2Ddiffusion

2Ddiffusion

"""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)

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!