When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each material are different, or at the very least don't have continuous derivatives at the boundary (for example: poisson's equation for electric potential moving from gas to metal).
My question is, how do I handle these cells. Do I split the cell in half so each partial cell is entirely contained in one material or do I treat the boundaries of the cell as the material boundaries (i.e. purely gas cells see the cell boundaries as metal and metal cells see the cell boundaries as gas)? If I split the cell, do I move the cell center for each off of the new boundary? Any book or reference handling this would be greatly appreciated, since all the references I have found for dual mesh FVM limit themselves to dirichlet conditions, and don't hanlde interfaces at all.
