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import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
figure, axes = plt.subplots()
class SIMPLE:
def __init__(self, domain_size, bfs_size, step, Re, alpha=0.8):
np.set_printoptions(precision=2, floatmode="maxprec", suppress=True)
self.Re = Re
self.nu = 1 / Re
self.alpha = alpha
self.domain_size = domain_size
self.bfs_size = bfs_size
self.step = step
self.shape = tuple(int(x / step) for x in domain_size)
self.x, self.y = np.meshgrid(
np.linspace(0, domain_size[1], self.shape[1]),
np.linspace(0, domain_size[0], self.shape[0]),
)
self.plt = None
self.colorbar = None
self.patch = None
def allocate_field(self, random=False):
if random:
return np.random.rand(*self.shape)
return np.zeros(shape=self.shape, dtype=float)
def prep(self):
self.u = self.allocate_field()
self.u_star = self.allocate_field()
self.v = self.allocate_field()
self.v_star = self.allocate_field()
self.p = self.allocate_field()
self.p_star = self.allocate_field(True)
self.p_prime = self.allocate_field()
self.d_e = self.allocate_field()
self.d_n = self.allocate_field()
self.b = self.allocate_field()
def apply_inflow_boundary(self):
for i in range(self.shape[0]):
self.u_star[i][0] = 1
self.v_star[i][0] = 0
def assert_rule2(self, value):
'''Assert that the value is nearly positive'''
if value < -0.1:
# TODO: assert
print(f'WARNING: Value must be positive: {value}')
return value
def solve_momentum_equations(self):
# Momentum along X direction
for i in range(1, self.shape[0] - 1):
for j in range(1, self.shape[1] - 1):
u_E = 0.5 * (self.u[i][j] + self.u[i][j + 1])
u_W = 0.5 * (self.u[i][j] + self.u[i][j - 1])
v_N = 0.5 * (self.v[i - 1][j] + self.v[i - 1][j + 1])
v_S = 0.5 * (self.v[i][j] + self.v[i][j + 1])
a_E = self.assert_rule2(-0.5 * u_E * self.step + self.nu)
a_W = self.assert_rule2(+0.5 * u_W * self.step + self.nu)
a_N = self.assert_rule2(-0.5 * v_N * self.step + self.nu)
a_S = self.assert_rule2(+0.5 * v_S * self.step + self.nu)
a_e = 0.5 * self.step * (u_E - u_W + v_N - v_S) + 4 * self.nu
A_e = -self.step
self.d_e[i][j] = A_e / a_e
self.u_star[i][j] = (
a_E * self.u[i][j + 1] +
a_W * self.u[i][j - 1] +
a_N * self.u[i - 1][j] +
a_S * self.u[i + 1][j]
) / a_e + self.d_e[i][j] * (self.p_star[i][j + 1] - self.p_star[i][j])
# Momentum along Y direction
for i in range(1, self.shape[0] - 1):
for j in range(1, self.shape[1] - 1):
u_E = 0.5 * (self.u[i][j] + self.u[i + 1][j])
u_W = 0.5 * (self.u[i][j - 1] + self.u[i + 1][j - 1])
v_N = 0.5 * (self.v[i - 1][j] + self.v[i][j])
v_S = 0.5 * (self.v[i][j] + self.v[i + 1][j])
a_E = self.assert_rule2(-0.5 * u_E * self.step + self.nu)
a_W = self.assert_rule2(+0.5 * u_W * self.step + self.nu)
a_N = self.assert_rule2(-0.5 * v_N * self.step + self.nu)
a_S = self.assert_rule2(+0.5 * v_S * self.step + self.nu)
a_n = 0.5 * self.step * (u_E - u_W + v_N - v_S) + 4 * self.nu
A_n = -self.step
self.d_n[i][j] = A_n / a_n
self.v_star[i][j] = (
a_E * self.v[i][j + 1] +
a_W * self.v[i][j - 1] +
a_N * self.v[i - 1][j] +
a_S * self.v[i + 1][j]
) / a_n + self.d_n[i][j] * (self.p_star[i][j] - self.p_star[i + 1][j])
def apply_sides_boundary(self):
for j in range(self.shape[1]):
self.v_star[0][j] = 0
self.u_star[0][j] = 0
self.u_star[self.shape[0] - 1][j] = 0
self.v_star[self.shape[0] - 1][j] = 0
def apply_bfs_boundary(self):
'''Apply Backwards Facing Step boundary conditions'''
for i in range(int(self.bfs_size[0] / self.step) + 1):
for j in range(int(self.bfs_size[1] / self.step) + 1):
self.u_star[i][j] = 0
self.v_star[i][j] = 0
def correct_pressure(self):
self.p_prime = self.allocate_field()
for i in range(1, self.shape[0] - 1):
for j in range(1, self.shape[1] - 1):
a_E = self.assert_rule2(-self.d_e[i][j] * self.step)
a_W = self.assert_rule2(-self.d_e[i][j-1] * self.step)
a_N = self.assert_rule2(-self.d_n[i-1][j] * self.step)
a_S = self.assert_rule2(-self.d_n[i][j] * self.step)
a_P = a_E + a_W + a_N + a_S
self.b[i][j] = self.step * (
-(self.u_star[i][j] - self.u_star[i][j-1])
+ (self.v_star[i][j] - self.v_star[i-1][j])
)
self.p_prime[i][j] = (
a_E * self.p_prime[i][j+1] +
a_W * self.p_prime[i][j-1] +
a_N * self.p_prime[i-1][j] +
a_S * self.p_prime[i+1][j] +
self.b[i][j]
) / a_P
self.p = self.p_star + self.p_prime * self.alpha
self.p_star = self.p
def correct_velocities(self):
for i in range(1, self.shape[0] - 1):
for j in range(1, self.shape[1] - 1):
self.u[i][j] = self.u_star[i][j] + self.d_e[i][j] * (self.p_prime[i][j + 1] - self.p_prime[i][j])
self.v[i][j] = self.v_star[i][j] + self.d_n[i][j] * (self.p_prime[i][j] - self.p_prime[i + 1][j])
def apply_outflow_boundary(self):
for i in range(self.shape[0]):
self.u[i][self.shape[1] - 1] = self.u[i][self.shape[1] - 2]
self.v[i][self.shape[1] - 1] = self.v[i][self.shape[1] - 2]
def iterate(self):
self.apply_inflow_boundary()
self.solve_momentum_equations()
self.apply_sides_boundary()
self.apply_bfs_boundary()
self.correct_pressure()
self.correct_velocities()
# self.apply_outflow_boundary()
self.apply_bfs_boundary() # Is it needed?
def plot(self, normalize=False, density=1):
if self.patch:
self.patch.remove()
if self.colorbar:
self.colorbar.remove()
if self.plt:
self.plt.remove()
self.patch = axes.add_patch(Rectangle((0, 0), *reversed(self.bfs_size)))
u, v = self.u, self.v
if normalize:
factor = np.sqrt(u ** 2 + v ** 2)
u = u / factor
v = v / factor
self.plt = plt.quiver(
self.x[::density, ::density],
self.y[::density, ::density],
u[::density, ::density],
v[::density, ::density],
self.p[::density, ::density],
scale=30,
cmap='inferno'
)
self.colorbar = plt.colorbar()
plt.pause(0.0001)
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