
+grid_v = ti.Vector(2, dt=ti.f32, shape=(n_grid, n_grid)) # grid node momentum/velocity
+grid_m = ti.var(dt=ti.f32, shape=(n_grid, n_grid)) # grid node mass
+gravity = ti.Vector(2, dt=ti.f32, shape=())
+attractor_strength = ti.var(dt=ti.f32, shape=())
+attractor_pos = ti.Vector(2, dt=ti.f32, shape=())
+
+@ti.kernel
+def substep():
+  for i, j in grid_m:
+    grid_v[i, j] = [0, 0]
+    grid_m[i, j] = 0
+  for p in x: # Particle state update and scatter to grid (P2G)
+    base = (x[p] * inv_dx - 0.5).cast(int)
+    fx = x[p] * inv_dx - base.cast(float)
+    # Quadratic kernels  [http://mpm.graphics   Eqn. 123, with x=fx, fx-1,fx-2]
+    w = [0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1), 0.5 * ti.sqr(fx - 0.5)]
+    F[p] = (ti.Matrix.identity(ti.f32, 2) + dt * C[p]) @ F[p] # deformation gradient update
+    h = max(0.1, min(5, ti.exp(10 * (1.0 - Jp[p])))) # Hardening coefficient: snow gets harder when compressed
+    if material[p] == 1: # jelly, make it softer
+      h = 0.3
+    mu, la = mu_0 * h, lambda_0 * h
+    if material[p] == 0: # liquid
+      mu = 0.0
+    U, sig, V = ti.svd(F[p])
+    J = 1.0
+    for d in ti.static(range(2)):
+      new_sig = sig[d, d]
+      if material[p] == 2:  # Snow
+        new_sig = min(max(sig[d, d], 1 - 2.5e-2), 1 + 4.5e-3)  # Plasticity
+      Jp[p] *= sig[d, d] / new_sig
+      sig[d, d] = new_sig
+      J *= new_sig
+    if material[p] == 0:  # Reset deformation gradient to avoid numerical instability
+      F[p] = ti.Matrix.identity(ti.f32, 2) * ti.sqrt(J)
+    elif material[p] == 2:
+      F[p] = U @ sig @ V.T() # Reconstruct elastic deformation gradient after plasticity
+    stress = 2 * mu * (F[p] - U @ V.T()) @ F[p].T() + ti.Matrix.identity(ti.f32, 2) * la * J * (J - 1)
+    stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
+    affine = stress + p_mass * C[p]
+    for i, j in ti.static(ti.ndrange(3, 3)): # Loop over 3x3 grid node neighborhood
+      offset = ti.Vector([i, j])
+      dpos = (offset.cast(float) - fx) * dx
+      weight = w[i][0] * w[j][1]
+      grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos)
+      grid_m[base + offset] += weight * p_mass
+  for i, j in grid_m:
+    if grid_m[i, j] > 0: # No need for epsilon here
+      grid_v[i, j] = (1 / grid_m[i, j]) * grid_v[i, j] # Momentum to velocity
+      grid_v[i, j] += dt * gravity[None] * 30 # gravity
+      dist = attractor_pos[None] - dx * ti.Vector([i, j])
+      grid_v[i, j] += dist / (0.01 + dist.norm()) * attractor_strength[None] * dt * 100
+      if i < 3 and grid_v[i, j][0] < 0:          grid_v[i, j][0] = 0 # Boundary conditions
+      if i > n_grid - 3 and grid_v[i, j][0] > 0: grid_v[i, j][0] = 0
+      if j < 3 and grid_v[i, j][1] < 0:          grid_v[i, j][1] = 0
+      if j > n_grid - 3 and grid_v[i, j][1] > 0: grid_v[i, j][1] = 0
+  for p in x: # grid to particle (G2P)
+    base = (x[p] * inv_dx - 0.5).cast(int)
