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IISPH.py
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IISPH.py
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import taichi as ti
from sph_base import SPHBase
class IISPHSolver(SPHBase):
def __init__(self, particle_system):
super().__init__(particle_system)
self.a_ii = ti.field(dtype=float, shape=self.ps.particle_max_num)
self.density_deviation = ti.field(dtype=float, shape=self.ps.particle_max_num)
self.last_pressure = ti.field(dtype=float, shape=self.ps.particle_max_num)
self.avg_density_error = ti.field(dtype=float, shape=())
self.ps.acceleration = ti.Vector.field(self.ps.dim, dtype=float)
self.pressure_accel = ti.Vector.field(self.ps.dim, dtype=float)
particle_node = ti.root.dense(ti.i, self.ps.particle_max_num)
particle_node.place(self.ps.acceleration, self.pressure_accel)
self.dt[None] = 2e-4
@ti.kernel
def predict_advection(self):
# Compute a_ii
for p_i in range(self.ps.particle_num[None]):
x_i = self.ps.x[p_i]
sum_neighbor = 0.0
sum_neighbor_of_neighbor = 0.0
m_Vi = self.ps.m_V[p_i]
density_i = self.ps.density[p_i]
density_i2 = density_i * density_i
density_02 = self.density_0 * self.density_0
self.a_ii[p_i] = 0.0
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
sum_neighbor_inner = ti.Vector([0.0 for _ in range(self.ps.dim)])
for k in range(self.ps.fluid_neighbors_num[p_i]):
density_k = self.ps.density[k]
density_k2 = density_k * density_k
p_k = self.ps.fluid_neighbors[p_i, j]
x_k = self.ps.x[p_k]
sum_neighbor_inner += self.ps.m_V[p_k] * self.cubic_kernel_derivative(x_i - x_k) / density_k2
kernel_grad_ij = self.cubic_kernel_derivative(x_i - x_j)
sum_neighbor -= (self.ps.m_V[p_j] * sum_neighbor_inner).dot(kernel_grad_ij)
sum_neighbor_of_neighbor -= (self.ps.m_V[p_j] * kernel_grad_ij).dot(kernel_grad_ij)
sum_neighbor_of_neighbor *= m_Vi / density_i2
self.a_ii[p_i] += (sum_neighbor + sum_neighbor_of_neighbor) * self.dt[None] * self.dt[None] * density_02
# Boundary neighbors
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
sum_neighbor_inner = ti.Vector([0.0 for _ in range(self.ps.dim)])
for k in range(self.ps.solid_neighbors_num[p_i]):
density_k = self.ps.density[k]
density_k2 = density_k * density_k
p_k = self.ps.solid_neighbors[p_i, j]
x_k = self.ps.x[p_k]
sum_neighbor_inner += self.ps.m_V[p_k] * self.cubic_kernel_derivative(x_i - x_k) / density_k2
kernel_grad_ij = self.cubic_kernel_derivative(x_i - x_j)
sum_neighbor -= (self.ps.m_V[p_j] * sum_neighbor_inner).dot(kernel_grad_ij)
sum_neighbor_of_neighbor -= (self.ps.m_V[p_j] * kernel_grad_ij).dot(kernel_grad_ij)
sum_neighbor_of_neighbor *= m_Vi / density_i2
self.a_ii[p_i] += (sum_neighbor + sum_neighbor_of_neighbor) * self.dt[None] * self.dt[None] * density_02
# Compute source term (i.e., density deviation)
# Compute the predicted v^star
for p_i in range(self.ps.particle_num[None]):
if self.ps.material[p_i] == self.ps.material_fluid:
self.ps.v[p_i] += self.dt[None] * self.ps.acceleration[p_i]
for p_i in range(self.ps.particle_num[None]):
x_i = self.ps.x[p_i]
density_i = self.ps.density[p_i]
divergence = 0.0
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
divergence += self.ps.m_V[p_j] * (self.ps.v[p_i] - self.ps.v[p_j]).dot(self.cubic_kernel_derivative(x_i - x_j))
# Boundary neighbors
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
divergence += self.ps.m_V[p_j] * (self.ps.v[p_i] - self.ps.v[p_j]).dot(self.cubic_kernel_derivative(x_i - x_j))
self.density_deviation[p_i] = self.density_0 - density_i - self.dt[None] * divergence * self.density_0
# Clear all pressures
for p_i in range(self.ps.particle_num[None]):
# self.last_pressure[p_i] = 0.0
# self.ps.pressure[p_i] = 0.0
self.last_pressure[p_i] = 0.5 * self.ps.pressure[p_i]
def pressure_solve(self):
iteration = 0
while iteration < 1000:
self.avg_density_error[None] = 0.0
self.pressure_solve_iteration()
iteration += 1
if iteration % 100 == 0:
print(f'iter {iteration}, density err {self.avg_density_error[None]}')
if self.avg_density_error[None] < 1e-3:
# print(f'Stop criterion satisfied at iter {iteration}, density err {self.avg_density_error[None]}')
break
@ti.kernel
def pressure_solve_iteration(self):
omega = 0.5
# Compute pressure acceleration
for p_i in range(self.ps.particle_num[None]):
# if self.ps.material[p_i] != self.ps.material_fluid:
# self.pressure_accel[p_i].fill(0)
# continue
x_i = self.ps.x[p_i]
d_v = ti.Vector([0.0 for _ in range(self.ps.dim)])
