Solving a system of PDE, not on the same control volume
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Hello, i'm trying to solve a problem similar to the one in the attached photo(not the same one...but the same concept): a system of parabolic PDEs, like the heat transfer problem between different materials. how can i do it with MATLAB? from what i understood, PDEPE can solve a system, but only on the same control volume. any other ideas?
i'll thanks your help in implementing a solution of my problem
Thanks, in advance! Bar
2 Comments
Accepted Answer
Bill Greene
on 10 Dec 2013
Your pdefun function should look something like this:
function [c,f,s] = pdefun(x,t,u,DuDx)
if(x < L)
k = alpha1;
else
k = alpha2;
end
c=1;
f = k*DuDx;
s=0;
end
I probably should also mention that you should experiment with different mesh densities because the mesh affects the accuracy of the pdepe solution. But that recommendation applies whether you have continuous or discontinuous coefficients.
Bill
More Answers (1)
Bill Greene
on 7 Dec 2013
Hi,
There is no difficulty using pdepe to solve your equation. You define xmesh over the full 2L length and, for best results, you want to define the number of elements in xmesh so that there is a node point at x=L. Beyond that, in your pdefun function, you just define the flux in terms of a1 if x<L and a2 if x>L.
Bill
3 Comments
Bill Greene
on 9 Dec 2013
By flux term, I simply mean the f output from pdefun. This is the heat flux in your example-- either alpha_1*dT/dx or alpha_2*dT/dx. The only boundary conditions to be specified are at x=0 and x=2L.
Bill
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