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import numpy as np
class SIMPLE:
def __init__(self, shape, bfs_shape, step, Re, alpha_p=0.8, alpha_uv=0.5):
np.set_printoptions(precision=2, floatmode="maxprec", suppress=True)
self.Re = Re
self.nu = 1 / Re
self.alpha_p = alpha_p
self.alpha_uv = alpha_uv
self.step = step
self.bfs_shape = bfs_shape
# Allocations
self.u = np.zeros(shape=(shape[0], shape[1] + 1), dtype=float)
self.u_star = np.zeros(shape=(shape[0], shape[1] + 1), dtype=float)
self.v = np.zeros(shape=(shape[0] + 1, shape[1]), dtype=float)
self.v_star = np.zeros(shape=(shape[0] + 1, shape[1]), dtype=float)
self.p = np.zeros(shape=shape, dtype=float)
self.p_star = np.random.rand(*shape)
self.p_prime = np.zeros(shape=shape, dtype=float)
self.d_e = np.zeros(shape=self.u.shape, dtype=float)
self.d_n = np.zeros(shape=self.v.shape, dtype=float)
self.b = np.zeros(shape=shape, dtype=float)
def assert_positive(self, value):
'''Assert that the value is nearly positive'''
assert value > -0.01, f'WARNING: Value must be positive: {value}'
return value
def solve_momentum_equations(self):
# Momentum along X direction
for i in range(1, self.u.shape[0] - 1):
for j in range(1, self.u.shape[1] - 1):
if i >= self.bfs_shape[0] or j >= self.bfs_shape[1]:
u_W = 0.5 * (self.u[i][j] + self.u[i][j - 1])
u_E = 0.5 * (self.u[i][j] + self.u[i][j + 1])
v_S = 0.5 * (self.v[i][j - 1] + self.v[i][j])
v_N = 0.5 * (self.v[i + 1][j - 1] + self.v[i + 1][j])
a_E = self.assert_positive(-0.5 * u_E * self.step + self.nu)
a_W = self.assert_positive(+0.5 * u_W * self.step + self.nu)
a_N = self.assert_positive(-0.5 * v_N * self.step + self.nu)
a_S = self.assert_positive(+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] +
self.b[i][j - 1]
) / a_e + self.d_e[i][j] * (self.p_star[i][j - 1] - self.p_star[i][j]) # p - p_e
# Momentum along Y direction
for i in range(1, self.v.shape[0] - 1):
for j in range(1, self.v.shape[1] - 1):
if i >= self.bfs_shape[0] or j >= self.bfs_shape[1]:
u_W = 0.5 * (self.u[i - 1][j] + self.u[i][j])
u_E = 0.5 * (self.u[i - 1][j + 1] + self.u[i][j + 1])
v_N = 0.5 * (self.v[i][j] + self.v[i + 1][j])
v_S = 0.5 * (self.v[i][j] + self.v[i - 1][j])
a_E = self.assert_positive(-0.5 * u_E * self.step + self.nu)
a_W = self.assert_positive(+0.5 * u_W * self.step + self.nu)
a_N = self.assert_positive(-0.5 * v_N * self.step + self.nu)
a_S = self.assert_positive(+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] +
self.b[i - 1][j]
) / a_n + self.d_n[i][j] * (self.p_star[i - 1][j] - self.p_star[i][j]) # p - p_n
def correct_pressure(self):
self.p_prime = np.zeros(shape=self.p.shape, dtype=float)
for i in range(1, self.p.shape[0] - 1):
for j in range(1, self.p.shape[1] - 1):
if i >= self.bfs_shape[0] or j >= self.bfs_shape[1]:
a_E = 0 if j == self.p.shape[1] - 1 else self.assert_positive(-self.d_e[i][j+1] * self.step)
a_W = 0 if j == 1 else self.assert_positive(-self.d_e[i][j] * self.step)
a_N = 0 if i == self.p.shape[0] - 1 else self.assert_positive(-self.d_n[i+1][j] * self.step)
a_S = 0 if i == 1 else self.assert_positive(-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+1] - self.u_star[i][j]) +
(self.v_star[i+1][j] - self.v_star[i][j])
)
self.p_prime[i][j] = (
(a_E * self.p_prime[i][j+1] if a_E > 0 else 0) +
(a_W * self.p_prime[i][j-1] if a_W > 0 else 0) +
(a_N * self.p_prime[i+1][j] if a_N > 0 else 0) +
(a_S * self.p_prime[i-1][j] if a_S > 0 else 0) +
self.b[i][j]
) / a_P
self.p = self.p_star + self.p_prime * self.alpha_p
self.p_star = self.p
def correct_velocities(self):
for i in range(self.u.shape[0]):
for j in range(1, self.u.shape[1] - 1):
self.u[i][j] = self.u_star[i][j] + self.alpha_uv * self.d_e[i][j] * (self.p_prime[i][j - 1] - self.p_prime[i][j])
for i in range(1, self.v.shape[0] - 1):
for j in range(self.v.shape[1]):
self.v[i][j] = self.v_star[i][j] + self.alpha_uv * self.d_n[i][j] * (self.p_prime[i - 1][j] - self.p_prime[i][j])
def iterate(self):
self.solve_momentum_equations()
# Boundary
self.u_star[:, 0] = 2 - self.u_star[:, 1]
self.v_star[:, 0] = 0
self.v_star[-2, :] = -self.v_star[-1, :]
self.v_star[1, :] = -self.v_star[0, :]
self.v_star[self.bfs_shape[0], :self.bfs_shape[1]] = self.v_star[self.bfs_shape[0] - 1, :self.bfs_shape[1]]
self.u_star[:self.bfs_shape[0], self.bfs_shape[1]] = self.u_star[:self.bfs_shape[0], self.bfs_shape[1] - 1]
self.p_star[:self.bfs_shape[0], :self.bfs_shape[1]] = 0
self.correct_pressure()
self.correct_velocities()
# Boundary enforce
self.u[:, 0] = 2 - self.u[:, 1]
self.v[:, 0] = 0
self.v[-2, :] = -self.v[-1, :]
self.v[1, :] = -self.v[0, :]
self.v[self.bfs_shape[0], :self.bfs_shape[1]] = self.v[self.bfs_shape[0] - 1, :self.bfs_shape[1]]
self.u[:self.bfs_shape[0], self.bfs_shape[1]] = self.u[:self.bfs_shape[0], self.bfs_shape[1] - 1]
self.p[:self.bfs_shape[0], :self.bfs_shape[1]] = 0
def avg_error(self):
return np.absolute(self.b).sum()
def save(self, path):
print('SAVE', path)
with open(path, 'wb') as file:
np.save(file, self.u)
np.save(file, self.v)
np.save(file, self.p)
np.save(file, self.b)
def load(self, path):
print('LOAD', path)
with open(path, 'rb') as file:
self.u = np.load(file)
self.v = np.load(file)
self.p = np.load(file)
self.b = np.load(file)
self.p_star = self.p
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