-
Notifications
You must be signed in to change notification settings - Fork 0
/
2D_Linear_convection.py
64 lines (51 loc) · 1.3 KB
/
2D_Linear_convection.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
#2D convection equation by FDM
import numpy as np
from matplotlib import pyplot,cm
#pre-processing
l=2 #in meter
h=2
nx=101
dx=l/(nx-1)
ny=nx
dy=h/(ny-1)
nt=101
sigma=0.2
dt=dx*sigma
#solving in 2D
u=np.zeros((ny,nx))
v=np.zeros((ny,nx))
u[:,:]=1
v[:,:]=1
u[int(0.5/dy):int((1/dy)+1),int(0.5/dx):int((1/dx)+1)]=2
v[int(0.5/dy):int((1/dy)+1),int(0.5/dx):int((1/dx)+1)]=2
print(u)
un=np.zeros((ny,nx))
vn=np.zeros((ny,nx))
for n in range(nt):
un=u.copy()
vn=v.copy()
for i in range(1,nx):
for j in range(1,ny):
u[j, i] = un[j, i] - (un[j, i]* 1 * dt / dx * (un[j, i] - un[j,i-1])) - vn[j, i]* 1 * dt / dy * (un[j,i] - un[j-1,i])
v[j, i] = vn[j, i] - (un[j, i]* 1 * dt / dx * (vn[j, i] - vn[j,i-1])) - vn[j, i]* 1 * dt / dy * (vn[j,i] - vn[j-1,i])
u[0, :] = 1
u[-1, :] = 1
u[:, 0] = 1
u[:, -1] = 1
v[0, :] = 1
v[-1, :] = 1
v[:, 0] = 1
v[:, -1] = 1
#post-processing
x=np.linspace(0,l,nx)
y=np.linspace(0,h,ny)
X,Y=np.meshgrid(x,y)
fig = pyplot.figure(figsize=(11, 7), dpi=100)
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, v, cmap=cm.viridis, rstride=2, cstride=2)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$');
#pyplot.contourf(X,Y,u,v,levels=20,vmin=0,vmax=2)
#pyplot.quiver(X,Y,u,v)
#pyplot.streamplot(X, Y, u, v)
pyplot.show()