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phase_change.py
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phase_change.py
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import taichi as ti
# from CGSolver import CGSolver
from Pressure_CGSolver import Pressure_CGSolver
from Temperature_CGSolver import Temperature_CGSolver
from MICPCGSolver import MICPCGSolver
# from MGPCGSolver import MGPCGSolver
from Pressure_MGPCGSolver import Pressure_MGPCGSolver
from Temperature_MGPCGSolver import Temperature_MGPCGSolver
import numpy as np
from utils import ColorMap, vec2, vec3, clamp
import utils
import time
import math
debug = True
# ti.init(arch=ti.gpu, default_fp=ti.f32)
ti.init(arch = 'cpu', default_fp=ti.f32, debug=debug)
# ---------------params in simulation----------------
cell_res = 256
npar = 2
m = cell_res
n = cell_res
w = 10
h = 10 * n / m
grid_x = w / m
grid_y = h / n
inv_grid_x = 1.0 / grid_x
inv_grid_y = 1.0 / grid_y
pspace_x = grid_x / npar
pspace_y = grid_y / npar
p_vol, p_rho = (grid_x * 0.5)**2, 1 # vol: m^2, rho: kg/m^2
p_mass = p_vol * p_rho # mass: kg
g = -9.8
substeps = 4
# mass_min_thres = 1e-4
# Young's modulas , Poisson's ratio and lame parameter
# E_solid_phase, nu_solid_phase = 9, 0.3 # Young's modulus(Gpa) and Poisson's ratio for ice
E_solid_phase, nu_solid_phase = 9 * 1e-4, 0.3 # Young's modulus(Gpa) and Poisson's ratio for ice
mu_solid_phase_init, lambda_solid_phase_init = E_solid_phase / (2 * (1 + nu_solid_phase)), E_solid_phase * nu_solid_phase / (
(1 + nu_solid_phase) * (1 - 2 * nu_solid_phase)) # Lame parameters
# E_fluid_phase, nu_fluid_phase = 2, 0.45 # Young's modulus(Gpa) and Poisson's ratio for water
E_fluid_phase, nu_fluid_phase = 2 * 1e-4, 0.45 # Young's modulus(Gpa) and Poisson's ratio for water
mu_fluid_phase_init, lambda_fluid_phase_init = E_fluid_phase / (2 * (1 + nu_fluid_phase)), E_fluid_phase * nu_fluid_phase / (
(1 + nu_fluid_phase) * (1 - 2 * nu_fluid_phase)) # Lame parameters
# Initial value
T_air_init = 60 # 60 C
T_solid_phase_init = 100 # 100 C
T_fluid_phase_init = 0
# heat capacity (J/kg*c)
c_solid_phase_init = 2093
c_fluid_phase_init = 4182
# heat conductivity(W/mK)
k_solid_phase_init = 2.18
k_fluid_phase_init = 0.606
k_air_init = 0.04
# phase change parameters
freezing_point = 0 # 273K
latent = 382000 # latent of ice，J/kg
# ----------------fields---------------
# face part
# velocity field
u = ti.field(dtype=ti.f32, shape=(m + 1, n))
v = ti.field(dtype=ti.f32, shape=(m, n + 1))
u_face_mass = ti.field(dtype=ti.f32, shape=(m + 1, n))
v_face_mass = ti.field(dtype=ti.f32, shape=(m, n + 1))
# internal force
fu = ti.field(dtype=ti.f32, shape=(m + 1, n))
fv = ti.field(dtype=ti.f32, shape=(m, n + 1))
# heat conductivity field
k_u = ti.field(dtype=ti.f32, shape=(m + 1, n))
k_v = ti.field(dtype=ti.f32, shape=(m, n + 1))
# volume
vol_u = ti.field(dtype=ti.f32, shape=(m + 1, n))
vol_v = ti.field(dtype=ti.f32, shape=(m, n + 1))
# cell part
cell_mass = ti.field(dtype=ti.f32, shape=(m, n))
# pressure field
p = ti.field(dtype=ti.f32, shape=(m, n))
# J & Je & Jp
J = ti.field(dtype=ti.f32, shape=(m , n))
Je = ti.field(dtype=ti.f32, shape=(m , n))
Jp = ti.field(dtype=ti.f32, shape=(m , n))
# heat capacity
c = ti.field(dtype=ti.f32, shape=(m , n))
# temperature
T = ti.field(dtype=ti.f32, shape=(m , n))
# 1 / lambda
inv_lambda = ti.field(dtype=ti.f32, shape=(m , n))
