lattice Boltzmann example/playground
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FluidSim/LatticeBoltzmann.py
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181
FluidSim/LatticeBoltzmann.py
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import matplotlib.pyplot as plt
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import numpy as np
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"""
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Create Your Own Lattice Boltzmann Simulation (With Python)
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Philip Mocz (2020) Princeton Univeristy, @PMocz
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Simulate flow past cylinder
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for an isothermal fluid
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"""
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def main():
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""" Finite Volume simulation """
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# Simulation parameters
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Nx = 400 # resolution x-dir
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Ny = 100 # resolution y-dir
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rho0 = 100 # average density
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tau = 0.6 # collision timescale
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Nt = 80000 # number of timesteps
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plotRealTime = True # switch on for plotting as the simulation goes along
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# Lattice speeds / weights
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NL = 9
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idxs = np.arange(NL)
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cxs = np.array([0, 0, 1, 1, 1, 0, -1, -1, -1])
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cys = np.array([0, 1, 1, 0, -1, -1, -1, 0, 1])
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weights = np.array([4 / 9, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 9, 1 / 36, 1 / 9, 1 / 36]) # sums to 1
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# Initial Conditions
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F = np.ones((Ny, Nx, NL)) # * rho0 / NL
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has_fluid = np.ones((Ny, Nx), dtype=np.bool)
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has_fluid[int(Ny/2):, :] = False
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np.random.seed(42)
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F += 0.01 * np.random.randn(Ny, Nx, NL)
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X, Y = np.meshgrid(range(Nx), range(Ny))
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F[:, :, 3] += 2 * (1 + 0.2 * np.cos(2 * np.pi * X / Nx * 4))
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# F[:, :, 5] += 1
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rho = np.sum(F, 2)
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for i in idxs:
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F[:, :, i] *= rho0 / rho
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# Cylinder boundary
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X, Y = np.meshgrid(range(Nx), range(Ny))
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cylinder = (X - Nx / 4) ** 2 + (Y - Ny / 2) ** 2 < (Ny / 4) ** 2
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inner_cylinder = (X - Nx / 4) ** 2 + (Y - Ny / 2) ** 2 < (Ny / 4 - 2) ** 2
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F[cylinder] = 0
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F[0, :] = 0
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F[Ny - 1, :] = 0
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# F[int(Ny/2):, :] = 0
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has_fluid[cylinder] = False
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has_fluid[0, :] = False
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has_fluid[Ny - 1, :] = False
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# for i in idxs:
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# F[:, :, i] *= has_fluid
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# Prep figure
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fig = plt.figure(figsize=(4, 2), dpi=80)
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reflection_mapping = [0, 5, 6, 7, 8, 1, 2, 3, 4]
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# Simulation Main Loop
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for it in range(Nt):
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print(it)
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# Drift
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new_has_fluid = np.zeros((Ny, Nx))
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F_sum = np.sum(F, 2)
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for i, cx, cy in zip(idxs, cxs, cys):
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F_part = F[:, :, i] / F_sum
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F_part[F_sum == 0] = 0
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to_move = F_part * (has_fluid * 1.0)
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to_move = (np.roll(to_move, cx, axis=1))
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to_move = (np.roll(to_move, cy, axis=0))
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new_has_fluid += to_move
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F[:, :, i] = np.roll(F[:, :, i], cx, axis=1)
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F[:, :, i] = np.roll(F[:, :, i], cy, axis=0)
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# has_fluid = new_has_fluid > 0.5
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# new_has_fluid[F_sum == 0] += has_fluid[F_sum == 0] * 1.0
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# new_has_fluid[(np.abs(F_sum) < 0.000000001)] = 0
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fluid_sum = np.sum(has_fluid * 1.0)
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has_fluid = (new_has_fluid / np.sum(new_has_fluid * 1.0)) * fluid_sum
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print('fluid_cells: %d' % np.sum(has_fluid * 1))
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# for i in idxs:
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# F[:, :, i] *= has_fluid
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bndry = np.zeros((Ny, Nx), dtype=np.bool)
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bndry[0, :] = True
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bndry[Ny - 1, :] = True
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# bndry[:, 0] = True
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# bndry[:, Nx - 1] = True
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bndry = np.logical_or(bndry, cylinder)
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# bndry = np.logical_or(bndry, has_fluid < 0.5)
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# Set reflective boundaries
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bndryF = F[bndry, :]
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bndryF = bndryF[:, reflection_mapping]
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sum_f = np.sum(F)
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print('Sum of Forces: %f' % sum_f)
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# sum_f_cyl = np.sum(F[cylinder])
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# print('Sum of Forces in cylinder: %f' % sum_f_cyl)
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# sum_f_inner_cyl = np.sum(F[inner_cylinder])
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# print('Sum of Forces in inner cylinder: %f' % sum_f_inner_cyl)
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# if sum_f > 4000000.000000:
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# test = 1
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# F[Ny - 1, :, 5] += 0.1
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# F[0, :, 1] -= 0.1
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# F[0, :, 5] += 0.1
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# F[Ny - 1, :, 1] -= 0.1
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# Calculate fluid variables
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rho = np.sum(F, 2)
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ux = np.sum(F * cxs, 2) / rho
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uy = np.sum(F * cys, 2) / rho
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ux[(np.abs(rho) < 0.000000001)] = 0
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uy[(np.abs(rho) < 0.000000001)] = 0
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# print('minimum rho: %f' % np.min(np.abs(rho)))
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# print('Maximum F: %f' % np.max(F))
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# print('Minimum F: %f' % np.min(F))
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# Apply Collision
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Feq = np.zeros(F.shape)
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for i, cx, cy, w in zip(idxs, cxs, cys, weights):
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Feq[:, :, i] = rho * w * (
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1 + 3 * (cx * ux + cy * uy) + 9 * (cx * ux + cy * uy) ** 2 / 2 - 3 * (ux ** 2 + uy ** 2) / 2)
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F += -(1.0 / tau) * (F - Feq)
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# Apply boundary
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F[bndry, :] = bndryF
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# plot in real time - color 1/2 particles blue, other half red
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if (plotRealTime and (it % 10) == 0) or (it == Nt - 1):
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plt.cla()
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ux[cylinder] = 0
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uy[cylinder] = 0
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vorticity = (np.roll(ux, -1, axis=0) - np.roll(ux, 1, axis=0)) - (
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np.roll(uy, -1, axis=1) - np.roll(uy, 1, axis=1))
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vorticity[cylinder] = np.nan
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# vorticity *= has_fluid
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cmap = plt.cm.bwr
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cmap.set_bad('black')
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# plt.imshow(vorticity, cmap='bwr')
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plt.imshow(has_fluid * 2.0 - 1.0, cmap='bwr')
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# plt.imshow(bndry * 2.0 - 1.0, cmap='bwr')
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plt.clim(-.1, .1)
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ax = plt.gca()
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ax.invert_yaxis()
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ax.get_xaxis().set_visible(False)
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ax.get_yaxis().set_visible(False)
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ax.set_aspect('equal')
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plt.pause(0.001)
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# Save figure
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# plt.savefig('latticeboltzmann.png', dpi=240)
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plt.show()
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return 0
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if __name__ == "__main__":
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main()
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