I would like to solve for the electric potential and magnetic vector potential using the finite volume method (collocated grid). My equations are:
$\nabla \cdot \nabla A = \mu_m \sigma \nabla\phi$
The domain is a wedge, with the following boundary conditions:
- A fixed gradient for the electric potential $\phi$ on the top, zero gradient at the bottom and a zero value at the side boundary
- Zero gradient for the magnetic vector potential $A$ on all boundaries
I didn't expect this would be a tough problem, but the linear solver (GAMG) only converges with under-relaxation, and the result is dependent on the value of the under-relaxation factor. Can anyone give me a hint where things are going wrong?
Additional information: The software package I use is OpenFOAM. The gradients are discretized using the Gauss linear scheme, and the laplacian with "Gauss linear corrected" (explicit non-orthogonal correction).