# -------------particle properties------------
# particle x, y
particle_positions = ti.Vector.field(2, dtype=ti.f32, shape=(m, n, npar, npar))
particle_velocities = ti.Vector.field(2,
dtype=ti.f32,
shape=(m, n, npar, npar))
# particle physical parameter
# particle C
cp_x = ti.Vector.field(2, dtype=ti.f32, shape=(m, n, npar, npar))
cp_y = ti.Vector.field(2, dtype=ti.f32, shape=(m, n, npar, npar))
# particle F
particle_Fe = ti.Matrix.field(2, 2, dtype=ti.f32, shape=(m, n, npar, npar)) # Elastic deformation gradient (F_E)
particle_Fp = ti.Matrix.field(2, 2, dtype=ti.f32, shape=(m, n, npar, npar)) # Plastic deformation gradient (F_P)
# particle type
particle_type = ti.field(dtype=ti.i32, shape=(m, n, npar, npar))
P_FLUID = 1
P_OTHER = 0
# particle lame's parameter
particle_mu = ti.field(dtype=ti.f32, shape=(m, n, npar, npar))
particle_la = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # lambda
# particle heat parameters
particle_T = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # temperature
particle_last_T = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # last temperature
particle_U = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # heat
particle_c = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # heat capacity
particle_k = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # heat conductivity
particle_l = ti.field(dtype=ti.f32, shape=(m, n, npar, npar)) # latent heat
particle_Phase = ti.field(dtype=ti.i32, shape=(m, n, npar, npar))
P_FLUID_PHASE = 3
P_SOLID_PHASE = 4
P_OTHER_PHASE = 5
# -----------------params in render-----------
screen_res = (800, 800 * n // m)
bwrR = ColorMap(1.0, .25, 1, .5)
bwrG = ColorMap(1.0, .5, .5, .5)
bwrB = ColorMap(1.0, 1, .25, .5)
color_buffer = ti.Vector.field(3, dtype=ti.f32, shape=screen_res)
gui = ti.GUI("watersim2D", screen_res, show_gui = False)
# cell type
cell_type = ti.field(dtype=ti.i32, shape=(m, n))
# pressure solver
# preconditioning = 'MG'
preconditioning = None
MIC_blending = 0.97
mg_level = 4
pre_and_post_smoothing = 2
bottom_smoothing = 10
dt = 0.01
if preconditioning == None:
# solver = CGSolver(m, n, u, v, cell_type)
pressure_solver = Pressure_CGSolver(m, n, u, v, dt, Jp, Je, inv_lambda, cell_type, vol_u, vol_v, u_face_mass, v_face_mass)
temperature_solver = Temperature_CGSolver(m, n, k_u, k_v, T, c, cell_type, cell_mass, grid_x)
elif preconditioning == 'MIC':
solver = MICPCGSolver(m, n, u, v, cell_type, MIC_blending=MIC_blending)
elif preconditioning == 'MG':
pressure_solver = Pressure_MGPCGSolver(m, n, u, v, dt, Jp, Je, inv_lambda, cell_type, multigrid_level=mg_level,
pre_and_post_smoothing=pre_and_post_smoothing,
bottom_smoothing=bottom_smoothing)
temperature_solver = Temperature_MGPCGSolver(m, n, k_u, k_v, T, c, cell_type, multigrid_level=mg_level,
pre_and_post_smoothing=pre_and_post_smoothing,
bottom_smoothing=bottom_smoothing)
# temperature_solver = Temperature_CGSolver(m, n, k_u, k_v, T, c, cell_type)
# save to gif
result_dir = "./results"
video_manager = ti.tools.VideoManager(output_dir=result_dir,
framerate=24,
automatic_build=False)
# --------------------rendering------------------
def render():
render_type = 'particles'
@ti.func
def map_color(c):
return vec3(bwrR.map(c), bwrG.map(c), bwrB.map(c))
@ti.kernel
def fill_marker():
for i, j in color_buffer:
x = int((i + 0.5) / screen_res[0] * w / grid_x)
y = int((j + 0.5) / screen_res[1] * h / grid_y)
m = cell_type[x, y]
