VoxelEngine/FluidSim/LatticeBoltzmann.py

import matplotlib.pyplot as plt
import numpy as np
from FluidSim.FluidSimParameters import *

"""
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
    epsilon = 0.000000001
    Nx = 400  # resolution x-dir
    Ny = 100  # resolution y-dir
    rho0 = 1  # average density
    tau = 0.6  # collision timescale
    Nt = 80000  # number of timesteps
    plotRealTime = True  # switch on for plotting as the simulation goes along
    render_frequency = 10
    close_up_frequency = 10
    friction = 0.0001

    params = FluidSimParameter(Ny)
    # params = WaterParameter(Ny)
    # params = MagmaParameter(Ny)

    # 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
    xx, yy = np.meshgrid(range(Nx), range(Ny))

    # Initial Conditions
    N = np.ones((Ny, Nx, NL))  # * rho0 / NL
    temperature = np.ones((Ny, Nx, NL), np.float)  # * rho0 / NL

    tracked_fluid = np.zeros((Ny, Nx, NL), np.float)  # * rho0 / NL
    tracked_fluid[50:, :, 0] = 1

    has_fluid = np.ones((Ny, Nx), dtype=np.bool)
    has_fluid[int(Ny/2):, :] = False
    np.random.seed(42)
    N += 0.01 * np.random.randn(Ny, Nx, NL)
    X, Y = np.meshgrid(range(Nx), range(Ny))
    N[:, :, 3] += 2 * (1 + 0.2 * np.cos(2 * np.pi * X / Nx * 4))
    # N[:, :, 5] += 1
    rho = np.sum(N, 2)
    temperature_rho = np.sum(temperature, 2)
    for i in idxs:
        N[:, :, i] *= rho0 / rho
        temperature[:, :, i] *= 1 / temperature_rho
    # N[50:, :] = 0
    temperature[:, :] = 0
    # temperature += 0.01 * np.random.randn(Ny, Nx, NL)


    # Cylinder boundary
    X, Y = np.meshgrid(range(Nx), range(Ny))

    cylinder = (X - Nx / 4) ** 2 + (Y - Ny / 2) ** 2 < (Ny / 4) ** 2
    cylinder[:, :] = False

    N[cylinder] = 0
    N[0, :] = 0
    N[Ny - 1, :] = 0

    temperature[cylinder] = 0

    tracked_fluid[cylinder] = 0
    # N[int(Ny/2):, :] = 0

    has_fluid[cylinder] = False
    has_fluid[0, :] = False
    has_fluid[Ny - 1, :] = False

    # for i in idxs:
    #     N[:, :, 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(N, 2)
        for i, cx, cy in zip(idxs, cxs, cys):
            F_part = N[:, :, 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

            N[:, :, i] = np.roll(N[:, :, i], cx, axis=1)
            N[:, :, i] = np.roll(N[:, :, i], cy, axis=0)

            temperature[:, :, i] = np.roll(temperature[:, :, i], cx, axis=1)
            temperature[:, :, i] = np.roll(temperature[:, :, i], cy, axis=0)

            tracked_fluid[:, :, i] = np.roll(tracked_fluid[:, :, i], cx, axis=1)
            tracked_fluid[:, :, i] = np.roll(tracked_fluid[:, :, 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:
        #     N[:, :, 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
        bndryN = N[bndry, :]
        bndryN = bndryN[:, reflection_mapping]

        bndryTemp = temperature[bndry, :]
        bndryTemp = bndryTemp[:, reflection_mapping]

        bndryTracked = tracked_fluid[bndry, :]
        bndryTracked = bndryTracked[:, reflection_mapping]

        sum_f = np.sum(N)
        print('Sum of Particles: %f' % sum_f)
        print('Sum of Temperature: %f' % np.sum(temperature))
        print('Sum of tacked particles: %f' % np.sum(tracked_fluid))

