353 lines
12 KiB
Python
353 lines
12 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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from FluidSim.FluidSimParameters import *
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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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epsilon = 0.000000001
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Nx = 400 # resolution x-dir
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Ny = 100 # resolution y-dir
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rho0 = 1 # 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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render_frequency = 10
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close_up_frequency = 10
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friction = 0.0001
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params = FluidSimParameter(Ny)
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# params = WaterParameter(Ny)
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# params = MagmaParameter(Ny)
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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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xx, yy = np.meshgrid(range(Nx), range(Ny))
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# Initial Conditions
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N = np.ones((Ny, Nx, NL)) # * rho0 / NL
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temperature = np.ones((Ny, Nx, NL), np.float) # * rho0 / NL
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tracked_fluid = np.zeros((Ny, Nx, NL), np.float) # * rho0 / NL
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tracked_fluid[50:, :, 0] = 1
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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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N += 0.01 * np.random.randn(Ny, Nx, NL)
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X, Y = np.meshgrid(range(Nx), range(Ny))
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N[:, :, 3] += 2 * (1 + 0.2 * np.cos(2 * np.pi * X / Nx * 4))
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# N[:, :, 5] += 1
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rho = np.sum(N, 2)
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temperature_rho = np.sum(temperature, 2)
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for i in idxs:
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N[:, :, i] *= rho0 / rho
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temperature[:, :, i] *= 1 / temperature_rho
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# N[50:, :] = 0
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temperature[:, :] = 0
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# temperature += 0.01 * np.random.randn(Ny, Nx, NL)
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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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cylinder[:, :] = False
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N[cylinder] = 0
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N[0, :] = 0
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N[Ny - 1, :] = 0
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temperature[cylinder] = 0
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tracked_fluid[cylinder] = 0
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# N[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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# N[:, :, 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(N, 2)
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for i, cx, cy in zip(idxs, cxs, cys):
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F_part = N[:, :, 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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N[:, :, i] = np.roll(N[:, :, i], cx, axis=1)
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N[:, :, i] = np.roll(N[:, :, i], cy, axis=0)
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temperature[:, :, i] = np.roll(temperature[:, :, i], cx, axis=1)
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temperature[:, :, i] = np.roll(temperature[:, :, i], cy, axis=0)
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tracked_fluid[:, :, i] = np.roll(tracked_fluid[:, :, i], cx, axis=1)
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tracked_fluid[:, :, i] = np.roll(tracked_fluid[:, :, 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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#
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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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#
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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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# N[:, :, 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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bndryN = N[bndry, :]
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bndryN = bndryN[:, reflection_mapping]
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bndryTemp = temperature[bndry, :]
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bndryTemp = bndryTemp[:, reflection_mapping]
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bndryTracked = tracked_fluid[bndry, :]
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bndryTracked = bndryTracked[:, reflection_mapping]
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sum_f = np.sum(N)
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print('Sum of Particles: %f' % sum_f)
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print('Sum of Temperature: %f' % np.sum(temperature))
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print('Sum of tacked particles: %f' % np.sum(tracked_fluid))
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# sum_f_cyl = np.sum(N[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(N[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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# N[Ny - 1, :, 5] += 0.1
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# N[0, :, 1] -= 0.1
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# N[0, :, 5] += 0.1
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# N[Ny - 1, :, 1] -= 0.1
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# Calculate fluid variables
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rho = np.sum(N, 2)
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temp_rho = np.sum(temperature, 2)
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tracked_rho = np.sum(tracked_fluid, 2)
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ux = np.sum(N * cxs, 2) / rho
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uy = np.sum(N * cys, 2) / rho
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ux[(np.abs(rho) < epsilon)] = 0
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uy[(np.abs(rho) < epsilon)] = 0
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g = -params.g * (temp_rho - yy / Ny)
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uy1 = (uy + g * params.t1 * (tracked_rho * 0.9 + 0.1))
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uy2 = (uy + g * params.t2 * (tracked_rho * 0.9 + 0.1))
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# uy[np.abs(rho) >= epsilon] += g[np.abs(rho) >= epsilon] / 2.0
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# uy += g / 2.0
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# u_length = np.maximum(np.abs(ux), np.abs(uy))
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# safe guard against supersonic streams WIP
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u_length1 = np.sqrt(np.square(ux) + np.square(uy1))
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u_length2 = np.sqrt(np.square(ux) + np.square(uy2))
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u_max_length1 = np.max(u_length1)
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u_max_length2 = np.max(u_length2)
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u_max_length = max(u_max_length1, u_max_length2)
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if u_max_length > 2:
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test = 1
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if u_max_length > np.sqrt(2):
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ux = (ux / u_max_length) * np.sqrt(2)
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uy1 = (uy1 / u_max_length) * np.sqrt(2)
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uy2 = (uy2 / u_max_length) * np.sqrt(2)
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# apply friction
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ux *= (1 - friction)
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uy1 *= (1 - friction)
