Anisotropic f coefficient for PDE solving

Hello everybody,

I am modelling a multyphysics simulation between current flowing within plate and the consequent Joule heating. I have a system of 2 PDEs: 1) the Laplace equation of the electric potential; 2) the heat equation.

The coupling between the two is given by the Joule heating term (forcing term of the heat equation) that is: σ*|∇ V|^2, with σ the electrical conductivity, and V the potential.

The complexity is given by the fact that σ is anisotropic, and there are two different values for x-direction and y-direction (2.5 and 0.042 respectively).

In the definition of the fcoefficient for the heat equation (the second in order) I wrote this:

f(2,:)= 2.5.*(state.ux(1,:)).^2+0.042.*(state.uy(1,:)).^2;

with state.ux(1,:) I suppose it refers to the gradeint (in x) of the potential, that should be the solution of the first PDE.

but the system gives me an error. How can I overcame this? Moreover, written in this way, does this expression take in account the anisotropy of σ?

Thanks for the help!!!!!

Answer 1

[Torsten]

Maybe page 2-79 under

http://uk.mathworks.com/help/pdf_doc/pde/pde.pdf

?

[Andrea Zacheo]

Hi thanks for the asnwer, but under the page 2-79 of the manual, there is the explanation of the c coefficent, nothing related to the f coefficent.

The given error is: Number 1 of rows in the f coefficient matrix must be equal to the number 2 of equations in the system.

[Torsten]

According to the documentation, this should work:

specifyCoefficients(model,'f',@fcoeffunction,...)
    
function f = fcoeffunction(location,state)
  N = 2; % Number of equations
  nr = length(location.x); % Number of columns
  f = zeros(N,nr); % Allocate f
  % Now the particular functional form of f
  f(1,:) = 0.0;   % or whatever you want to set here
  f(2,:) = 2.5*(state.ux(1,:)).^2+0.042*(state.uy(1,:)).^2;
end

If not, I wouldn't know.

[Andrea Zacheo]

That's exactly what I wrote :( :(

[Torsten]

What do you get for

size(state.uy)
size(state.ux)

Are they equal ?