Numerical scheme to complete a compressible gas flow in variable porosity media

Abstract

We present an approximate Riemann solver coupled with a finite volume method to compute non conservative Euler equations in variable porosity media using ideal gas state law. The non conservative term is numerically taken into account from an original idea of LeRoux (1998) but here Riemann problems at each interface of the mesh are linearized using a VFRoe approach. The main goal is the resolution of the non conservative system even if the porosity is discontinuous. Stationary solutions are determined with continuous and discontinuous porosity in order to test numerical scheme and computations of gas shock subsonic wave moving in a non continuous porosity medium are presented.