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uy2 *= (1 - friction)
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print('max vector part: %f' % u_max_length)
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# ux /= u_max_length
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# uy /= u_max_length
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# scale = abs(np.max(np.maximum(np.abs(ux), np.abs(uy))) - 1.0) < epsilon
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# if scale:
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# g = 0.01 * (temp_rho - yy / Ny)
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#
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# # F = np.zeros((Ny, Nx), dtype=np.bool)
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# # F = -0.1 * rho
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#
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# # uy[np.abs(rho) >= epsilon] += tau * F[np.abs(rho) >= epsilon] / rho[np.abs(rho) >= epsilon]
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# uy[np.abs(rho) >= epsilon] += g[np.abs(rho) >= epsilon] / 2.0
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#
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# u_length = np.maximum(np.abs(ux), np.abs(uy))
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# u_max_length = np.max(u_length)
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#
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# print('max vector part: %f' % u_max_length)
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#
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# ux /= u_max_length
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# uy /= u_max_length
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# print('minimum rho: %f' % np.min(np.abs(rho)))
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# print('Maximum N: %f' % np.max(N))
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# print('Minimum N: %f' % np.min(N))
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# Apply Collision
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temperature_eq = np.zeros(temperature.shape)
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tracked_eq = np.zeros(temperature.shape)
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Neq = np.zeros(N.shape)
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for i, cx, cy, w in zip(idxs, cxs, cys, weights):
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Neq[:, :, i] = rho * w * (
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1 + 3 * (cx * ux + cy * uy1) + 9 * (cx * ux + cy * uy1) ** 2 / 2 - 3 * (ux ** 2 + uy1 ** 2) / 2)
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temperature_eq[:, :, i] = temp_rho * w * (
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1 + 3 * (cx * ux + cy * uy2) + 9 * (cx * ux + cy * uy2) ** 2 / 2 - 3 * (ux ** 2 + uy2 ** 2) / 2)
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tracked_eq[:, :, i] = tracked_rho * w * (
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1 + 3 * (cx * ux + cy * uy1) + 9 * (cx * ux + cy * uy1) ** 2 / 2 - 3 * (ux ** 2 + uy1 ** 2) / 2)
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# test1 = np.sum(Neq)
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test2 = np.sum(N-Neq)
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if abs(test2) > 0.0001:
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test = ''
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print('Overall change: %f' % test2)
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n_pre_sum = np.sum(N[np.logical_not(bndry)])
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temperature_pre_sum = np.sum(temperature[np.logical_not(bndry)])
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N += -(1.0 / params.t1) * (N - Neq)
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temperature += -(1.0 / params.t2) * (temperature - temperature_eq)
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tracked_fluid += -(1.0 / params.t1) * (tracked_fluid - tracked_eq)
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# Apply boundary
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N[bndry, :] = bndryN
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temperature[bndry, :] = bndryTemp
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tracked_fluid[bndry, :] = bndryTracked
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# temperature[0, :, 0] = 0
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# temperature[1, :, 0] = 0
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temperature[0, :, 0] /= 2
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temperature[1, :, 0] /= 2
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if it <= 3000:
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temperature[Ny - 1, :, 0] = 1
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temperature[Ny - 2, :, 0] = 1
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# n_sum = np.sum(N, 2)
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# n_sum_min = np.min(n_sum)
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# if n_sum_min < 0:
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# N[np.logical_not(bndry)] += abs(n_sum_min)
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# N[np.logical_not(bndry)] /= np.sum(N[np.logical_not(bndry)])
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# N[np.logical_not(bndry)] *= n_pre_sum
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# print('Sum of Forces: %f' % np.sum(N))
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# temperature_sum = np.sum(temperature, 2)
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# temperature_sum_min = np.min(temperature_sum)
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# if temperature_sum_min < 0:
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# temperature[np.logical_not(bndry)] += abs(temperature_sum_min)
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# temperature[np.logical_not(bndry)] /= np.sum(temperature[np.logical_not(bndry)])
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# temperature[np.logical_not(bndry)] *= temperature_pre_sum
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# print('Sum of Temperature: %f' % np.sum(temperature))
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no_cylinder_mask = np.sum(N, 2) != 0
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print('min N: %f' % np.min(np.sum(N, 2)[no_cylinder_mask]))
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print('max N: %f' % np.max(np.sum(N, 2)))
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print('min Temp: %f' % np.min(np.sum(temperature, 2)[no_cylinder_mask]))
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print('max Temp: %f' % np.max(np.sum(temperature, 2)))
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if it > render_frequency:
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render_frequency = close_up_frequency
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# plot in real time - color 1/2 particles blue, other half red
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if (plotRealTime and (it % render_frequency) == 0) or (it == Nt - 1):
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fig.clear()
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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.subplot(2, 2, 1)
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plt.imshow(vorticity, cmap='bwr')
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plt.clim(-.1, .1)
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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.imshow(np.sum(N, 2) * 2.0 - 1.0, cmap='bwr')
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# plt.imshow((np.sum(temperature, 2) / np.max(np.sum(temperature, 2))) * 2.0 - 1.0, cmap='bwr')
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plt.subplot(2, 2, 2)
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max_temp = np.max(np.sum(temperature, 2))
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# plt.imshow(np.sum(temperature, 2) / max_temp * 2.0 - 1.0, cmap='bwr')
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plt.imshow(np.sum(temperature, 2) * 2.0 - 1.0, cmap='bwr')
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plt.clim(-.1, .1)
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plt.subplot(2, 2, 3)
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max_N = np.max(np.sum(N, 2))
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plt.imshow(np.sum(N, 2) / max_N * 2.0 - 1.0, cmap='bwr')
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plt.clim(-.1, .1)
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plt.subplot(2, 2, 4)
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plt.imshow(np.sum(tracked_fluid, 2) * 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() |