+    fx = x[p] * inv_dx - base.cast(float)
+    w = [0.5 * ti.sqr(1.5 - fx), 0.75 - ti.sqr(fx - 1.0), 0.5 * ti.sqr(fx - 0.5)]
+    new_v = ti.Vector.zero(ti.f32, 2)
+    new_C = ti.Matrix.zero(ti.f32, 2, 2)
+    for i, j in ti.static(ti.ndrange(3, 3)): # loop over 3x3 grid node neighborhood
+      dpos = ti.Vector([i, j]).cast(float) - fx
+      g_v = grid_v[base + ti.Vector([i, j])]
+      weight = w[i][0] * w[j][1]
+      new_v += weight * g_v
+      new_C += 4 * inv_dx * weight * ti.outer_product(g_v, dpos)
+    v[p], C[p] = new_v, new_C
+    x[p] += dt * v[p] # advection
+
+import random
+
+def reset():
+  group_size = n_particles // 3
+  for i in range(n_particles):
+    x[i] = [random.random() * 0.2 + 0.3 + 0.10 * (i // group_size), random.random() * 0.2 + 0.05 + 0.32 * (i // group_size)]
+    material[i] = i // group_size # 0: fluid 1: jelly 2: snow
+  v.fill([0, -1])
+  F.fill(ti.Matrix([[1, 0], [0, 1]]))
+  Jp.fill(1)
+  C.fill(0)
+
+print("[Hint] Use WSAD/arrow keys to control gravity. Use left/right mouse bottons to attract/repel. (OS X not yet supported)")
+gui = ti.GUI("Taichi MLS-MPM-128", res=512, background_color=0x112F41)
+reset()
+
+for frame in range(20000):
+  gravity[None] = [0, 0]
+  while gui.has_key_event():
+    e = gui.get_key_event()
+    if e.type == ti.GUI.RELEASE: continue
+    elif e.key == 'r': reset()
+    elif e.key == ti.GUI.ESCAPE: exit(0)
+  if gui.is_pressed(ti.GUI.LEFT,  'a'): gravity[None][0] = -1
+  if gui.is_pressed(ti.GUI.RIGHT, 'd'): gravity[None][0] = 1
+  if gui.is_pressed(ti.GUI.UP,    'w'): gravity[None][1] = 1
+  if gui.is_pressed(ti.GUI.DOWN,  's'): gravity[None][1] = -1
+  mouse = gui.get_cursor_pos()
+  gui.circle((mouse[0], mouse[1]), color=0x336699, radius=15)
+  attractor_pos[None] = [mouse[0], mouse[1]]
+  attractor_strength[None] = 0
+  if gui.is_pressed(ti.GUI.LMB):
+    attractor_strength[None] = 1
+  if gui.is_pressed(ti.GUI.RMB):
+    attractor_strength[None] = -1
+  for s in range(int(2e-3 // dt)):
+    substep()
+  colors = np.array([0x068587, 0xED553B, 0xEEEEF0], dtype=np.uint32)
+  gui.circles(x.to_numpy(), radius=1.5, color=colors[material.to_numpy()])
+  gui.show() # Change to gui.show(f'{frame:06d}.png') to write images to disk

taichi/runtime/runtime.cpp

@@ -1046,7 +1046,8 @@ u32 cuda_rand_u32(Context *context) {
   // TODO: whether this leads to a deadlock or not depends on how nvcc schedules
   // the instructions...
   while (!done) {
-    if (atomic_exchange_i32((i32 *)lock, 1) == 1) {
+    if (atomic_exchange_i32((i32 *)lock, 1) == 0) {
+      grid_memfence();
       auto &x = state->x;
       auto &y = state->y;
       auto &z = state->z;
@@ -1058,6 +1059,7 @@ u32 cuda_rand_u32(Context *context) {
       w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
       ret = w;
       done = true;
+      grid_memfence();
       mutex_unlock_i32(lock);
     }
   }