VoxelEngine/FluidSim/LatticeBoltzmann.py

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Python
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2021-08-03 10:33:07 +02:00
import matplotlib.pyplot as plt
import numpy as np
"""
Create Your Own Lattice Boltzmann Simulation (With Python)
Philip Mocz (2020) Princeton Univeristy, @PMocz
Simulate flow past cylinder
for an isothermal fluid
"""
def main():
""" Finite Volume simulation """
# Simulation parameters
Nx = 400 # resolution x-dir
Ny = 100 # resolution y-dir
rho0 = 100 # average density
tau = 0.6 # collision timescale
Nt = 80000 # number of timesteps
plotRealTime = True # switch on for plotting as the simulation goes along
# Lattice speeds / weights
NL = 9
idxs = np.arange(NL)
cxs = np.array([0, 0, 1, 1, 1, 0, -1, -1, -1])
cys = np.array([0, 1, 1, 0, -1, -1, -1, 0, 1])
weights = np.array([4 / 9, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 9, 1 / 36]) # sums to 1
# Initial Conditions
F = np.ones((Ny, Nx, NL)) # * rho0 / NL
has_fluid = np.ones((Ny, Nx), dtype=np.bool)
has_fluid[int(Ny/2):, :] = False
np.random.seed(42)
F += 0.01 * np.random.randn(Ny, Nx, NL)
X, Y = np.meshgrid(range(Nx), range(Ny))
F[:, :, 3] += 2 * (1 + 0.2 * np.cos(2 * np.pi * X / Nx * 4))
# F[:, :, 5] += 1
rho = np.sum(F, 2)
for i in idxs:
F[:, :, i] *= rho0 / rho
# Cylinder boundary
X, Y = np.meshgrid(range(Nx), range(Ny))
cylinder = (X - Nx / 4) ** 2 + (Y - Ny / 2) ** 2 < (Ny / 4) ** 2
inner_cylinder = (X - Nx / 4) ** 2 + (Y - Ny / 2) ** 2 < (Ny / 4 - 2) ** 2
F[cylinder] = 0
F[0, :] = 0
F[Ny - 1, :] = 0
# F[int(Ny/2):, :] = 0
has_fluid[cylinder] = False
has_fluid[0, :] = False
has_fluid[Ny - 1, :] = False
# for i in idxs:
# F[:, :, i] *= has_fluid
# Prep figure
fig = plt.figure(figsize=(4, 2), dpi=80)
reflection_mapping = [0, 5, 6, 7, 8, 1, 2, 3, 4]
# Simulation Main Loop
for it in range(Nt):
print(it)
# Drift
new_has_fluid = np.zeros((Ny, Nx))
F_sum = np.sum(F, 2)
for i, cx, cy in zip(idxs, cxs, cys):
F_part = F[:, :, i] / F_sum
F_part[F_sum == 0] = 0
to_move = F_part * (has_fluid * 1.0)
to_move = (np.roll(to_move, cx, axis=1))
to_move = (np.roll(to_move, cy, axis=0))
new_has_fluid += to_move
F[:, :, i] = np.roll(F[:, :, i], cx, axis=1)
F[:, :, i] = np.roll(F[:, :, i], cy, axis=0)
# has_fluid = new_has_fluid > 0.5
# new_has_fluid[F_sum == 0] += has_fluid[F_sum == 0] * 1.0
# new_has_fluid[(np.abs(F_sum) < 0.000000001)] = 0
fluid_sum = np.sum(has_fluid * 1.0)
has_fluid = (new_has_fluid / np.sum(new_has_fluid * 1.0)) * fluid_sum
print('fluid_cells: %d' % np.sum(has_fluid * 1))
# for i in idxs:
# F[:, :, i] *= has_fluid
bndry = np.zeros((Ny, Nx), dtype=np.bool)
bndry[0, :] = True
bndry[Ny - 1, :] = True
# bndry[:, 0] = True
# bndry[:, Nx - 1] = True
bndry = np.logical_or(bndry, cylinder)
# bndry = np.logical_or(bndry, has_fluid < 0.5)
# Set reflective boundaries
bndryF = F[bndry, :]
bndryF = bndryF[:, reflection_mapping]
sum_f = np.sum(F)
print('Sum of Forces: %f' % sum_f)
# sum_f_cyl = np.sum(F[cylinder])
# print('Sum of Forces in cylinder: %f' % sum_f_cyl)
# sum_f_inner_cyl = np.sum(F[inner_cylinder])
# print('Sum of Forces in inner cylinder: %f' % sum_f_inner_cyl)
# if sum_f > 4000000.000000:
# test = 1
# F[Ny - 1, :, 5] += 0.1
# F[0, :, 1] -= 0.1
# F[0, :, 5] += 0.1
# F[Ny - 1, :, 1] -= 0.1
# Calculate fluid variables
rho = np.sum(F, 2)
ux = np.sum(F * cxs, 2) / rho
uy = np.sum(F * cys, 2) / rho
ux[(np.abs(rho) < 0.000000001)] = 0
uy[(np.abs(rho) < 0.000000001)] = 0
# print('minimum rho: %f' % np.min(np.abs(rho)))
# print('Maximum F: %f' % np.max(F))
# print('Minimum F: %f' % np.min(F))
# Apply Collision
Feq = np.zeros(F.shape)
for i, cx, cy, w in zip(idxs, cxs, cys, weights):
Feq[:, :, i] = rho * w * (
1 + 3 * (cx * ux + cy * uy) + 9 * (cx * ux + cy * uy) ** 2 / 2 - 3 * (ux ** 2 + uy ** 2) / 2)
F += -(1.0 / tau) * (F - Feq)
# Apply boundary
F[bndry, :] = bndryF
# plot in real time - color 1/2 particles blue, other half red
if (plotRealTime and (it % 10) == 0) or (it == Nt - 1):
plt.cla()
ux[cylinder] = 0
uy[cylinder] = 0
vorticity = (np.roll(ux, -1, axis=0) - np.roll(ux, 1, axis=0)) - (
np.roll(uy, -1, axis=1) - np.roll(uy, 1, axis=1))
vorticity[cylinder] = np.nan
# vorticity *= has_fluid
cmap = plt.cm.bwr
cmap.set_bad('black')
# plt.imshow(vorticity, cmap='bwr')
plt.imshow(has_fluid * 2.0 - 1.0, cmap='bwr')
# plt.imshow(bndry * 2.0 - 1.0, cmap='bwr')
plt.clim(-.1, .1)
ax = plt.gca()
ax.invert_yaxis()
ax.get_xaxis().set_visible(False)
ax.get_yaxis().set_visible(False)
ax.set_aspect('equal')
plt.pause(0.001)
# Save figure
# plt.savefig('latticeboltzmann.png', dpi=240)
plt.show()
return 0
if __name__ == "__main__":
main()