Amiga-Freak |
March 1, 2016 11:39 |
Diffusion Equations coupled by Boundary Conditions
Hi, I'm new here and not sure whether my question is in the right place.
I have the following problem:
I'd like to solve two diffusion equations, e.g.
and
which means the PDEs are coupled by their boundary conditions.
The solution of u depends on w by a Dirichlet BC.
And w depends on u by a Neumann BC.
At the moment I first solve the equation for u, then compute g(u) and afterwards solve the equation for w, which allows me to compute f(w) for the next iteration, etc. ....
This works very nice for the stationary case, i.e. for
For the time dependent case however....the method is highly unstable.
I'm searching now for a method to solve both equations simultaneously, somehow - instead of one after another.
But I have no clue how to do this. If one searches for literature about this issue, it seems nobody has ever had the problem to solve PDEs coupled by boundary conditions.
Any hint? Any literature? Ideas?
BTW: I'm not working with any commercial software, but a own FEM software written in Fortran. Therefore please don't recommend commercial software.
Greetings,
Amiga-Freak
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