Created
June 2, 2011 17:40
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2Ddiffusion
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"""Solve the 2D diffusion equation using CN and finite differences.""" | |
from time import sleep | |
import numpy as np | |
import matplotlib.pyplot as plt | |
import networkx as nx | |
from pylab import * | |
# The total number of nodes | |
nodx = 3 | |
nody = 3 | |
nnodes = nodx*nody | |
#this is for the plotting | |
xmin = 0.0 | |
xmax = 1.0 | |
ymin = 0.0 | |
ymax = 1.0 | |
# Ny = 4 | |
# Nx = 4 | |
# tmin = 0.0 | |
# tmax = 1000.0 | |
# Nt = 3000 | |
# The total number of times | |
ntimes = 100 | |
# The time step | |
dt = 0.5 | |
# The diffusion constant | |
D = 0.1 | |
# The spatial mesh size | |
h = 1.0 | |
tmin = 0 | |
tmax = dt*ntimes | |
x, dx = np.linspace(xmin, xmax, nodx, retstep=True) | |
y, dy = np.linspace(ymin, ymax, nody, retstep=True) | |
t, dt = np.linspace(tmin, tmax, ntimes, retstep=True) | |
G = nx.grid_graph(dim=[nodx,nody]) | |
L = np.matrix(nx.laplacian(G)) | |
#making an expression for the heat source to go into the rhs section | |
C = np.matrix(np.zeros((nnodes,nnodes))) | |
C[nnodes/2,nnodes/2] = 0 | |
# The rhs of the diffusion equation | |
rhs = -D*L/h**2 + C | |
# Setting initial temperature | |
T = 60*np.matrix(np.ones((nnodes,ntimes))) | |
for i in range(nnodes/2): | |
T[i,0] = 0; | |
# Setup the time propagator. In this case the rhs is time-independent so we | |
# can do this once. | |
ident = np.matrix(np.eye(nnodes,nnodes)) | |
pmat = ident+(dt/2.0)*rhs | |
mmat = ident-(dt/2.0)*rhs | |
propagator = np.linalg.inv(mmat)*pmat | |
# Propagate E is for energy conservation | |
E = np.zeros(ntimes) | |
for i in range(ntimes-1): | |
E[i] = sum(T[:,i]) | |
T[:,i+1] = propagator*T[:,i] | |
# To plot 1 time | |
print E[2] | |
#need to convert the big string T into a matrix for plotting and visualization | |
w = 0 | |
# R = np.matrix(np.zeros((nodx,nody,ntimes))) | |
# t[:,:,:] = R[:,:,:] | |
# a 3d array (two stacked 2d arrays) | |
t = np.zeros((nodx, nody, ntimes)) | |
w = 0 | |
for p in range(ntimes): | |
for i in range(nodx): | |
for j in range(nody): | |
t[i,j,p] = T[w, p] | |
w = w + 1 | |
w = 0 | |
# print w | |
print t[:,:,1] | |
#cannot plot numpy arrays! so we have to use a normal u array | |
# u[:,:] = T[:,:] | |
V, dV = np.linspace(0, 70, 21, retstep=True) | |
print V | |
CS = plt.contourf(x,y,t[:,:,0], V) | |
plt.ylabel('distance (m)') | |
plt.xlabel('distance (m)') | |
# Make a colorbar for the ContourSet returned by the contourf call. | |
cbar = colorbar(CS) | |
cbar.ax.set_ylabel('Temperature (K)') | |
plt.show() | |
# To plot all times | |
#plt.plot(T) |
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Hi! I've been trying to run your code, but I keep getting an error at line 52 reading unsupported operand type(s) for *: 'int' and 'NoneType'. Could you please help me fix this so I can run the code? Thanks!