# m = T[x, y] / 373
color_buffer[i, j] = map_color(m * 0.5)
def render_pixels():
fill_marker()
img = color_buffer.to_numpy()
gui.set_image(img)
def render_particles():
bg_color = 0x112f41
particle_color = 0x068587
particle_radius = 1.0
fluid_color = 0xC8D804
solid_color = 0xC3ABCD
pf = particle_type.to_numpy()
np_type = pf.copy()
np_type = np.reshape(np_type, -1)
pp = particle_Phase.to_numpy()
np_phase = pp.copy()
np_phase = np.reshape(np_phase, -1)
pos = particle_positions.to_numpy()
np_pos = pos.copy()
np_pos_fluid = pos.copy()
np_pos_solid = pos.copy()
np_pos = np.reshape(pos, (-1, 2))
np_pos_fluid = np.reshape(pos, (-1, 2))
np_pos_solid = np.reshape(pos, (-1, 2))
np_pos = np_pos[np.where(np_type == P_FLUID)]
np_pos_fluid = np_pos_fluid[np.where(np_phase == P_FLUID_PHASE)]
np_pos_solid = np_pos_solid[np.where(np_phase == P_SOLID_PHASE)]
for i in range(np_pos.shape[0]):
np_pos[i][0] /= w
np_pos[i][1] /= h
for i in range(np_pos_fluid.shape[0]):
np_pos_fluid[i][0] /= w
np_pos_fluid[i][1] /= h
for i in range(np_pos_solid.shape[0]):
np_pos_solid[i][0] /= w
np_pos_solid[i][1] /= h
gui.clear(bg_color)
# gui.circles(np_pos, radius=particle_radius, color=particle_color)
gui.circles(np_pos_fluid, radius=particle_radius, color=fluid_color)
gui.circles(np_pos_solid, radius=particle_radius, color=solid_color)
if render_type == 'particles':
render_particles()
else:
render_pixels()
video_manager.write_frame(gui.get_image())
# ------------initialization-----------
def init():
# init scene
@ti.kernel
def init_dambreak(x: ti.f32, y: ti.f32):
xn = int(x / grid_x)
yn = int(y / grid_y)
for i, j in cell_type:
if i == 0 or i == m - 1 or j == 0 or j == n - 1:
cell_type[i, j] = utils.SOLID # boundary
else:
if i <= xn and j <= yn:
cell_type[i, j] = utils.FLUID
else:
cell_type[i, j] = utils.AIR
@ti.kernel
def init_spherefall(xc: ti.f32, yc: ti.f32, r: ti.f32):
for i, j in cell_type:
if i == 0 or i == m - 1 or j == 0 or j == n - 1:
cell_type[i, j] = utils.SOLID # boundary
else:
x = (i + 0.5) * grid_x
y = (j + 0.5) * grid_y
phi = (x - xc)**2 + (y - yc) ** 2 - r**2
if phi <= 0 :
cell_type[i, j] = utils.FLUID
else:
cell_type[i, j] = utils.AIR
#init simulation
@ti.kernel
def init_field():
for i, j in u:
u[i, j] = 0.0
for i, j in v:
v[i, j] = 0.0
for i, j in u_face_mass:
u_face_mass[i, j] = -1.0
for i, j in v_face_mass:
v_face_mass[i, j] = -1.0
for i, j in fu:
fu[i, j] = 0.0
for i, j in fv:
fv[i, j] = 0.0
for i, j in k_u:
k_u[i, j] = 0
for i, j in k_v:
k_v[i, j] = 0
for i, j in vol_u:
vol_u[i, j] = 0.0
for i, j in vol_v:
vol_v[i, j] = 0.0
for i, j in cell_mass:
cell_mass[i, j] = -1.0
for i, j in p:
p[i, j] = 0.0
for i, j in J:
J[i, j] = 1
Je[i, j] = 1
Jp[i, j] = 1
c[i, j] = 0
T[i, j] = 0
inv_lambda[i, j] = 0
@ti.kernel
def init_particles():
for i, j, ix, jx in particle_positions:
if cell_type[i, j] == utils.FLUID:
particle_type[i, j, ix, jx] = P_FLUID
particle_Phase[i, j, ix, jx] = P_SOLID_PHASE
else:
particle_type[i, j, ix, jx] = P_OTHER
particle_type[i, j, ix, jx] = P_OTHER_PHASE
px = i * grid_x + (ix + ti.random(ti.f32)) * pspace_x
py = j * grid_y + (jx + ti.random(ti.f32)) * pspace_y
particle_positions[i, j, ix, jx] = vec2(px, py)
particle_velocities[i, j, ix, jx] = vec2(0.0, 0.0)
cp_x[i, j, ix, jx] = vec2(0.0, 0.0)
cp_y[i, j, ix, jx] = vec2(0.0, 0.0)
particle_Fe[i, j, ix, jx] = ti.Matrix.identity(dt = ti.f32, n=2)
particle_Fp[i, j, ix, jx] = ti.Matrix.identity(dt = ti.f32, n=2)
