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Titanic188.py
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Titanic188.py
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import taichi as ti
ti.init(arch=ti.gpu, debug=True)
n_material = 3
n_particle = ti.Vector.field(n_material, int, ())
n_particle_ = [6000, 1000, 6000]
n_particles = sum(n_particle_)
n_grid = 128
dx, inv_dx = 1 / n_grid, float(n_grid)
dt = 5e-5
grid_m = ti.field(float, (n_grid, n_grid, n_material))
grid_v = ti.Vector.field(2, float, (n_grid, n_grid, n_material))
grid_doff = ti.Vector.field(2, float, (n_grid, n_grid, n_material))
m = ti.field(dtype=float, shape=n_material) # mass
x = ti.Vector.field(2, dtype=float, shape=n_particles) # position
v = ti.Vector.field(2, dtype=float, shape=n_particles) # velocity
C = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) # affine velocity field
F = ti.Matrix.field(2, 2, dtype=float, shape=n_particles) # deformation gradient
Jp = ti.field(dtype=float, shape=n_particles) # plastic
material = ti.field(dtype=int, shape=n_particles) # material id
p_vol = (dx * 0.5)**2
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
touch_freeze_1_3=ti.field(ti.i32, ())
touch_freeze_1_3[None]=False
acc = ti.Vector.field(2, dtype=float, shape=())
@ti.kernel
def substep():
for i, j, k in grid_m:
grid_v[i, j, k] = [0, 0]
grid_m[i, j, k] = 0
for p in x:
k = material[p]
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
F[p] = (ti.Matrix.identity(float, 2) + dt * C[p]) @ F[p]
h = max(0.1, min(5, ti.exp(10 * (1.0 - Jp[p]))))
mu, la = mu_0 * h, lambda_0 * h
if k == 0:
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 k == 2: # ice
new_sig = min(max(sig[d, d], 1 - 2.5e-1),
1 + 4.5e-1) # Plasticity
if k == 1: # boat
new_sig = min(max(sig[d, d], 1 - 2.5e-2),
1 + 4.5e-2) # Plasticity
Jp[p] *= sig[d, d] / new_sig
sig[d, d] = new_sig
J *= new_sig
if k == 0:
F[p] = ti.Matrix.identity(float, 2) * ti.sqrt(J)
elif k==1 or k==2:
F[p] = U @ sig @ V.transpose()
stress = 2 * mu * (F[p] - U @ V.transpose()) @ F[p].transpose(
) + ti.Matrix.identity(float, 2) * la * J * (J - 1)
stress = (-dt * p_vol * 4 * inv_dx * inv_dx) * stress
affine = stress + m[k] * C[p]
for i, j in ti.static(ti.ndrange(3, 3)):
offset = ti.Vector([i, j])
dpos = (offset.cast(float) - fx) * dx
weight = w[i][0] * w[j][1]
grid_v[base + offset, k] += weight * (m[k] * v[p] + affine @ dpos)
grid_m[base + offset, k] += weight * m[k]
grid_doff[base + offset, k] += -(offset.cast(float) - fx)
for i, j in ti.ndrange(n_grid, n_grid):
if grid_m[i, j, 1]>0:
grid_v[i, j, 1] += acc[None] * dt * 3e-3
if grid_m[i, j, 2]>0 and grid_m[i, j, 1]>0:
grid_v[i, j, 2], grid_v[i, j, 1] = \
grid_v[i, j, 2]*0.7 +grid_v[i, j, 1]*0.3, \
grid_v[i, j, 2]*0.3 +grid_v[i, j, 1]*0.7
if grid_m[i, j, 1]>0 and grid_m[i, j, 0]>0:
grid_v[i, j, 1], grid_v[i, j, 0] = \
grid_v[i, j, 1]*0.99 + grid_v[i, j, 0]*0.01, \
grid_v[i, j, 1]*0.01 + grid_v[i, j, 0]*0.99
