|
| 1 | +import dpnp as np |
| 2 | + |
| 3 | +def build_up_b(rho, dt, dx, dy, u, v): |
| 4 | + b = np.zeros_like(u) |
| 5 | + b[1:-1, |
| 6 | + 1:-1] = (rho * (1 / dt * ((u[1:-1, 2:] - u[1:-1, 0:-2]) / (2 * dx) + |
| 7 | + (v[2:, 1:-1] - v[0:-2, 1:-1]) / (2 * dy)) - |
| 8 | + ((u[1:-1, 2:] - u[1:-1, 0:-2]) / (2 * dx))**2 - 2 * |
| 9 | + ((u[2:, 1:-1] - u[0:-2, 1:-1]) / (2 * dy) * |
| 10 | + (v[1:-1, 2:] - v[1:-1, 0:-2]) / (2 * dx)) - |
| 11 | + ((v[2:, 1:-1] - v[0:-2, 1:-1]) / (2 * dy))**2)) |
| 12 | + |
| 13 | + # Periodic BC Pressure @ x = 2 |
| 14 | + b[1:-1, -1] = (rho * (1 / dt * ((u[1:-1, 0] - u[1:-1, -2]) / (2 * dx) + |
| 15 | + (v[2:, -1] - v[0:-2, -1]) / (2 * dy)) - |
| 16 | + ((u[1:-1, 0] - u[1:-1, -2]) / (2 * dx))**2 - 2 * |
| 17 | + ((u[2:, -1] - u[0:-2, -1]) / (2 * dy) * |
| 18 | + (v[1:-1, 0] - v[1:-1, -2]) / (2 * dx)) - |
| 19 | + ((v[2:, -1] - v[0:-2, -1]) / (2 * dy))**2)) |
| 20 | + |
| 21 | + # Periodic BC Pressure @ x = 0 |
| 22 | + b[1:-1, 0] = (rho * (1 / dt * ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx) + |
| 23 | + (v[2:, 0] - v[0:-2, 0]) / (2 * dy)) - |
| 24 | + ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx))**2 - 2 * |
| 25 | + ((u[2:, 0] - u[0:-2, 0]) / (2 * dy) * |
| 26 | + (v[1:-1, 1] - v[1:-1, -1]) / |
| 27 | + (2 * dx)) - ((v[2:, 0] - v[0:-2, 0]) / (2 * dy))**2)) |
| 28 | + |
| 29 | + return b |
| 30 | + |
| 31 | + |
| 32 | +def pressure_poisson_periodic(nit, p, dx, dy, b): |
| 33 | + pn = np.empty_like(p) |
| 34 | + |
| 35 | + for q in range(nit): |
| 36 | + pn = p.copy() |
| 37 | + p[1:-1, 1:-1] = (((pn[1:-1, 2:] + pn[1:-1, 0:-2]) * dy**2 + |
| 38 | + (pn[2:, 1:-1] + pn[0:-2, 1:-1]) * dx**2) / |
| 39 | + (2 * (dx**2 + dy**2)) - dx**2 * dy**2 / |
| 40 | + (2 * (dx**2 + dy**2)) * b[1:-1, 1:-1]) |
| 41 | + |
| 42 | + # Periodic BC Pressure @ x = 2 |
| 43 | + p[1:-1, -1] = (((pn[1:-1, 0] + pn[1:-1, -2]) * dy**2 + |
| 44 | + (pn[2:, -1] + pn[0:-2, -1]) * dx**2) / |
| 45 | + (2 * (dx**2 + dy**2)) - dx**2 * dy**2 / |
| 46 | + (2 * (dx**2 + dy**2)) * b[1:-1, -1]) |
| 47 | + |
| 48 | + # Periodic BC Pressure @ x = 0 |
| 49 | + p[1:-1, |
| 50 | + 0] = (((pn[1:-1, 1] + pn[1:-1, -1]) * dy**2 + |
| 51 | + (pn[2:, 0] + pn[0:-2, 0]) * dx**2) / (2 * (dx**2 + dy**2)) - |
| 52 | + dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, 0]) |
| 53 | + |
| 54 | + # Wall boundary conditions, pressure |
| 55 | + p[-1, :] = p[-2, :] # dp/dy = 0 at y = 2 |
| 56 | + p[0, :] = p[1, :] # dp/dy = 0 at y = 0 |
| 57 | + |
| 58 | + |
| 59 | +def channel_flow(nit, u, v, dt, dx, dy, p, rho, nu, F): |
| 60 | + udiff = 1 |
| 61 | + stepcount = 0 |
| 62 | + |
| 63 | + while udiff > .001: |
| 64 | + un = u.copy() |
| 65 | + vn = v.copy() |
| 66 | + |
| 67 | + b = build_up_b(rho, dt, dx, dy, u, v) |
| 68 | + pressure_poisson_periodic(nit, p, dx, dy, b) |
| 69 | + |
| 70 | + u[1:-1, |
| 71 | + 1:-1] = (un[1:-1, 1:-1] - un[1:-1, 1:-1] * dt / dx * |
| 72 | + (un[1:-1, 1:-1] - un[1:-1, 0:-2]) - |
| 73 | + vn[1:-1, 1:-1] * dt / dy * |
