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

摘要

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.