-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathCFD.py
269 lines (227 loc) · 9.51 KB
/
CFD.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
import numpy as np
import sys
from matplotlib import pyplot as plt
from IPython import display
from base import plot2d
class NavierStokes (plot2d):
def __init__(self):
plot2d.__init__(self)
# 流体の密度[kg/m^3]
self.rho = 1e3
# 流体の動粘度[m^2/s]
self.ν = 1e-6
# フタの移動速度[m/s]
self.Uwall = 0.01
# unit [m]
self.lx = 0.01
self.ly = 0.01 / 2
self.nx = 21
self.ny = 11
self.x1d = np.linspace(0, self.lx, self.nx)
self.y1d = np.linspace(0, self.ly, self.ny)
self.x, self.y = np.meshgrid(self.x1d, self.y1d)
self.dx = self.lx / (self.nx - 1)
self.dy = self.ly / (self.ny - 1)
self.lt = 3 * self.lx / self.Uwall
self.dt = 0.1 * self.dx / self.Uwall
self.nt = int(np.ceil(self.lt / self.dt))
# 加速係数
self.t = 0
self.alp = 1.74
self.eps = 1e-5
# Veclocity
self.u = np.zeros_like(self.x)
self.v = np.zeros_like(self.y)
self.p = np.zeros_like(self.x)
self.u_aux = np.zeros_like(self.u)
self.v_aux = np.zeros_like(self.v)
self.tetha = np.zeros_like(self.p)
self.velocityBoundary()
# figure
xyz = self.norm_p()
self.img = self.axs.contourf(self.x, self.y, self.p, cmap="jet")
self.vec = self.axs.quiver(self.x, self.y, self.u, self.v, scale=1000)
self.cbr = self.fig.colorbar(self.img)
self.fig.savefig(self.tmpdir + "CFD_{:d}.png".format(self.t))
def run(self):
for n in range(500):
self.t += 1
# 中間速度を計算
self.computeAuxiallyVelocity()
# 中間速度の発散を計算
self.computeDivergenceAuxiallyVelocity()
# 圧力を計算
self.computePressurePoisson()
# 中間速度を修正して速度を計算
self.computeVelocity()
# self.axs.clear()
# self.cbr.remove()
# for col in self.img.collections:
# self.axs.collections.remove(col)
# for col in self.fig.collections:
# self.fig.collections.remove(col)
self.new_fig()
self.img = self.axs.contourf(self.x, self.y, self.p, cmap="jet")
self.cbr = self.fig.colorbar(self.img)
self.vec.set_UVC(self.u * 1000, self.v * 1000)
cbr_ticks = np.linspace(self.p.min(), self.p.max(), 11)
# self.cbr.update_bruteforce(self.img)
# self.cbr.set_ticks(cbr_ticks)
# plt.draw()
# self.cbr.draw_all()
self.fig.savefig(self.tmpdir + "CFD_{:03d}.png".format(self.t))
self.fig.savefig(self.tmpdir + "CFD.png")
plt.close()
def norm_p(self):
p_min = self.p.min()
p_max = self.p.max()
return (self.p - p_min) / (p_max - self.p)
def velocityBoundary(self):
"""
速度に境界条件を反映する関数．
"""
# Left Wall
self.u[:, 0] = 0.0