particle_mu[i, j, ix, jx] = mu_solid_phase_init
particle_la[i, j, ix, jx] = lambda_solid_phase_init
particle_T[i, j, ix, jx] = T_fluid_phase_init
particle_last_T[i, j, ix, jx] = T_fluid_phase_init
particle_U[i, j, ix, jx] = 0 # [0, Lp], initialilly at 0
particle_c[i, j, ix, jx] = c_solid_phase_init # for ice J/kg * C
particle_k[i, j, ix, jx] = k_solid_phase_init
particle_l[i, j, ix, jx] = p_mass * latent # for ice J/kg to melt
# init_dambreak(4, 4)
# init_spherefall(5,3,2)
init_spherefall(5, 2, 2)
init_field()
init_particles()
# -------------subprocesses----------------
@ti.kernel
def deformation_gradient_add_plasticity():
for p in ti.grouped(particle_positions):
if particle_type[p] == P_FLUID:
U, sig, V = ti.svd(particle_Fe[p])
theta_c = 2.5e-2
theta_s = 4.5e-3
for d in ti.static(range(2)):
sig[d, d] = ti.min(ti.max(sig[d, d], 1 - theta_c), 1 + theta_s) # Plasticity
Jp = particle_Fp[p].determinant()
# Note: this part is (Jp)^(1/d), here d = 2
particle_Fe[p] = ti.sqrt(Jp) * U@sig@V
particle_Fp[p] = (1 / ti.sqrt(Jp)) * particle_Fp[p]
@ti.func
def cubic_bspline_kernal(fx):
w = [vec2(1.0, 1.0), vec2(1.0, 1.0), vec2(1.0, 1.0)]
if fx[0] > 1.0:
w[0][0] *= ( (-1.0 / 6.0) * (fx[0] ** 3) + (fx[0] ** 2) - 2 * fx[0] + (4.0 / 3.0))
else:
w[0][0] *= ((1.0 / 2.0) * (fx[0] ** 3) - (fx[0] ** 2) + (2.0 / 3.0))
if fx[1] > 1.0:
w[0][1] *= ( (-1.0 / 6.0) * (fx[1] ** 3) + (fx[1] ** 2) - 2 * fx[1] + (4.0 / 3.0))
else:
w[0][1] *= ((1.0 / 2.0) * (fx[1] ** 3) - (fx[1] ** 2) + (2.0 / 3.0))
w[1] = ((1.0 / 2.0) * (ti.abs(fx-1) ** 3) - (ti.abs(fx-1) ** 2) + (2.0 / 3.0))
if fx[0]-2 < -1.0:
w[2][0] *= ( (-1.0 / 6.0) * (ti.abs(fx[0]-2) ** 3) + ((fx[0]-2) ** 2) - 2 * ti.abs(fx[0]-2) + (4.0 / 3.0))
else:
w[2][0] *= ((1.0 / 2.0) * (ti.abs(fx[0]-2) ** 3) - ((fx[0]-2) ** 2) + (2.0 / 3.0))
if fx[1]-2 < -1.0:
w[2][1] *= ( (-1.0 / 6.0) * (ti.abs(fx[1]-2) ** 3) + ((fx[1]-2) ** 2) - 2 * ti.abs(fx[1]-2) + (4.0 / 3.0))
else:
w[2][1] *= ((1.0 / 2.0) * (ti.abs(fx[1]-2) ** 3) - ((fx[1]-2) ** 2) + (2.0 / 3.0))
return w
@ti.func
def cubic_bspline_kernal_grad(fx):
return [(-1.0/2.0) * (fx ** 2) + 2 * fx - 2, (3.0 / 2.0) * ((fx-1) ** 2) - (2 * (fx-1)), (-1.0/2.0) * ((fx-2) ** 2) + 2 * (fx-2) - 2]
@ti.func
def scatter_face_u(xp, vp, cp, PFT, kp):
stagger = vec2(0.0, 0.5)
e = vec2(1.0, 0.0)
inv_dx = vec2(inv_grid_x, inv_grid_y).cast(ti.f32)
# inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# print(xp)
# Note, in SSJCTS14, they use cubic B-spline
w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Quadratic Bspline
# cubic spline
# w_cdf = [1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0]
w_grad = [fx-1.5, -2*(fx-1), fx-3.5] # Bspline gradient
# w = cubic_bspline_kernal(fx)
# w_grad = cubic_bspline_kernal_grad(fx)
# print("vp: ", vp)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
dpos = (offset.cast(ti.f32) - fx) * vec2(grid_x, grid_y)
# print(w)
weight_grad = vec2(w_grad[i][0]*w[j][1], w[i][0]*w_grad[j][1])
weight = w[i][0] * w[j][1] # x, y directions, respectively
# weight_cdf = w_cdf[i] * w_cdf[j]
# su = base + offset
u[base + offset] += weight * p_mass * vp#(vp + ti.math.dot(cp, dpos))
k_u[base + offset] += weight * p_mass * kp # Need not to multiply affine to heat conductivity(maybe?)
if u_face_mass[base + offset] < 0:
u_face_mass[base + offset] = weight * p_mass # Maybe in waterSim2d, they assume that every particles' mass is 1?
