我正在尝试以数值方式求解热方程,并使用颜色映射实时可视化解。但是,地图中的颜色不会更新。是什么原因?这是代码:
from __future__ import division
from pylab import *
dx, dy = 0.01, 0.01
D = 0.01
dx2, dy2 = dx**2 ,dy**2
dt = (dx2*dy2)/(2*D*(dx2+dy2))
endt = 0.1
Nt = int (endt/dt)
endX,endY = 1,1
nx, ny = int(endX/dx), int(endY/dy)
T = zeros([nx,ny])
Tcopy = zeros([nx,ny])
"""initial conditions"""
for i in range(nx):
for j in range(ny):
if( ((i*dx - 0.5)**2 +(j*dy - 0.5)**2 < 0.1) and ((i*dx - 0.5)**2 +(j*dy - 0.5)**2 >0.05) ):
T[i][j] = 10
def integrate(T,Tcopy):
T[1:-1, 1:-1] = Tcopy[1:-1, 1:-1] + D*dt*( (Tcopy[2:, 1:-1] - 2*Tcopy[1:-1, 1:-1] + T[:-2, 1:-1])/dx2 + (Tcopy[1:-1, 2:] - 2*Tcopy[1:-1, 1:-1] + T[1:-1, :-2])/dy2 )
Tcopy = copy(T)
return Tcopy,T
x = arange(0, endX, dx)
y = arange(0, endY, dy)
X,Y = meshgrid(x, y)
"""creating the plot"""
fig, ax_lst = plt.subplots(1, 1)
im = ax_lst.imshow(T, interpolation='nearest',
origin='bottom',
aspect='auto',
vmin=np.min(T),
vmax=np.max(T),
cmap='hot',extent=[0,1,0,1])
fig.colorbar(im)
"""main loop"""
for t in range(Nt):
im.set_data(T)
plt.draw()
plt.pause(0.1)
Tcopy,T = integrate(T,Tcopy)