self.v[:, 0] = 0.0
# Right Wall
self.u[:, -1] = 0.0
self.v[:, -1] = 0.0
# Bot Wall
self.u[0, :] = 0.0
self.v[0, :] = 0.0
# Top Wall
self.u[-1, :] = self.Uwall
self.v[-1, :] = self.Uwall / 2
def computeAuxiallyVelocity(self):
"""
中間速度を計算する関数．
"""
# val = u[1:-1, 1:-1] - (
# dt * (
# u[1:-1, 1:-1] * (u[1:-1, 2:] - u[1:-1, :-2]) / (dx * 2.0) +
# v[1:-1, 1:-1] * (u[2:, 1:-1] - u[:-2, 1:-1]) / (dy * 2.0)
# ) +
# dt * ν * (
# (u[1:-1, 2:] - 2.0 * u[1:-1, 1:-1] + u[1:-1, :-2]) / (dx**2) +
# (u[2:, 1:-1] - 2.0 * u[1:-1, 1:-1] + u[:-2, 1:-1]) / (dy**2)
# )
# )
#
# val = v[1:-1, 1:-1] - (
# dt * (
# u[1:-1, 1:-1] * (v[1:-1, 2:] - v[1:-1, :-2]) / (dx * 2.0) +
# v[1:-1, 1:-1] * (v[2:, 1:-1] - v[:-2, 1:-1]) / (dy * 2.0)
# ) +
# dt * ν * (
# (v[1:-1, 2:] - 2.0 * v[1:-1, 1:-1] + v[1:-1, :-2]) / (dx**2) +
# (v[2:, 1:-1] - 2.0 * v[1:-1, 1:-1] + v[:-2, 1:-1]) / (dy**2)
# )
# )
u_11 = self.u[1:-1, 1:-1]
u_11_20 = self.u[1:-1, 2:]
u_11_21 = self.u[1:-1, :-2]
u_20_11 = self.u[2:, 1:-1]
u_21_11 = self.u[:-2, 1:-1]
v_11 = self.v[1:-1, 1:-1]
v_11_20 = self.v[1:-1, 2:]
v_11_21 = self.v[1:-1, :-2]
v_20_11 = self.v[2:, 1:-1]
v_21_11 = self.v[:-2, 1:-1]
u_1120 = u_11 * (u_11_20 - u_11_21) / (2 * self.dx)
u_1121 = v_11 * (u_20_11 - u_21_11) / (2 * self.dy)
u_2011 = (u_11_20 - 2.0 * u_11 + u_11_21) / self.dx**2
u_2111 = (u_20_11 - 2.0 * u_11 + u_21_11) / self.dy**2
v_1120 = u_11 * (v_11_20 - v_11_21) / (2 * self.dx)
v_1121 = v_11 * (v_20_11 - v_21_11) / (2 * self.dy)
v_2011 = (v_11_20 - 2.0 * v_11 + v_11_21) / (self.dx**2)
v_2111 = (v_20_11 - 2.0 * v_11 + v_21_11) / (self.dx**2)
self.u_aux[1:-1, 1:-1] = u_11
self.u_aux[1:-1, 1:-1] += -self.dt * (u_1120 + u_1121)
self.u_aux[1:-1, 1:-1] += +self.dt * self.ν * (u_2011 + u_2111)
self.v_aux[1:-1, 1:-1] = v_11
self.v_aux[1:-1, 1:-1] += -self.dt * (v_1120 + v_1121)
self.v_aux[1:-1, 1:-1] += +self.dt * self.ν * (v_2011 + v_2111)
self.velocityBoundary()
def computeDivergenceAuxiallyVelocity(self):
"""
中間速度の発散を計算する関数．
"""
u_aux_11_20 = self.u_aux[1:-1, 2:]
u_aux_11_21 = self.u_aux[1:-1, :-2]
u_aux_112 = (u_aux_11_20 - u_aux_11_21) / (2 * self.dx)
v_aux_20_11 = self.v_aux[1:-1, 2:]
v_aux_21_11 = self.v_aux[1:-1, :-2]
v_aux_211 = (v_aux_20_11 - v_aux_21_11) / (2 * self.dy)
self.tetha[1:-1, 1:-1] = u_aux_112 + v_aux_211
def computePressurePoisson(self):
"""
圧力Poisson方程式を解いて圧力を計算する関数．
"""
dp = np.zeros_like(self.p)
err = 1.0
ite = 0
while err > self.eps:
# forを使った逐次計算
# for j in range(1,Ny-1):
# for i in range(1,Nx-1):
# dp[j,i] =( dy**2*(p[j+1,i]+p[j-1,i]) + dx**2*(p[j,i+1]+p[j,i-1]) - (tetha[j,i]*ρ/dt)*(dx**2*dy**2)\
# )/(2.*(dx**2+dy**2)) - p[j,i]
# p[j,i] += α*dp[j,i]
# Black,odd-numbered row
dp[1:-1:2, 2:-1:2] = (
self.dy**2 * (self.p[1:-1:2, 1:-2:2] + self.p[1:-1:2, 3::2]) +
self.dx**2 * (self.p[:-2:2, 2:-1:2] + self.p[2::2, 2:-1:2]) -
(self.dx * self.dy)**2 * self.rho /
self.dt * self.tetha[1:-1:2, 2:-1:2]
) / (2.0 * (self.dx**2 + self.dy**2)) - self.p[1:-1:2, 2:-1:2]
self.p[1:-1:2, 2:-1:2] += self.alp * dp[1:-1:2, 2:-1:2]
# Black,even-numbered row
dp[2:-1:2, 1:-1:2] = (
self.dy**2 * (self.p[2:-1:2, :-2:2] + self.p[2:-1:2, 2::2]) +
self.dx**2 * (self.p[1:-2:2, 1:-1:2] + self.p[3::2, 1:-1:2]) -
(self.dx * self.dy)**2 * self.rho /
self.dt * self.tetha[2:-1:2, 1:-1:2]
) / (2.0 * (self.dx**2 + self.dy**2)) - self.p[2:-1:2, 1:-1:2]
self.p[2:-1:2, 1:-1:2] += self.alp * dp[2:-1:2, 1:-1:2]
# Red,odd-numbered row
dp[1:-1:2, 1:-1:2] = (
self.dy**2 * (self.p[1:-1:2, :-2:2] + self.p[1:-1:2, 2::2]) +
self.dx**2 * (self.p[:-2:2, 1:-1:2] + self.p[2::2, 1:-1:2]) -
(self.dx * self.dy)**2 * self.rho /
self.dt * self.tetha[1:-1:2, 1:-1:2]
) / (2.0 * (self.dx**2 + self.dy**2)) - self.p[1:-1:2, 1:-1:2]
self.p[1:-1:2, 1:-1:2] += self.alp * dp[1:-1:2, 1:-1:2]
# Red,even-numbered row
dp[2:-1:2, 2:-1:2] = (
self.dy**2 * (self.p[2:-1:2, 1:-2:2] + self.p[2:-1:2, 3::2]) +
self.dx**2 * (self.p[1:-2:2, 2:-1:2] + self.p[3::2, 2:-1:2]) -
(self.dx * self.dy)**2 * self.rho /
self.dt * self.tetha[2:-1:2, 2:-1:2]
) / (2.0 * (self.dx**2 + self.dy**2)) - self.p[2:-1:2, 2:-1:2]
self.p[2:-1:2, 2:-1:2] += self.alp * dp[2:-1:2, 2:-1:2]
# ノイマン境界条件
self.p[0, :] = self.p[1, :]
self.p[:, 0] = self.p[:, 1]
self.p[:, -1] = self.p[:, -2]
self.p[-1, :] = self.p[-2, :]
err_d = np.sum(np.abs(self.p))
if err_d < 1e-20:
err_d = 1.0
# 全てのpが0だと分母が0になるので，合計小さいときは1にする
err = np.sum(np.abs(dp[:])) / err_d
sys.stdout.write(
"\r {:d} {:.10f} / {:.10f}".format(self.t, err, self.eps))
sys.stdout.flush()
print("\n")
def computeVelocity(self):
"""
時刻n+1の速度を計算する関数．
"""
self.u[1:-1, 1:-1] = self.u_aux[1:-1, 1:-1] - self.dt / self.rho * \
(self.p[1:-1, 2:] - self.p[1:-1, :-2]) / (self.dx * 2.0)
self.v[1:-1, 1:-1] = self.v_aux[1:-1, 1:-1] - self.dt / self.rho * \
(self.p[2:, 1:-1] - self.p[:-2, 1:-1]) / (self.dy * 2.0)
self.velocityBoundary()
if __name__ == "__main__":
obj = NavierStokes()
obj.run()