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(self.p.shape[0]): for j in range(self.p.shape[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 == 0 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 == 0 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]) ) if a_P != 0: 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.u_star[:, -1] = self.u_star[:, -2] 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 self.u[:, -1] = self.u[:, -2] 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