else:
u_face_mass[base + offset] += weight * p_mass # Maybe in waterSim2d, they assume that every particles' mass is 1?
fu[base + offset] += ti.math.dot(e, (-PFT) @ weight_grad )
# vol_u[base + offset] += weight_cdf
@ti.func
def scatter_face_v(xp, vp, cp, PFT, kp):
stagger = vec2(0.5, 0.0)
e = vec2(0.0, 1.0)
inv_dx = vec2(inv_grid_x, inv_grid_y).cast(ti.f32)
# inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# print(xp)
# Note, in SSJCTS14, they use cubic B-splinew = cubic_bspline_kernal(fx)
# w = cubic_bspline_kernal(fx)
# w_grad = cubic_bspline_kernal_grad(fx)
w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Quadratic Bspline
# w_cdf = [1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0]
w_grad = [fx-1.5, -2*(fx-1), fx-3.5] # Bspline gradient
# print("vp: ", vp)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
dpos = (offset.cast(ti.f32) - fx) * vec2(grid_x, grid_y)
weight_grad = vec2(w_grad[i][0]*w[j][1], w[i][0]*w_grad[j][1])
weight = w[i][0] * w[j][1] # x, y directions, respectively
# weight_cdf = w_cdf[i] * w_cdf[j]
# print("v" + str(i) + ", " + str(j) + ": ", weight * p_mass * (vp + cp.dot(dpos)))
v[base + offset] += weight * p_mass * vp#(vp + ti.math.dot(cp, dpos))
k_v[base + offset] += weight * p_mass * kp # Need not to multiply affine to heat conductivity(maybe?)
if v_face_mass[base + offset] < 0.0:
v_face_mass[base + offset] = weight * p_mass # Maybe in waterSim2d, they assume that every particles' mass is 1?
else:
v_face_mass[base + offset] += weight * p_mass # Maybe in waterSim2d, they assume that every particles' mass is 1?
fv[base + offset] += ti.math.dot(e, (-PFT) @ weight_grad )
# vol_v[base + offset] += weight_cdf
@ti.func
def scatter_cell(xp, par_J, par_Je, par_c, par_T, par_inv_lambda):
inv_dx = vec2(inv_grid_x, inv_grid_y).cast(ti.f32)
base = (xp * inv_dx - 0.5).cast(ti.i32)
fx = xp * inv_dx - base.cast(ti.f32)
# Note, in SSJCTS14, they use cubic B-splines
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2] # Quadratic Bspline
# w = cubic_bspline_kernal(fx)
# inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
# base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
# fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
# dpos = (offset.cast(ti.f32) - fx) * vec2(grid_x, grid_y)
weight = w[i][0] * w[j][1] # x, y directions, respectively
if cell_mass[i, j] < 0.0:
cell_mass[base + offset] = weight * p_mass
else:
cell_mass[base + offset] += weight * p_mass
Je[base + offset] += weight * p_mass * par_Je
J[base + offset] += weight * p_mass * par_J
c[base + offset] += weight * p_mass * par_c
T[base + offset] += weight * p_mass * par_T
inv_lambda[base + offset] += weight * p_mass * par_inv_lambda
# print("index:", i, j)
# print("weight: ", weight)
"""
su = base + offset
if Je[su] < 1e-10:
print("index: ", su[0], su[1])
print("Je: ", Je[su])
print("pmass: ", p_mass)
print("weight: ", weight)
"""
@ti.func
def set_Jp():
for i, j in Jp:
if Je[i, j] > 0.0:
Jp[i, j] = J[i, j] / Je[i, j]
@ti.kernel
def P2G():
# stagger_u = vec2(0.0, 0.5)
# stagger_v = vec2(0.5, 0.0)
for p in ti.grouped(particle_positions):
if particle_type[p] == P_FLUID:
xp = particle_positions[p]
# par_F = particle_Fe[p] @ particle_Fp[p]
par_Fe = particle_Fe[p]
par_Je = par_Fe.determinant()
par_Jp = particle_Fp[p].determinant()
"""
if par_Je < 0.0 or par_Jp < 0.0:
print("par_Je: ", par_Je)
print("Fe: ", particle_Fe[p])
print("par_Jp: ", par_Jp)
print("Fp: ", particle_Fp[p])
"""
par_J = par_Je * par_Jp
