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fluid_simulator.py
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fluid_simulator.py
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import taichi as ti
import taichi_glsl as ts
import utils
from utils import *
from mgpcg import MGPCGPoissonSolver
from pressure_project import PressureProjectStrategy
from level_set import FastMarchingLevelSet, FastSweepingLevelSet
from surface_tension import SurfaceTension
from volume_control import PressureProjectWithVolumeControlStrategy
from functools import reduce
import time
import numpy as np
ti.init(arch=ti.cuda, kernel_profiler=True)
ADVECT_REDISTANCE = 0
MARKERS = 1
FAST_SWEEPING_METHOD = 0
FAST_MARCHING_METHOD = 1
@ti.data_oriented
class FluidSimulator:
def __init__(self,
dim = 2,
res = (128, 128),
dt = 1.25e-2,
substeps = 1,
dx = 1.0,
rho = 1000.0,
gravity = [0, -9.8],
p0 = 1e-3,
real = float):
# ADVECT_REDISTANCE: advect the level-set with Semi-Lagrangian, then redistance it (Standard)
# MARKERS: advect markers with Semi-Lagrangian, then build the level-set from markers
self.solver_type = ADVECT_REDISTANCE
self.dim = dim
self.real = real
self.res = res
self.dx = dx
self.dt = dt
self.total_t = 0.0 # total simulation time
self.p0 = p0 # the standard atmospheric pressure
self.rho = rho # density
self.gravity = gravity # body force
self.substeps = substeps
# cell_type
self.cell_type = ti.field(dtype=ti.i32)
self.velocity = [ti.field(dtype=real) for _ in range(self.dim)] # MAC grid
self.velocity_backup = [ti.field(dtype=real) for _ in range(self.dim)] # backup / use as weight in apic update
self.pressure = ti.field(dtype=real)
# extrap utils
self.valid = ti.field(dtype=ti.i32)
self.valid_temp = ti.field(dtype=ti.i32)
# marker/apic particles
self.total_mk = ti.field(dtype=ti.i32, shape = ()) # total number of particles/markers
self.p_x = ti.Vector.field(dim, dtype=real) # positions
indices = ti.ijk if self.dim == 3 else ti.ij
max_particles = reduce(lambda x, y : x * y, res) * (2 ** dim)
ti.root.dense(ti.i, max_particles).place(self.p_x)
ti.root.dense(indices, res).place(self.cell_type, self.pressure)
ti.root.dense(indices, [res[_] + 1 for _ in range(self.dim)]).place(self.valid, self.valid_temp)
for d in range(self.dim):
ti.root.dense(indices, [res[_] + (d == _) for _ in range(self.dim)]).place(self.velocity[d], self.velocity_backup[d])
# Level-Set
self.loop_order = FAST_SWEEPING_METHOD
if self.loop_order == FAST_SWEEPING_METHOD:
self.level_set = FastSweepingLevelSet(self.dim,
self.res,
self.dx,
self.real)
else:
self.level_set = FastMarchingLevelSet(self.dim,
self.res,
self.dx,
self.real)
# MGPCG
self.n_mg_levels = 4
self.pre_and_post_smoothing = 2
self.bottom_smoothing = 10
self.iterations = 500
self.verbose = True
self.poisson_solver = MGPCGPoissonSolver(self.dim,
self.res,
self.n_mg_levels,
self.pre_and_post_smoothing,
self.bottom_smoothing,
self.real)
# Pressure Solve
self.ghost_fluid_method = True # Gibou et al. [GFCK02]
self.strategy = PressureProjectStrategy(self.dim,
self.velocity,
self.ghost_fluid_method,
self.level_set.phi,
self.p0)
self.volume_control_stragtegy = PressureProjectWithVolumeControlStrategy(self.dim,
self.velocity,
self.ghost_fluid_method,
self.level_set.phi,
self.p0,
self.level_set,
self.dt) # [Losasso et al. 2008]
# capillary surface tension [Zheng et al. 2006]
self.surface_tension = SurfaceTension(simulator = self)
@ti.func
def is_valid(self, I):
return all(I >= 0) and all(I < self.res)
@ti.func
def is_fluid(self, I):
return self.is_valid(I) and self.cell_type[I] == utils.FLUID
@ti.func
def is_solid(self, I):
