A convergence of a MFE-FV method for immiscible compressible flow in heterogeneous porous media

This paper deals with the development and analysis of a numerical method for a coupled system describing immiscible compressible two-phase flow through heterogeneous porous media. The system is modelled in a fractional flow formulation which consists of a parabolic equation (the global pressure equation) coupled with a nonlinear degenerated diffusion-convection one (the saturation equation). A mixed finite element (MFE) method is used to discretize the pressure equation and is combined with a conservative finite volume (FV) method on unstructured grids for the saturation equation. It is shown that the FV scheme satisfies a discrete maximum principle. We derive L∞ and BV estimates under an appropriate CFL condition. Then we prove the convergence of the approximate solution to a weak solution of the coupled system. Numerical results for water-gas flow through engineered and geological barriers for a geological repository of radioactive waste are presented to illustrate the performance of the method in two space dimensions.