        # sum_f_cyl = np.sum(N[cylinder])
        # print('Sum of Forces in cylinder: %f' % sum_f_cyl)

        # sum_f_inner_cyl = np.sum(N[inner_cylinder])
        # print('Sum of Forces in inner cylinder: %f' % sum_f_inner_cyl)

        # if sum_f > 4000000.000000:
        #     test = 1

        # N[Ny - 1, :, 5] += 0.1
        # N[0, :, 1] -= 0.1
        # N[0, :, 5] += 0.1
        # N[Ny - 1, :, 1] -= 0.1

        # Calculate fluid variables
        rho = np.sum(N, 2)
        temp_rho = np.sum(temperature, 2)

        tracked_rho = np.sum(tracked_fluid, 2)

        ux = np.sum(N * cxs, 2) / rho
        uy = np.sum(N * cys, 2) / rho

        ux[(np.abs(rho) < epsilon)] = 0
        uy[(np.abs(rho) < epsilon)] = 0

        g = -params.g * (temp_rho - yy / Ny)

        uy1 = (uy + g * params.t1 * (tracked_rho * 0.9 + 0.1))
        uy2 = (uy + g * params.t2 * (tracked_rho * 0.9 + 0.1))

        # uy[np.abs(rho) >= epsilon] += g[np.abs(rho) >= epsilon] / 2.0
        # uy += g / 2.0

        # u_length = np.maximum(np.abs(ux), np.abs(uy))

        # safe guard against supersonic streams WIP
        u_length1 = np.sqrt(np.square(ux) + np.square(uy1))
        u_length2 = np.sqrt(np.square(ux) + np.square(uy2))

        u_max_length1 = np.max(u_length1)
        u_max_length2 = np.max(u_length2)
        u_max_length = max(u_max_length1, u_max_length2)

        if u_max_length > 2:
            test = 1

        if u_max_length > np.sqrt(2):
            ux = (ux / u_max_length) * np.sqrt(2)
            uy1 = (uy1 / u_max_length) * np.sqrt(2)
            uy2 = (uy2 / u_max_length) * np.sqrt(2)

        # apply friction
        ux *= (1 - friction)
        uy1 *= (1 - friction)
        uy2 *= (1 - friction)

        print('max vector part: %f' % u_max_length)
        # ux /= u_max_length
        # uy /= u_max_length

        # scale = abs(np.max(np.maximum(np.abs(ux), np.abs(uy))) - 1.0) < epsilon
        # if scale:
        #     g = 0.01 * (temp_rho - yy / Ny)
        #
        #     # F = np.zeros((Ny, Nx), dtype=np.bool)
        #     # F = -0.1 * rho
        #
        #     # uy[np.abs(rho) >= epsilon] += tau * F[np.abs(rho) >= epsilon] / rho[np.abs(rho) >= epsilon]
        #     uy[np.abs(rho) >= epsilon] += g[np.abs(rho) >= epsilon] / 2.0
        #
        #     u_length = np.maximum(np.abs(ux), np.abs(uy))
        #     u_max_length = np.max(u_length)
        #
        #     print('max vector part: %f' % u_max_length)
        #
        #     ux /= u_max_length
        #     uy /= u_max_length

        # print('minimum rho: %f' % np.min(np.abs(rho)))
        # print('Maximum N: %f' % np.max(N))
        # print('Minimum N: %f' % np.min(N))

        # Apply Collision
        temperature_eq = np.zeros(temperature.shape)
        tracked_eq = np.zeros(temperature.shape)
        Neq = np.zeros(N.shape)
        for i, cx, cy, w in zip(idxs, cxs, cys, weights):
            Neq[:, :, i] = rho * w * (
                        1 + 3 * (cx * ux + cy * uy1) + 9 * (cx * ux + cy * uy1) ** 2 / 2 - 3 * (ux ** 2 + uy1 ** 2) / 2)

            temperature_eq[:, :, i] = temp_rho * w * (
                    1 + 3 * (cx * ux + cy * uy2) + 9 * (cx * ux + cy * uy2) ** 2 / 2 - 3 * (ux ** 2 + uy2 ** 2) / 2)

            tracked_eq[:, :, i] = tracked_rho * w * (
                    1 + 3 * (cx * ux + cy * uy1) + 9 * (cx * ux + cy * uy1) ** 2 / 2 - 3 * (ux ** 2 + uy1 ** 2) / 2)
        # test1 = np.sum(Neq)
        test2 = np.sum(N-Neq)
        if abs(test2) > 0.0001:
            test = ''

        print('Overall change: %f' % test2)

        n_pre_sum = np.sum(N[np.logical_not(bndry)])
        temperature_pre_sum = np.sum(temperature[np.logical_not(bndry)])