return not self.is_valid(I) or self.cell_type[I] == utils.SOLID
@ti.func
def is_air(self, I):
return self.is_valid(I) and self.cell_type[I] == utils.AIR
@ti.func
def vel_interp(self, pos):
v = ti.Vector.zero(self.real, self.dim)
for k in ti.static(range(self.dim)):
v[k] = utils.sample(self.velocity[k], pos / self.dx - 0.5 * (1 - ti.Vector.unit(self.dim, k)))
return v
@ti.kernel
def advect_markers(self, dt : ti.f32):
for p in range(self.total_mk[None]):
midpos = self.p_x[p] + self.vel_interp(self.p_x[p]) * (0.5 * dt)
self.p_x[p] += self.vel_interp(midpos) * dt
@ti.kernel
def apply_markers(self):
for I in ti.grouped(self.cell_type):
if self.cell_type[I] != utils.SOLID:
self.cell_type[I] = utils.AIR
for I in ti.grouped(self.cell_type):
if self.cell_type[I] != utils.SOLID and self.level_set.phi[I] <= 0:
self.cell_type[I] = utils.FLUID
@ti.kernel
def add_gravity(self, dt : ti.f32):
for k in ti.static(range(self.dim)):
if ti.static(self.gravity[k] != 0):
g = self.gravity[k]
for I in ti.grouped(self.velocity[k]):
self.velocity[k][I] += g * dt
@ti.kernel
def enforce_boundary(self):
for I in ti.grouped(self.cell_type):
if self.cell_type[I] == utils.SOLID:
for k in ti.static(range(self.dim)):
self.velocity[k][I] = 0
self.velocity[k][I + ti.Vector.unit(self.dim, k)] = 0
def solve_pressure(self, dt, strategy):
strategy.scale_A = dt / (self.rho * self.dx * self.dx)
strategy.scale_b = 1 / self.dx
start1 = time.perf_counter()
self.poisson_solver.reinitialize(self.cell_type, strategy)
end1 = time.perf_counter()
start2 = time.perf_counter()
self.poisson_solver.solve(self.iterations, self.verbose)
end2 = time.perf_counter()
print(f'\033[33minit cost {end1 - start1}s, solve cost {end2 - start2}s\033[0m')
self.pressure.copy_from(self.poisson_solver.x)
@ti.kernel
def apply_pressure(self, dt : ti.f32):
scale = dt / (self.rho * self.dx)
for k in ti.static(range(self.dim)):
for I in ti.grouped(self.cell_type):
I_1 = I - ti.Vector.unit(self.dim, k)
if self.is_fluid(I_1) or self.is_fluid(I):
if self.is_solid(I_1) or self.is_solid(I): self.velocity[k][I] = 0
# FLuid-Air
elif self.is_air(I):
if ti.static(self.ghost_fluid_method):
c = (self.level_set.phi[I_1] - self.level_set.phi[I]) / self.level_set.phi[I_1]
self.velocity[k][I] -= scale * (self.p0 - self.pressure[I_1]) * min(c, 1e3) # # limit the coefficient
else: self.velocity[k][I] -= scale * (self.p0 - self.pressure[I_1])
# Air-Fluid
elif self.is_air(I_1):
if ti.static(self.ghost_fluid_method):
c = (self.level_set.phi[I] - self.level_set.phi[I_1]) / self.level_set.phi[I]
self.velocity[k][I] -= scale * (self.pressure[I] - self.p0) * min(c, 1e3)
else: self.velocity[k][I] -= scale * (self.pressure[I] - self.p0)
# Fluid-Fluid
else: self.velocity[k][I] -= scale * (self.pressure[I] - self.pressure[I_1])
@ti.func
def advect(self, I, dst, src, offset, dt):
pos = (I + offset) * self.dx
midpos = pos - self.vel_interp(pos) * (0.5 * dt)
p0 = pos - self.vel_interp(midpos) * dt
dst[I] = utils.sample(src, p0 / self.dx - offset)
@ti.kernel
def advect_quantity(self, dt : ti.f32):
if ti.static(self.solver_type == ADVECT_REDISTANCE):
for I in ti.grouped(self.level_set.phi):
self.advect(I, self.level_set.phi_temp, self.level_set.phi, 0.5, dt)
for k in ti.static(range(self.dim)):
offset = 0.5 * (1 - ti.Vector.unit(self.dim, k))
for I in ti.grouped(self.velocity_backup[k]):
self.advect(I, self.velocity_backup[k], self.velocity[k], offset, dt)
def update_quantity(self):
if ti.static(self.solver_type == ADVECT_REDISTANCE):
self.level_set.phi.copy_from(self.level_set.phi_temp)
for k in range(self.dim):
self.velocity[k].copy_from(self.velocity_backup[k])
