Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump

A finite volume method based on a VFRoe solver to simulate the flow of compressible gas in a variable porous medium for two-dimensional geometries is proposed. The modeling is based on the Euler system where a non-conservative term is added to take the porosity variation into account. A detailed presentation of the scheme is given, the main point is the construction of non-conservative fluxes to reproduce the non-conservation aspect of the problem. We compare the numerical method with an exact solution of the Riemann problem and we check that the method preserves steady-state situations even if we use a discontinuous jump for the porosity. Finally, we present two simulations involving a two-dimensional gas flow.