From 7458a12223ece8b4ea1cbf80aa7ba62d84063ab9 Mon Sep 17 00:00:00 2001 From: eug-vs <eugene@eug-vs.xyz> Date: Tue, 17 May 2022 23:22:55 +0400 Subject: feat: add initial python implementation --- src/main.py | 164 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 164 insertions(+) create mode 100644 src/main.py diff --git a/src/main.py b/src/main.py new file mode 100644 index 0000000..69a612a --- /dev/null +++ b/src/main.py @@ -0,0 +1,164 @@ +import numpy as np +import matplotlib.pyplot as plt + +PI = np.pi + +np.set_printoptions(precision=2, floatmode="maxprec", suppress=True) +figure, axes = plt.subplots() + + +Re = 100 +nu = 1 / Re +domain_size = (1, 2) +step = 0.05 +N = int(domain_size[1] / step) +M = int(domain_size[0] / step) +shape = (N, M) +alpha = 0.8 # Coefficient + +t_m = 1 +h_c = 0.5 + +# Staggered vars +u = np.zeros(shape=shape, dtype=float) +u_star = np.zeros(shape=shape, dtype=float) +u_new = np.zeros(shape=shape, dtype=float) + +v = np.zeros(shape=shape, dtype=float) +v_star = np.zeros(shape=shape, dtype=float) +v_new = np.zeros(shape=shape, dtype=float) + +p = np.zeros(shape=shape, dtype=float) +p_star = np.zeros(shape=shape, dtype=float) +p_new = np.zeros(shape=shape, dtype=float) + +d_e = np.zeros(shape=shape, dtype=float) +d_n = np.zeros(shape=shape, dtype=float) +b = np.zeros(shape=shape, dtype=float) + + +def u_boundary(t, y): + def f(t): + return 1 if t_m < t else 0.5 * (np.sin(0.5 * PI * (2 * t / t_m - 1)) + 1) + return 6 * f(t) * (y - h_c) * (1 - y) / (1 - h_c)**2 + + +# Loop +error = 1 +precision = 10 ** -7 + +t = 0.15 + +iteration = 0 +while error > precision: + iteration += 1 + # Inflow boundary condition + for i in range(N): + y = i * step + u_star[i][0] = u_boundary(t, y) + v_star[i][0] = 0 + + # Sides boundary conditions + for j in range(M): + v_star[0][j] = 0 + v_star[N - 1][j] = 0 + u_star[0][j] = 0 + u_star[N - 1][j] = 0 + + # x-momentum + for i in range(1, N - 1): + for j in range(1, M - 1): + u_E = 0.5 * (u[i][j] + u[i][j + 1]) + u_W = 0.5 * (u[i][j] + u[i][j - 1]) + v_N = 0.5 * (v[i - 1][j] + v[i - 1][j + 1]) + v_S = 0.5 * (v[i][j] + v[i][j + 1]) + + a_E = -0.5 * u_E * step + nu + a_W = +0.5 * u_W * step + nu + a_N = -0.5 * v_N * step + nu + a_S = +0.5 * v_S * step + nu + + a_e = 0.5 * step * (u_E - u_W + v_N - v_S) + 4 * nu + A_e = -step + + d_e[i][j] = A_e / a_e + + u_star[i][j] = (a_E * u[i][j + 1] + a_W * u[i][j - 1] + a_N * u[i - 1][j] + a_S * u[i + 1][j]) / a_e + + d_e[i][j] * (p[i][j + 1] - p[i][j]) + + # y-momentum + for i in range(1, N - 1): + for j in range(1, M - 1): + u_E = 0.5 * (u[i][j] + u[i + 1][j]) + u_W = 0.5 * (u[i][j - 1] + u[i + 1][j - 1]) + v_N = 0.5 * (v[i - 1][j] + v[i][j]) + v_S = 0.5 * (v[i][j] + v[i + 1][j]) + + a_E = -0.5 * u_E * step + nu + a_W = +0.5 * u_W * step + nu + a_N = -0.5 * v_N * step + nu + a_S = +0.5 * v_S * step + nu + + a_n = 0.5 * step * (u_E - u_W + v_N - v_S) + 4 * nu + A_n = -step + + d_n[i][j] = A_n / a_n + + v_star[i][j] = (a_E * v[i][j + 1] + a_W * v[i][j - 1] + a_N * v[i - 1][j] + a_S * v[i + 1][j]) / a_n + + d_n[i][j] * (p[i][j] - p[i + 1][j]) + + # Pressure correction + p_c = np.zeros(shape=shape, dtype=float) + for i in range(1, N - 1): + for j in range(1, M - 1): + a_E = -d_e[i][j] * step + a_W = -d_e[i][j-1] * step + a_N = -d_n[i-1][j] * step + a_S = -d_n[i][j] * step + a_P = a_E + a_W + a_N + a_S + b[i][j] = step * (-(u_star[i][j] - u_star[i][j-1]) + (v_star[i][j] - v_star[i-1][j])) + + p_c[i][j] = (a_E * p_c[i][j+1] + a_W * p_c[i][j-1] + a_N * p_c[i-1][j] + a_S * p_c[i+1][j] + b[i][j]) / a_P + p_new = p + p_c * alpha + + # Pressure boundaries + for i in range(N - 1): + p_new[i][0] = p_new[i][1] + p_new[i][M - 1] = p_new[i][M - 2] + for j in range(M - 1): + p_new[0][j] = p_new[1][j] + p_new[N - 1][j] = p_new[N - 2][j] + + # Velocity correction + for i in range(1, N - 1): + for j in range(1, M - 1): + u_new[i][j] = u_star[i][j] + alpha * d_e[i][j] * (p_c[i + 1][j] - p_c[i][j]) + v_new[i][j] = v_star[i][j] + alpha * d_n[i][j] * (p_c[i][j] - p_c[i + 1][j]) + + # Continuity residual as error measure + error = 0 + for i in range(N): + for j in range(M): + error += abs(b[i][j]) + + u = u_new + v = v_new + p = p_new + + # Plotting + print(u) + print(v) + print(p) + print(error) + x, y = np.meshgrid( + np.linspace(0, domain_size[1], shape[1]), + np.linspace(0, domain_size[0], shape[0]), + ) + + if iteration % 5 == 0: + axes.pcolormesh(x, y, p, cmap='hot') + plt.quiver(x, y, u, v, scale=1) + plt.pause(0.0001) + + +plt.show() -- cgit v1.2.3