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October 30, 2021 04:10
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import taichi as ti | |
ti.init(arch=ti.gpu) | |
n_particles = 8192 | |
n_grid = 128 | |
dx = 1 / n_grid | |
dt = 2e-4 | |
p_rho = 1 | |
p_vol = (dx * 0.5)**2 | |
p_mass = p_vol * p_rho | |
gravity = 9.8 | |
bound = 3 | |
E = 400 | |
x = ti.Vector.field(2, float, n_particles) | |
v = ti.Vector.field(2, float, n_particles) | |
C = ti.Matrix.field(2, 2, float, n_particles) | |
J = ti.field(float, n_particles) | |
grid_v = ti.Vector.field(2, float, (n_grid, n_grid)) | |
grid_m = ti.field(float, (n_grid, n_grid)) | |
@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: | |
Xp = x[p] / dx | |
base = int(Xp - 0.5) | |
fx = Xp - base | |
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2] | |
stress = -dt * 4 * E * p_vol * (J[p] - 1) / dx**2 | |
affine = ti.Matrix([[stress, 0], [0, stress]]) + p_mass * C[p] | |
for i, j in ti.static(ti.ndrange(3, 3)): | |
offset = ti.Vector([i, j]) | |
dpos = (offset - fx) * dx | |
weight = w[i].x * w[j].y | |
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: | |
grid_v[i, j] /= grid_m[i, j] | |
grid_v[i, j].y -= dt * gravity | |
if i < bound and grid_v[i, j].x < 0: | |
grid_v[i, j].x = 0 | |
if i > n_grid - bound and grid_v[i, j].x > 0: | |
grid_v[i, j].x = 0 | |
if j < bound and grid_v[i, j].y < 0: | |
grid_v[i, j].y = 0 | |
if j > n_grid - bound and grid_v[i, j].y > 0: | |
grid_v[i, j].y = 0 | |
for p in x: | |
Xp = x[p] / dx | |
base = int(Xp - 0.5) | |
fx = Xp - base | |
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2] | |
new_v = ti.Vector.zero(float, 2) | |
new_C = ti.Matrix.zero(float, 2, 2) | |
for i, j in ti.static(ti.ndrange(3, 3)): | |
offset = ti.Vector([i, j]) | |
dpos = (offset - fx) * dx | |
weight = w[i].x * w[j].y | |
g_v = grid_v[base + offset] | |
new_v += weight * g_v | |
new_C += 4 * weight * g_v.outer_product(dpos) / dx**2 | |
v[p] = new_v | |
x[p] += dt * v[p] | |
J[p] *= 1 + dt * new_C.trace() | |
C[p] = new_C | |
@ti.kernel | |
def init(): | |
for i in range(n_particles): | |
x[i] = [ti.random() * 0.4 + 0.2, ti.random() * 0.4 + 0.2] | |
v[i] = [0, -1] | |
J[i] = 1 | |
init() | |
gui = ti.GUI('MPM88') | |
while gui.running and not gui.get_event(gui.ESCAPE): | |
for s in range(50): | |
substep() | |
gui.clear(0x112F41) | |
gui.circles(x.to_numpy(), radius=1, color=0x068587) | |
gui.show() |
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