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fluid_sim.py
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"""
Based on the Jos Stam paper https://www.researchgate.net/publication/2560062_Real-Time_Fluid_Dynamics_for_Games
and the mike ash vulgarization https://mikeash.com/pyblog/fluid-simulation-for-dummies.html
"""
import numpy as np
import math
class Fluid:
def __init__(self):
self.size = 40 # map size
self.dt = 0.2 # time interval
self.iter = 8 # linear equation solving iteration number
self.diff = 0.0000 # Diffusion
self.visc = 0.0000 # viscosity
self.s = np.full((self.size, self.size), 0, dtype=float)
self.density = np.full((self.size, self.size), 0, dtype=float)
# array of 2d vectors, [x, y]
self.velo = np.full((self.size, self.size, 2), 0, dtype=float)
self.velo0 = np.full((self.size, self.size, 2), 0, dtype=float)
@property
def total_density(self):
"""Gives the total density amount, ignoring boundaries corrections"""
return self.density[1:-1, 1:-1].sum()
@property
def vector_divergence(self):
"""Compute vector divergence by pixel: (left - right) * x_component + (top - down) * y_component"""
divergence_map = np.full((self.size, self.size), 0, dtype=float)
for x in range(1, self.size-2):
for y in range(1, self.size-2):
velocity_window = self.velo[y-1:y+2, x-1:x+2]
divergence_map[y, x] = (np.gradient(velocity_window[:, :, 0], axis=0) +
np.gradient(velocity_window[:, :, 1], axis=1)).sum()
return divergence_map
@property
def total_divergence(self):
"""Sum of the absolute divergence value"""
return np.abs(self.vector_divergence).sum()
def step(self):
self.diffuse(self.velo0, self.velo, self.visc)
# x0, y0, x, y
self.project(self.velo0[:, :, 0], self.velo0[:, :, 1], self.velo[:, :, 0], self.velo[:, :, 1])
self.advect(self.velo[:, :, 0], self.velo0[:, :, 0], self.velo0)
self.advect(self.velo[:, :, 1], self.velo0[:, :, 1], self.velo0)
self.project(self.velo[:, :, 0], self.velo[:, :, 1], self.velo0[:, :, 0], self.velo0[:, :, 1])
self.diffuse(self.s, self.density, self.diff)
self.advect(self.density, self.s, self.velo)
def lin_solve(self, x, x0, a, c):
c_recip = 1 / c
for iteration in range(0, self.iter):
x[1:-1, 1:-1] = (x0[1:-1, 1:-1] + a * (x[2:, 1:-1] + x[:-2, 1:-1] + x[1:-1, 2:] + x[1:-1, :-2])) * c_recip
self.set_boundaries(x)
def set_boundaries(self, table):
"""
Boundaries handling. For density, border reflection may affect the total density sum
:return:
"""
if len(table.shape) > 2: # 3d velocity vector array
# vertical borders
table[:, 0, 0] = table[:, 1, 0]
table[:, 0, 1] = - table[:, 1, 1]
table[:, -1, 0] = table[:, -2, 0]
table[:, -1, 1] = - table[:, -2, 1]
# horizontal borders
table[0, :, 0] = - table[1, :, 0]
table[0, :, 1] = table[1, :, 1]
table[-1, :, 0] = - table[-2, :, 0]
table[-1, :, 1] = table[-2, :, 1]
else:
table[:, 0] = table[:, 1]
table[:, -1] = table[:, -2]
table[0, :] = table[1, :]
table[-1, :] = table[-2, :]
# pass through boundaries (loop over walls)
# table[:, 0] = table[:, -2]
# table[:, -1] = table[:, 1]
#
# table[0, :] = table[-2, :]
# table[-1, :] = table[1, :]
# corners
table[0, 0] = 0.5 * (table[1, 0] + table[0, 1])
table[0, -1] = 0.5 * (table[1, -1] + table[0, -2])
table[-1, 0] = 0.5 * (table[-2, 0] + table[- 1, 1])
table[-1, -1] = 0.5 * (table[-2, -1] + table[-1, -2])
def diffuse(self, x, x0, diff):
if diff != 0:
a = self.dt * diff * (self.size - 2) * (self.size - 2)
self.lin_solve(x, x0, a, 1 + 6 * a)
else: # equivalent to lin_solve with a = 0
x[:, :] = x0[:, :]
def project(self, velo_x, velo_y, p, div):
# numpy equivalent to this in a for loop:
# div[i, j] = -0.5 * (velo_x[i + 1, j] - velo_x[i - 1, j] + velo_y[i, j + 1] - velo_y[i, j - 1]) / self.size
div[1:-1, 1:-1] = -0.5 * (
velo_x[2:, 1:-1] -
velo_x[:-2, 1:-1] +
velo_y[1:-1, 2:] -
velo_y[1:-1, :-2]) \
/ self.size
p[:, :] = 0
self.set_boundaries(div)
self.set_boundaries(p)
self.lin_solve(p, div, 1, 6)
velo_x[1:-1, 1:-1] -= 0.5 * (p[2:, 1:-1] - p[:-2, 1:-1]) * self.size
velo_y[1:-1, 1:-1] -= 0.5 * (p[1:-1, 2:] - p[1:-1, :-2]) * self.size
self.set_boundaries(self.velo)
def advect(self, d, d0, velocity):
"""Basically move elements forward in time"""
dtx = self.dt * (self.size - 2)
dty = self.dt * (self.size - 2)
for j in range(1, self.size - 1):
for i in range(1, self.size - 1):
tmp1 = dtx * velocity[i, j, 0]
tmp2 = dty * velocity[i, j, 1]
x = i - tmp1
y = j - tmp2
if x < 0.5:
x = 0.5
if x > self.size + 0.5:
x = self.size + 0.5
i0 = math.floor(x)
i1 = i0 + 1.0
if y < 0.5:
y = 0.5
if y > self.size + 0.5:
y = self.size + 0.5
j0 = math.floor(y)
j1 = j0 + 1.0
s1 = x - i0
s0 = 1.0 - s1
t1 = y - j0
t0 = 1.0 - t1
i0i = int(i0)
i1i = int(i1)
j0i = int(j0)
j1i = int(j1)
d[i, j] = s0 * (t0 * d0[i0i, j0i] + t1 * d0[i0i, j1i]) + \
s1 * (t0 * d0[i1i, j0i] + t1 * d0[i1i, j1i])
self.set_boundaries(d)
if __name__ == "__main__":
import matplotlib.pyplot as plt
from matplotlib import animation
# Enable for pycharm users
# import matplotlib
# matplotlib.use('Qt5Agg')
inst = Fluid()
def update_im(i):
inst.density[4:7, 4:7] += 100 # add density into a 3*3 square
inst.velo[5, 5] += [1, 2]
inst.step()
im.set_array(inst.density)
# update vector field data
q.set_UVC(inst.velo[:, :, 1], inst.velo[:, :, 0])
# ! slows down processing if enabled
# print(f"Density sum: {inst.total_density:.2f}, Total divergence: {inst.total_divergence:.2f}")
# auto adjust heatmap "brightness"
# im.autoscale()
fig = plt.figure()
# plot density (set interpolation to none for raw view)
im = plt.imshow(inst.density, cmap='hot', vmax=100, interpolation='bilinear')
# plot vector field
q = plt.quiver(inst.velo[:, :, 1], inst.velo[:, :, 0], scale=10, angles='xy', color='w')
anim = animation.FuncAnimation(fig, update_im, interval=0)
plt.show()