import numpy as np class SIMPLE: def __init__(self, shape, bfs_shape, 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.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 allocate_field(self, random=False): if random: return np.random.rand(*self.shape) return np.zeros(shape=self.shape, dtype=float) def apply_inflow_boundary(self): for i in range(1, self.shape[0] - 1): self.u_star[i][0] = 1 self.v_star[i][0] = 0 def apply_outflow_boundary(self): for i in range(0, self.shape[0]): self.u_star[i][-1] = self.u_star[i][-2]; def assert_positive(self, value): '''Assert that the value is nearly positive''' assert value > -1, f'WARNING: Value must be positive: {value}' return value def grid(self): '''Iterator over all grid points, excluding the obstacle''' for i in range(1, self.shape[0] - 1): for j in range(1, self.shape[1] - 1): # if i > self.bfs_node_size[0] or j > self.bfs_node_size[1]: yield (i, j) 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): 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] ) / 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): 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] ) / a_n + self.d_n[i][j] * (self.p_star[i - 1][j] - self.p_star[i][j]) # p - p_n def apply_sides_boundary(self): for j in range(self.shape[1]): self.v_star[0][j] = 0 self.v_star[-2][j] = 0 # WORKSNICE: self.v_star[-3][j] = 0 def apply_bfs_boundary(self): '''Apply Backwards Facing Step boundary conditions''' for i in range(self.bfs_node_size[0]): self.u_star[i][self.bfs_node_size[1]] = 0 for j in range(self.bfs_node_size[1]): self.v_star[self.bfs_node_size[0]][j] = 0 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): a_E = 0 if j == self.p.shape[1] - 1 else self.assert_positive(-self.d_e[i][j] * self.step) a_W = 0 if j == 1 else self.assert_positive(-self.d_e[i][j+1] * 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] - self.u_star[i][j+1]) + (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 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.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.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] = -self.u_star[:, 1] self.v_star[:, 0] = 0 self.u_star[:, -1] = -self.u_star[:, -2] self.v_star[:, -1] = 0 self.u_star[-1, :] = 1 self.v_star[-1, :] = -self.v_star[-2, :] self.u_star[0, :] = 0 self.v_star[0, :] = -self.v_star[1, :] self.p_star[0, 0] = 0 self.correct_pressure() self.correct_velocities() # Boundary enforce self.u[:, 0] = -self.u[:, 1] self.v[:, 0] = 0 self.u[:, -1] = -self.u[:, -2] self.v[:, -1] = 0 self.u[-1, :] = 1 self.v[-1, :] = -self.v[-2, :] self.u[0, :] = 0 self.v[0, :] = -self.v[1, :] self.p[0, 0] = 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