2D convection 方程
离散形式
初始条件
#!/usr/bin/python
#coding = utf-8
from mpl_toolkits.mplot3d import Axes3D #3D图必须引入这个库
import numpy as np
import matplotlib.pylab as plt
nx = 81
ny = 81
nt = 60
c=1
dx = 2.0/(nx-1)
dy = 2.0/(ny-1)
sigma = .2
dt = sigma*dx
x = np.linspace(0,2,nx)
y = np.linspace(0,2,ny)
u = np.ones((ny,nx))
u[.5/dy:1/dy+1,.5/dx:1/dx+1]=2
"""
for n in range(nt+1):
un = u.copy()
for i in range(1,len(u)):
for j in range(1,len(u)):
u[i,j] = un[i, j] - (c*dt/dx*(un[i,j] - un[i-1,j]))-(c*dt/dy*(un[i,j]-un[i,j-1]))
u[0,:] = 1
u[-1,:] = 1
u[:,0] = 1
u[:,-1] = 1
"""
#下面的与上面的功能一样，只是形式简单
for n in range(nt+1):
un = u.copy()
u[1:,1:] = un[1:,1:] - c*(dt/dx)*(un[1:,1:]-un[0:-1,1:]) - (dt/dy)*(un[1:,1:]-un[1:,0:-1])
u[0,:] = 1
u[-1,:] = 1
u[:,0] = 1
u[:,-1] = 1
fig = plt.figure( dpi=100)
ax = plt.subplot(111,projection="3d")
X, Y = np.meshgrid(x,y)
surf = ax.plot_surface(X,Y,u[:])
plt.show()