U, sig, V = ti.svd(par_Fe)
# P(F) F^T
par_f = 2 * particle_mu[p] * (par_Fe - [email protected]()) @ par_Fe.transpose() + ti.Matrix.identity(ti.f32, 2) * particle_la[p] * par_J * (par_J-1)
par_f = p_vol * par_f # f is 2 by 2 matrix, which will be multiplid by weight gradient
# face
scatter_face_u(xp, particle_velocities[p][0], cp_x[p], par_f, particle_k[p])
scatter_face_v(xp, particle_velocities[p][1], cp_y[p], par_f, particle_k[p])
# scatter_face(u, u_face_mass, k_u, fu, xp, particle_velocities[p][0],
# cp_x[p], par_f, stagger_u, particle_k[p], vec2(1.0, 0.0))
# scatter_face(v, v_face_mass, k_v, fv, xp, particle_velocities[p][1],
# cp_y[p], par_f, stagger_v, particle_k[p], vec2(0.0, 1.0))
# cell
# par_Je = particle_Fe[p].determinant()
# par_Jp = particle_Fp[p].determinant()
# par_J = par_Je * par_Jp
par_c = particle_c[p]
par_T = particle_T[p]
par_inv_lambda = 1.0 / particle_la[p]
scatter_cell(xp, par_J, par_Je, par_c, par_T, par_inv_lambda)
set_Jp() # Jp = J / Je for all cell
@ti.kernel
def clear_field():
u.fill(0.0)
v.fill(0.0)
u_face_mass.fill(-1.0)
v_face_mass.fill(-1.0)
fu.fill(0.0)
fv.fill(0.0)
k_u.fill(0.0)
k_v.fill(0.0)
vol_u.fill(0.0)
vol_v.fill(0.0)
cell_mass.fill(-1.0)
p.fill(0.0)
J.fill(0.0)
Je.fill(0.0)
Jp.fill(0.0)
c.fill(0.0)
T.fill(0.0)
inv_lambda.fill(0.0)
@ti.func
def is_valid(i, j):
return i >= 0 and i < m and j >= 0 and j < n
@ti.func
def vec2_is_valid(v):
return is_valid(v[0], v[1])
@ti.func
def is_fluid(i, j):
return is_valid(i, j) and cell_type[i, j] == utils.FLUID
@ti.func
def is_solid(i, j):
# return is_valid(i, j) and cell_type[i, j] == utils.SOLID
return i == 0 or i == m - 1 or j == 0 or j == n - 1
@ti.func
def is_air(i, j):
return is_valid(i, j) and cell_type[i, j] == utils.AIR
@ti.kernel
def mark_cell():
# AIR: empty
# SOLID: colliding
# FLUID: interior
# mark cells corresponding to SSJCTS14
for i, j in cell_type:
if not is_solid(i, j):
# check if it's interior i.e. every face has mass
# for cell(i, j), faces are u(i, j), u(i+1, j), v(i, j), v(i, j+1)
# print(u_face_mass[i, j])
# print(u_face_mass[i+1, j])
# print(v_face_mass[i, j])
# print(v_face_mass[i, j+1])
if u_face_mass[i, j] > 0.0 and u_face_mass[i+1, j] > 0.0 and v_face_mass[i, j] > 0.0 and v_face_mass[i, j+1] > 0.0 and cell_mass[i, j] > 0.0:
cell_type[i, j] = utils.FLUID
else:
cell_type[i, j] = utils.AIR
@ti.kernel
def assign_temperature():
for i, j in cell_type:
if cell_type == utils.AIR:
# air: 60 C
T[i, j] = T_air_init
elif cell_type == utils.SOLID:
# solid(edge): 100 C
T[i, j] = T_solid_phase_init
@ti.kernel
def face_normalize():
for i, j in u:
if u_face_mass[i, j] > 0.0:
u[i, j] = u[i, j] / u_face_mass[i, j]
for i, j in v:
# pr = False
# if v[i, j] > 1e-2:
# print("Before v: ", v[i, j], " index: ", i, j)
# print("face_mass: ", v_face_mass[i, j])
# pr = True
if v_face_mass[i, j] > 0.0:
v[i, j] = v[i, j] / v_face_mass[i, j]
# if pr:
# print("After v: ", v[i, j], " index: ", i, j)
for i, j in k_u:
if u_face_mass[i, j] > 0.0:
k_u[i, j] = k_u[i, j] / u_face_mass[i, j]
for i, j in k_v:
if v_face_mass[i, j] > 0.0:
k_v[i, j] = k_v[i, j] / v_face_mass[i, j]
@ti.kernel
def cell_normalize():
for i, j in J:
if cell_mass[i, j] > 0.0:
J[i, j] /= cell_mass[i, j]
for i, j in Je:
if cell_mass[i, j] > 0.0:
Je[i, j] /= cell_mass[i, j]
for i, j in c:
if cell_mass[i, j] > 0.0:
c[i, j] /= cell_mass[i, j]
for i, j in T:
# print("Before temp: ", T[i, j], ", index: ", i, j)
# print("cell mass: ", cell_mass[i, j])
if cell_mass[i, j] > 0.0:
