Construction of a low Mach finite volume scheme for the isentropic Euler system with porosity

Classical finite volume schemes for the Euler system are not accurate at low Mach number and some fixes have to be used were developed in a vast literature over last two decades. The question we interested this article is: What about if porosity is no longer uniform? We first show that problem may understood on linear wave equation taking into account porosity. explain influence of cell geometry accuracy property number. In triangular case, stationary space Godunov scheme approaches well enough continuous constant pressure divergence-free velocity, while case Cartesian case. On meshes, fix proposed proved recovered. Based study, numerical non-linear system, with non-conservative source term due variations, tested.