        N += -(1.0 / params.t1) * (N - Neq)
        temperature += -(1.0 / params.t2) * (temperature - temperature_eq)
        tracked_fluid += -(1.0 / params.t1) * (tracked_fluid - tracked_eq)

        # Apply boundary
        N[bndry, :] = bndryN
        temperature[bndry, :] = bndryTemp
        tracked_fluid[bndry, :] = bndryTracked

        # temperature[0, :, 0] = 0
        # temperature[1, :, 0] = 0

        temperature[0, :, 0] /= 2
        temperature[1, :, 0] /= 2

        if it <= 3000:
            temperature[Ny - 1, :, 0] = 1
            temperature[Ny - 2, :, 0] = 1

        # n_sum = np.sum(N, 2)
        # n_sum_min = np.min(n_sum)
        # if n_sum_min < 0:
        #     N[np.logical_not(bndry)] += abs(n_sum_min)
        #     N[np.logical_not(bndry)] /= np.sum(N[np.logical_not(bndry)])
        #     N[np.logical_not(bndry)] *= n_pre_sum
        #     print('Sum of Forces: %f' % np.sum(N))

        # temperature_sum = np.sum(temperature, 2)
        # temperature_sum_min = np.min(temperature_sum)
        # if temperature_sum_min < 0:
        #     temperature[np.logical_not(bndry)] += abs(temperature_sum_min)
        #     temperature[np.logical_not(bndry)] /= np.sum(temperature[np.logical_not(bndry)])
        #     temperature[np.logical_not(bndry)] *= temperature_pre_sum
        #     print('Sum of Temperature: %f' % np.sum(temperature))

        no_cylinder_mask = np.sum(N, 2) != 0
        print('min N: %f' % np.min(np.sum(N, 2)[no_cylinder_mask]))
        print('max N: %f' % np.max(np.sum(N, 2)))

        print('min Temp: %f' % np.min(np.sum(temperature, 2)[no_cylinder_mask]))
        print('max Temp: %f' % np.max(np.sum(temperature, 2)))

        if it > render_frequency:
            render_frequency = close_up_frequency
        # plot in real time - color 1/2 particles blue, other half red
        if (plotRealTime and (it % render_frequency) == 0) or (it == Nt - 1):
            fig.clear()
            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.subplot(2, 2, 1)
            plt.imshow(vorticity, cmap='bwr')
            plt.clim(-.1, .1)
            # plt.imshow(has_fluid * 2.0 - 1.0, cmap='bwr')
            # plt.imshow(bndry * 2.0 - 1.0, cmap='bwr')
            # plt.imshow(np.sum(N, 2) * 2.0 - 1.0, cmap='bwr')
            # plt.imshow((np.sum(temperature, 2) / np.max(np.sum(temperature, 2))) * 2.0 - 1.0, cmap='bwr')
            plt.subplot(2, 2, 2)
            max_temp = np.max(np.sum(temperature, 2))
            # plt.imshow(np.sum(temperature, 2) / max_temp * 2.0 - 1.0, cmap='bwr')
            plt.imshow(np.sum(temperature, 2) * 2.0 - 1.0, cmap='bwr')
            plt.clim(-.1, .1)

            plt.subplot(2, 2, 3)
            max_N = np.max(np.sum(N, 2))
            plt.imshow(np.sum(N, 2) / max_N * 2.0 - 1.0, cmap='bwr')
            plt.clim(-.1, .1)

            plt.subplot(2, 2, 4)
            plt.imshow(np.sum(tracked_fluid, 2) * 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()