A Lax–Wendroff-IMPES scheme for a two-phase flow in porous media using interior penalty discontinuous Galerkin method

Abstract

An immiscible two-phase flow numerical model in the porous media is developed using the interior penalty Discontinuous Galerkin (DG) finite element method. As a novel approach, the implicit pressure explicit saturation (IMPES) in conjunction with the second-order Lax–Wendroff based on the Taylor expansion was used. Further, the exchanging numerical fluxes were stabilized using projection of the velocity field in the H (div) vectorial interpolation space for improvement of results at heterogeneities. At the end of each time step, nonphysical oscillations were removed using the modified Chavent–Jaffre slope limiter and the calculated saturation values were modified. In order to assess the performance of this novel approach, the Buckley–Leverett and Mc Worther benchmark problems were considered. The model efficiency and capabilities have also been evaluated using two test cases for high heterogeneous porous media.