@ti.kernel
def mark_valid(self, k : ti.template()):
for I in ti.grouped(self.velocity[k]):
# NOTE that the the air-liquid interface is valid
I_1 = I - ti.Vector.unit(self.dim, k)
if self.is_fluid(I_1) or self.is_fluid(I):
self.valid[I] = 1
else:
self.valid[I] = 0
@ti.kernel
def diffuse_quantity(self, dst : ti.template(), src : ti.template(), valid_dst : ti.template(), valid : ti.template()):
for I in ti.grouped(dst):
if valid[I] == 0:
tot = ti.cast(0, self.real)
cnt = 0
for offset in ti.static(ti.grouped(ti.ndrange(*((-1, 2), ) * self.dim))):
if valid[I + offset] == 1:
tot += src[I + offset]
cnt += 1
if cnt > 0:
dst[I] = tot / ti.cast(cnt, self.real)
valid_dst[I] = 1
def extrap_velocity(self):
for k in range(self.dim):
self.mark_valid(k)
for i in range(10):
self.velocity_backup[k].copy_from(self.velocity[k])
self.valid_temp.copy_from(self.valid)
self.diffuse_quantity(self.velocity[k], self.velocity_backup[k], self.valid, self.valid_temp)
def begin_substep(self, dt):
self.advect_markers(dt)
self.advect_quantity(dt)
self.update_quantity()
if self.solver_type == MARKERS:
self.level_set.build_from_markers(self.p_x, self.total_mk)
else:
self.level_set.redistance()
self.apply_markers()
self.enforce_boundary()
if self.verbose:
mks = max(np.max(self.velocity[0].to_numpy()), np.max(self.velocity[1].to_numpy()))
print(f'\033[36mMax advect velocity: {mks}\033[0m')
def end_substep(self, dt):
# Apply the capillary surface tension on the interface using a semi-implicit method
self.surface_tension.solve_surface_tension()
self.extrap_velocity()
self.enforce_boundary()
# Apply another projection step to enforce the divergence-free condition for the final state
self.solve_pressure(dt, self.volume_control_stragtegy) # with a volume correction term
if self.verbose:
prs = np.max(self.pressure.to_numpy())
print(f'\033[36mMax pressure: {prs}\033[0m')
self.apply_pressure(dt)
self.extrap_velocity()
self.enforce_boundary()
self.total_t += self.dt
def substep(self, dt):
self.begin_substep(dt)
self.add_gravity(dt)
self.enforce_boundary()
self.extrap_velocity()
self.enforce_boundary()
self.solve_pressure(dt, self.strategy)
if self.verbose:
prs = np.max(self.pressure.to_numpy())
print(f'\033[36mMax pressure: {prs}\033[0m')
self.apply_pressure(dt)
self.extrap_velocity()
self.enforce_boundary()
self.end_substep(dt)
def run(self, max_steps, visualizer, verbose = True):
self.verbose = verbose
step = 0
while step < max_steps or max_steps == -1:
print(f'Current progress: ({step} / {max_steps})')
for substep in range(self.substeps):
self.substep(self.dt)
visualizer.visualize(self)
step += 1
@ti.kernel
def init_boundary(self):
for I in ti.grouped(self.cell_type):
if any(I == 0) or any(I + 1 == self.res):
self.cell_type[I] = utils.SOLID
@ti.kernel
def init_markers(self):
self.total_mk[None] = 0
for I in ti.grouped(self.cell_type):
if self.cell_type[I] == utils.FLUID:
for offset in ti.static(ti.grouped(ti.ndrange(*((0, 2), ) * self.dim))):
num = ti.atomic_add(self.total_mk[None], 1)
self.p_x[num] = (I + (offset + [ti.random() for _ in ti.static(range(self.dim))]) / 2) * self.dx
@ti.kernel
def reinitialize(self):
for I in ti.grouped(ti.ndrange(* [self.res[_] for _ in range(self.dim)])):
self.cell_type[I] = 0
self.pressure[I] = 0
for k in ti.static(range(self.dim)):
I_1 = I + ti.Vector.unit(self.dim, k)
self.velocity[k][I] = 0
self.velocity[k][I_1] = 0
self.velocity_backup[k][I] = 0
self.velocity_backup[k][I_1] = 0
def initialize(self, initializer):
self.reinitialize()
self.cell_type.fill(utils.AIR)
initializer.init_scene(self)
self.init_boundary()
self.init_markers()