| 74 | + (un[1:-1, 1:-1] - un[0:-2, 1:-1]) - dt / (2 * rho * dx) * |
| 75 | + (p[1:-1, 2:] - p[1:-1, 0:-2]) + nu * |
| 76 | + (dt / dx**2 * |
| 77 | + (un[1:-1, 2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) + |
| 78 | + dt / dy**2 * |
| 79 | + (un[2:, 1:-1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1])) + |
| 80 | + F * dt) |
| 81 | + |
| 82 | + v[1:-1, |
| 83 | + 1:-1] = (vn[1:-1, 1:-1] - un[1:-1, 1:-1] * dt / dx * |
| 84 | + (vn[1:-1, 1:-1] - vn[1:-1, 0:-2]) - |
| 85 | + vn[1:-1, 1:-1] * dt / dy * |
| 86 | + (vn[1:-1, 1:-1] - vn[0:-2, 1:-1]) - dt / (2 * rho * dy) * |
| 87 | + (p[2:, 1:-1] - p[0:-2, 1:-1]) + nu * |
| 88 | + (dt / dx**2 * |
| 89 | + (vn[1:-1, 2:] - 2 * vn[1:-1, 1:-1] + vn[1:-1, 0:-2]) + |
| 90 | + dt / dy**2 * |
| 91 | + (vn[2:, 1:-1] - 2 * vn[1:-1, 1:-1] + vn[0:-2, 1:-1]))) |
| 92 | + |
| 93 | + # Periodic BC u @ x = 2 |
| 94 | + u[1:-1, -1] = ( |
| 95 | + un[1:-1, -1] - un[1:-1, -1] * dt / dx * |
| 96 | + (un[1:-1, -1] - un[1:-1, -2]) - vn[1:-1, -1] * dt / dy * |
| 97 | + (un[1:-1, -1] - un[0:-2, -1]) - dt / (2 * rho * dx) * |
| 98 | + (p[1:-1, 0] - p[1:-1, -2]) + nu * |
| 99 | + (dt / dx**2 * |
| 100 | + (un[1:-1, 0] - 2 * un[1:-1, -1] + un[1:-1, -2]) + dt / dy**2 * |
| 101 | + (un[2:, -1] - 2 * un[1:-1, -1] + un[0:-2, -1])) + F * dt) |
| 102 | + |
| 103 | + # Periodic BC u @ x = 0 |
| 104 | + u[1:-1, |
| 105 | + 0] = (un[1:-1, 0] - un[1:-1, 0] * dt / dx * |
| 106 | + (un[1:-1, 0] - un[1:-1, -1]) - vn[1:-1, 0] * dt / dy * |
| 107 | + (un[1:-1, 0] - un[0:-2, 0]) - dt / (2 * rho * dx) * |
| 108 | + (p[1:-1, 1] - p[1:-1, -1]) + nu * |
| 109 | + (dt / dx**2 * |
| 110 | + (un[1:-1, 1] - 2 * un[1:-1, 0] + un[1:-1, -1]) + dt / dy**2 * |
| 111 | + (un[2:, 0] - 2 * un[1:-1, 0] + un[0:-2, 0])) + F * dt) |
| 112 | + |
| 113 | + # Periodic BC v @ x = 2 |
| 114 | + v[1:-1, -1] = ( |
| 115 | + vn[1:-1, -1] - un[1:-1, -1] * dt / dx * |
| 116 | + (vn[1:-1, -1] - vn[1:-1, -2]) - vn[1:-1, -1] * dt / dy * |
| 117 | + (vn[1:-1, -1] - vn[0:-2, -1]) - dt / (2 * rho * dy) * |
| 118 | + (p[2:, -1] - p[0:-2, -1]) + nu * |
| 119 | + (dt / dx**2 * |
| 120 | + (vn[1:-1, 0] - 2 * vn[1:-1, -1] + vn[1:-1, -2]) + dt / dy**2 * |
| 121 | + (vn[2:, -1] - 2 * vn[1:-1, -1] + vn[0:-2, -1]))) |
| 122 | + |
| 123 | + # Periodic BC v @ x = 0 |
| 124 | + v[1:-1, |
| 125 | + 0] = (vn[1:-1, 0] - un[1:-1, 0] * dt / dx * |
| 126 | + (vn[1:-1, 0] - vn[1:-1, -1]) - vn[1:-1, 0] * dt / dy * |
| 127 | + (vn[1:-1, 0] - vn[0:-2, 0]) - dt / (2 * rho * dy) * |
| 128 | + (p[2:, 0] - p[0:-2, 0]) + nu * |
| 129 | + (dt / dx**2 * |
| 130 | + (vn[1:-1, 1] - 2 * vn[1:-1, 0] + vn[1:-1, -1]) + dt / dy**2 * |
| 131 | + (vn[2:, 0] - 2 * vn[1:-1, 0] + vn[0:-2, 0]))) |
| 132 | + |
| 133 | + # Wall BC: u,v = 0 @ y = 0,2 |
| 134 | + u[0, :] = 0 |
| 135 | + u[-1, :] = 0 |
| 136 | + v[0, :] = 0 |
| 137 | + v[-1, :] = 0 |
| 138 | + |
| 139 | + udiff = (np.sum(u) - np.sum(un)) / np.sum(u) |
| 140 | + stepcount += 1 |
| 141 | + |
| 142 | + return stepcount |
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