T[i, j] /= cell_mass[i, j]
# print("After temp: ", T[i, j], ", index: ", i, j)
for i, j in inv_lambda:
if cell_mass[i, j] > 0.0:
inv_lambda[i, j] /= cell_mass[i, j]
@ti.kernel
def apply_force(dt: ti.f32):
# internal force (have been calculated in P2G)
for i, j in u:
if u_face_mass[i, j] > 0.0:
u[i, j] += (fu[i, j]/u_face_mass[i, j]) * dt
for i, j in v:
if v_face_mass[i, j] > 0.0:
v[i, j] += (fv[i, j]/v_face_mass[i, j]) * dt
# gravity(only v(y) direction)
for i, j in v:
v[i, j] += g * dt
@ti.kernel
def enforce_boundary():
# u solid
for i, j in u:
if is_solid(i - 1, j) or is_solid(i, j):
u[i, j] = 0.0
# u[i, j] = -u[i, j]
# v solid
for i, j in v:
if is_solid(i, j - 1) or is_solid(i, j):
v[i, j] = 0.0
# v[i, j] = -v[i, j]
@ti.kernel
def collect_face_vol():
# cubic b spline cdf
w_4 = [0.041667, 0.45833, 0.45833, 0.041667]
w_5 = [0.0026042, 0.1979125, 0.59896, 0.1979125, 0.0026042]
for i, j in vol_u:
for offsetX in ti.static(range(4)):
for offsetY in ti.static(range(5)):
if is_fluid(i-2+offsetX, j-2+offsetY):
vol_u[i, j] += w_4[offsetX] * w_5[offsetY]
for i, j in vol_v:
for offsetX in ti.static(range(5)):
for offsetY in ti.static(range(4)):
if is_fluid(i-2+offsetX, j-2+offsetY):
vol_v[i, j] += w_5[offsetX] * w_4[offsetY]
def solve_pressure(dt: ti.f32):
scale_A = dt / (grid_x * grid_x)
scale_b = 1 / grid_x
"""
pressure_solver.u.copy_from(u)
pressure_solver.v.copy_from(v)
pressure_solver.Jp.copy_from(Jp)
pressure_solver.Je.copy_from(Je)
pressure_solver.inv_lambda.copy_from(inv_lambda)
pressure_solver.cell_type.copy_from(cell_type)
"""
pressure_solver.system_init(scale_A, scale_b)
pressure_solver.solve(500)
p.copy_from(pressure_solver.p)
@ti.kernel
def apply_pressure(dt: ti.f32):
# scale = dt / (p_rho * grid_x)
scale = dt / grid_x
for i, j in ti.ndrange(m, n):
if is_fluid(i - 1, j) or is_fluid(i, j):
if is_solid(i - 1, j) or is_solid(i, j):
u[i, j] = 0
else:
inv_rho = vol_u[i, j] / u_face_mass[i, j]
u[i, j] += scale * (p[i, j] - p[i - 1, j]) * inv_rho
"""
if isnan(u[i, j]):
print("apply pressure to let u be nan")
print("u[i, j]: ", u[i, j])
print("pressure: ", p[i, j], p[i-1, j])
print("index: ", i, j)
"""
if is_fluid(i, j - 1) or is_fluid(i, j):
if is_solid(i, j - 1) or is_solid(i, j):
v[i, j] = 0
else:
inv_rho = vol_v[i, j] / v_face_mass[i, j]
v[i, j] += scale * (p[i, j] - p[i, j - 1]) * inv_rho
"""
if isnan(v[i, j]):
print("apply pressure to let v be nan")
print("v[i, j]: ", v[i, j])
print("pressure: ", p[i, j], p[i-1, j])
print("index: ", i, j)
"""
def solve_temperature(dt: ti.f32):
scale_A = dt / (grid_x * grid_x)
# scale_b = 1 / grid_x
scale_b = 1
"""
temperature_solver.k_u.copy_from(k_u)
temperature_solver.k_v.copy_from(k_v)
temperature_solver.old_T.copy_from(T)
temperature_solver.c.copy_from(c)
temperature_solver.cell_type.copy_from(cell_type)
"""
temperature_solver.system_init(scale_A, scale_b)
temperature_solver.solve(500)
T.copy_from(temperature_solver.p)
@ti.func
def tight_quadra_kernal(fx):
return [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
@ti.func
def tight_quadra_kernal_grad(fx):
return [fx-(3.0/2.0), -2*(fx-1), (fx-2)-(3.0/2.0)]
@ti.func
def gather_vp_u(xp):
stagger = vec2(0.0, 0.5)
inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Bspline
# tight quadratic stencil
w = tight_quadra_kernal(fx)
v_pic = 0.0
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
weight = w[i][0] * w[j][1]
v_pic += weight * u[base + offset]
# print(weight * grid_v[base + offset])
"""
if isnan(v_pic):
print("u_pic is nan")
