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.