if not grid_doff[i, j, 0].y > grid_doff[i, j, 1].y:
grid_v[i, j, 1].y += grid_m[i, j, 0] * dt *1e2
if grid_m[i, j, 2]>0 and grid_m[i, j, 0]>0:
grid_v[i, j, 2], grid_v[i, j, 0] = \
grid_v[i, j, 2]*0.99 + grid_v[i, j, 0]*0.01, \
grid_v[i, j, 2]*0.01 + grid_v[i, j, 0]*0.99
for i, j, k in grid_m:
if grid_m[i, j, k] > 0:
grid_v[i, j, k] = (1 / grid_m[i, j, k]) * grid_v[i, j, k] # Momentum to velocity
if k==2:
grid_v[i, j, k][1] += dt * -1 * 50
else:
grid_v[i, j, k][1] += dt * -1 * 30
if i < 3 and grid_v[i, j, k][0] < 0:
grid_v[i, j, k][0] = 0 # Boundary conditions
if i > n_grid - 3 and grid_v[i, j, k][0] > 0: grid_v[i, j, k][0] = 0
if j < 3 and grid_v[i, j, k][1] < 0: grid_v[i, j, k][1] = 0
if j > n_grid - 3 and grid_v[i, j, k][1] > 0: grid_v[i, j, k][1] = 0
for p in x: # grid to particle (G2P)
pad=3.0/128
k = material[p]
base = (x[p] * inv_dx - 0.5).cast(int)
fx = x[p] * inv_dx - base.cast(float)
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1.0)**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)):
dpos = ti.Vector([i, j]).cast(float) - fx
g_v = grid_v[base + ti.Vector([i, j]), k]
weight = w[i][0] * w[j][1]
new_v += weight * g_v
new_C += 4 * inv_dx * weight * g_v.outer_product(dpos)
v[p], C[p] = new_v, new_C
x[p] += dt * v[p] # advection
pad=3.0/128
if x[p].x<pad: x[p].x=pad
if x[p].x>1-pad: x[p].x=1-pad
if x[p].y<pad: x[p].y=pad
if x[p].y>1-pad: x[p].y=1-pad
@ti.kernel
def init():
n_particle[None] = n_particle_
n_sum = 0
m[0] = p_vol * 1.0
m[1] = p_vol * 1.0
m[2] = p_vol * 1.0
for k in ti.static(range(n_material)):
for j in range(n_particle[None][k]):
i = n_sum+j
material[i] = k
v[i] = [0, 0]
F[i] = ti.Matrix([[1, 0], [0, 1]])
C[i] = ti.Matrix.zero(float, 2, 2)
Jp[i] = 1
if k==0: # water
x_ = ti.Vector([ti.random(), ti.random()])
x_y = x_.y * ti.sqrt((1-x_.x))
x[i] = [0.05 + x_.x*0.9, 0.05 + x_y*0.2]
if k==1: # boat
x_ = ti.Vector([ti.random()-0.5, ti.random()])
x_x = x_.x * ti.sqrt((x_.y+1))
x[i] = [0.2 + x_x*0.15, 0.22 + x_.y*0.04]
v[i] = [4, -1]
if k==2: # ice
x_ = ti.Vector([ti.random()-0.5, ti.random()])
x_x = x_.x * ti.sqrt((1-x_.y))
x[i] = [0.65 + x_x*0.2, 0 + x_.y*0.3]
n_sum+=n_particle[None][k]
gui = ti.GUI("Titanic188", res=512, background_color=0x112F41)
init()
tick=0
while True:
if gui.get_event(ti.GUI.PRESS):
if gui.event.key == 'r': init()
elif gui.event.key in [ti.GUI.ESCAPE, ti.GUI.EXIT]: break
if gui.event is not None: acc[None] = [0, 0]
if gui.is_pressed(ti.GUI.LEFT, 'a'): acc[None][0] = -1
if gui.is_pressed(ti.GUI.RIGHT, 'd'): acc[None][0] = 1
if gui.is_pressed(ti.GUI.UP, 'w'): acc[None][1] = 2e-1
if gui.is_pressed(ti.GUI.DOWN, 's'): acc[None][1] = -2e-1
for s in range(int(2e-3// dt)):
substep()
gui.circles(x.to_numpy(),
radius=1.5,
palette=[0x068587, 0xED553B, 0xEEEEF0, 0xA6B5F7, 0x3255A7, 0x6D35CB, 0xFE2E44, 0x26A5A7, 0xEDE53B],
palette_indices=material
)
gui.show()
# tick+=1
# if tick%5 ==1:
# gui.show(f'img/{tick:0>3d}.png')