print("u_pic: ", v_pic)
print("index: ", i, j)
print("weight: ", weight)
print("u: ", u[base + offset])
print("base: ", base)
"""
return v_pic
@ti.func
def gather_vp_v(xp):
stagger = vec2(0.5, 0.0)
inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Bspline
# w = [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
w = tight_quadra_kernal(fx)
v_pic = 0.0
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
weight = w[i][0] * w[j][1]
v_pic += weight * v[base + offset]
"""
if isnan(v_pic):
print("v_pic is nan")
print("v_pic: ", v_pic)
print("index: ", i, j)
print("weight: ", weight)
print("v: ", v[base + offset])
print("base: ", base)
# print(weight * grid_v[base + offset])
"""
return v_pic
@ti.func
def gather_cp_x(xp):
stagger = vec2(0.0, 0.5)
inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Bspline
# w = [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
w = tight_quadra_kernal(fx)
w_grad = tight_quadra_kernal_grad(fx)
# w_grad = [fx-(3.0/2.0), -2*(fx-1), (fx-2)-(3.0/2.0)]
# w_grad = [fx-1.5, -2*(fx-1), fx-3.5] # Bspline gradient
cp = vec2(0.0, 0.0)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
# dpos = offset.cast(ti.f32) - fx
# weight = w[i][0] * w[j][1]
# cp += 4 * weight * dpos * grid_v[base + offset] * inv_dx[0]
weight_grad = vec2(w_grad[i][0]*w[j][1], w[i][0]*w_grad[j][1])
cp += weight_grad * u[base + offset]
return cp
@ti.func
def gather_cp_y(xp):
stagger = vec2(0.5, 0.0)
inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Bspline
# w_grad = [fx-1.5, -2*(fx-1), fx-3.5] # Bspline gradient
# w = [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
# w_grad = [fx-(3.0/2.0), -2*(fx-1), (fx-2)-(3.0/2.0)]
w = tight_quadra_kernal(fx)
w_grad = tight_quadra_kernal_grad(fx)
cp = vec2(0.0, 0.0)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
# dpos = offset.cast(ti.f32) - fx
# weight = w[i][0] * w[j][1]
# cp += 4 * weight * dpos * grid_v[base + offset] * inv_dx[0]
weight_grad = vec2(w_grad[i][0]*w[j][1], w[i][0]*w_grad[j][1])
cp += weight_grad * v[base + offset]
return cp
@ti.func
def gather_Tp(xp):
inv_dx = vec2(inv_grid_x, inv_grid_y).cast(ti.f32)
base = (xp * inv_dx - 0.5).cast(ti.i32)
fx = xp * inv_dx - base.cast(ti.f32)
# w = [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
w = tight_quadra_kernal(fx)
Tp = 0.0
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
# dpos = offset.cast(ti.f32) - fx
weight = w[i][0] * w[j][1]
# cp += 4 * weight * dpos * grid_v[base + offset] * inv_dx[0]
Tp += weight * T[base + offset]
return Tp
@ti.func
def gather_vp_grad_u(xp):
stagger = vec2(0.0, 0.5)
e = vec2(1.0, 0.0)
inv_dx = vec2(1.0 / grid_x, 1.0 / grid_y).cast(ti.f32)
base = (xp * inv_dx - (stagger + 0.5)).cast(ti.i32)
fx = xp * inv_dx - (base.cast(ti.f32) + stagger)
# w = [0.5*(1.5-fx)**2, 0.75-(fx-1)**2, 0.5*(fx-0.5)**2] # Bspline
# w_grad = [fx-1.5, -2*(fx-1), fx-3.5] # Bspline gradient
# w = [(1.0 / 2.0) * (fx ** 2) - (3.0 / 2.0) * fx + (9.0 / 8.0), -((fx-1)**2) + (3.0/4.0), (1.0 / 2.0) * ((fx-2) ** 2) - (3.0 / 2.0) * (fx-2) + (9.0 / 8.0)]
w = tight_quadra_kernal(fx)
w_grad = tight_quadra_kernal_grad(fx)
# w_grad = [fx-(3.0/2.0), -2*(fx-1), (fx-2)-(3.0/2.0)]
vp_grad = ti.Matrix.zero(ti.f32, 2, 2)
for i in ti.static(range(3)):
for j in ti.static(range(3)):
offset = vec2(i, j)
if vec2_is_valid(base + offset):
# weight = w[i][0] * w[j][1]
weight_grad = vec2(w_grad[i][0]*w[j][1], w[i][0]*w_grad[j][1])
vp_grad += (u[base + offset] * e).outer_product(weight_grad)
return vp_grad