dpi = self.last_pressure[p_i] / self.ps.density[p_i] ** 2
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
dpj = self.last_pressure[p_j] / self.ps.density[p_j] ** 2
# Compute the pressure force contribution, Symmetric Formula
d_v += -self.density_0 * self.ps.m_V[p_j] * (dpi + dpj) \
* self.cubic_kernel_derivative(x_i - x_j)
# Boundary neighbors
dpj = self.last_pressure[p_i] / self.density_0 ** 2
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
# Compute the pressure force contribution, Symmetric Formula
d_v += -self.density_0 * self.ps.m_V[p_j] * (dpi + dpj) \
* self.cubic_kernel_derivative(x_i - x_j)
self.pressure_accel[p_i] += d_v
# Compute Ap and compute new pressure
for p_i in range(self.ps.particle_num[None]):
x_i = self.ps.x[p_i]
Ap = 0.0
dt2 = self.dt[None] * self.dt[None]
accel_p_i = self.pressure_accel[p_i]
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
Ap += self.ps.m_V[p_j] * (accel_p_i - self.pressure_accel[p_j]).dot(self.cubic_kernel_derivative(x_i - x_j))
# Boundary neighbors
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
Ap += self.ps.m_V[p_j] * (accel_p_i - self.pressure_accel[p_j]).dot(self.cubic_kernel_derivative(x_i - x_j))
Ap *= dt2 * self.density_0
# print(self.a_ii[1])
if abs(self.a_ii[p_i]) > 1e-6:
# Relaxed Jacobi
self.ps.pressure[p_i] = ti.max(self.last_pressure[p_i] + omega * (self.density_deviation[p_i] - Ap) / self.a_ii[p_i], 0.0)
else:
self.ps.pressure[p_i] = 0.0
if self.ps.pressure[p_i] != 0.0:
# new_density = self.density_0
# if p_i == 100:
# print(" Ap ", Ap, " density deviation ", self.density_deviation[p_i], 'a_ii ', self.a_ii[p_i])
self.avg_density_error[None] += abs(Ap - self.density_deviation[p_i]) / self.density_0
self.avg_density_error[None] /= self.ps.particle_num[None]
for p_i in range(self.ps.particle_num[None]):
# Update the pressure
self.last_pressure[p_i] = self.ps.pressure[p_i]
@ti.kernel
def compute_densities(self):
for p_i in range(self.ps.particle_num[None]):
if self.ps.material[p_i] != self.ps.material_fluid:
continue
x_i = self.ps.x[p_i]
self.ps.density[p_i] = self.ps.m_V[p_i] * self.cubic_kernel(0.0)
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
self.ps.density[p_i] += self.ps.m_V[p_j] * self.cubic_kernel((x_i - x_j).norm())
# Boundary neighbors
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
self.ps.density[p_i] += self.ps.m_V[p_j] * self.cubic_kernel((x_i - x_j).norm())
self.ps.density[p_i] *= self.density_0
@ti.kernel
def compute_pressure_forces(self):
for p_i in range(self.ps.particle_num[None]):
if self.ps.material[p_i] != self.ps.material_fluid:
self.pressure_accel[p_i].fill(0)
continue
self.pressure_accel[p_i].fill(0)
x_i = self.ps.x[p_i]
d_v = ti.Vector([0.0 for _ in range(self.ps.dim)])
dpi = self.ps.pressure[p_i] / self.ps.density[p_i] ** 2
# Fluid neighbors
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
dpj = self.ps.pressure[p_j] / self.ps.density[p_j] ** 2
# Compute the pressure force contribution, Symmetric Formula
d_v += -self.density_0 * self.ps.m_V[p_j] * (dpi + dpj) \
* self.cubic_kernel_derivative(x_i - x_j)
# Boundary neighbors
dpj = self.ps.pressure[p_i] / self.density_0 ** 2
# dpj = 0.0
## Akinci2012
for j in range(self.ps.solid_neighbors_num[p_i]):
p_j = self.ps.solid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
# Compute the pressure force contribution, Symmetric Formula
d_v += -self.density_0 * self.ps.m_V[p_j] * (dpi + dpj) \
* self.cubic_kernel_derivative(x_i - x_j)
self.pressure_accel[p_i] = d_v
@ti.kernel
def compute_non_pressure_forces(self):
for p_i in range(self.ps.particle_num[None]):
# if self.ps.material[p_i] != self.ps.material_fluid:
# self.ps.acceleration[p_i].fill(0)
# continue
x_i = self.ps.x[p_i]
# Add body force
d_v = ti.Vector([0.0 for _ in range(self.ps.dim)])
d_v[1] = self.g
for j in range(self.ps.fluid_neighbors_num[p_i]):
p_j = self.ps.fluid_neighbors[p_i, j]
x_j = self.ps.x[p_j]
d_v += self.viscosity_force(p_i, p_j, x_i - x_j)
self.ps.acceleration[p_i] = d_v
@ti.kernel
def advect(self):
# Symplectic Euler
for p_i in range(self.ps.particle_num[None]):
if self.ps.material[p_i] == self.ps.material_fluid:
self.ps.v[p_i] += self.dt[None] * self.pressure_accel[p_i]
self.ps.x[p_i] += self.dt[None] * self.ps.v[p_i]
def substep(self):
self.compute_densities()
self.compute_non_pressure_forces()
self.predict_advection()
self.pressure_solve()
self.compute_pressure_forces()
self.advect()