A Sequentially- Hybridized Locally Conservative Non-conforming Finite Element Scheme for Two-phase Flow Simulation through Heterogeneous Porous Media

Abstract

Accurate two-phase flow modeling has a crucial role in detecting pollution in aquifers and/or in the simulating immiscible flow through porous media. In this research, a new hybrid numerical method based on the lower order non-conforming finite element method (NCFEM) and interior penalty discontinuous Galerkin (DG) method is proposed to simulate two-phase incompressible flow in heterogeneous porous media. The pressure and transport saturation equations are discretized by using the non-conforming Crouzeix-Raviart (CR) finite element and the symmetric weighed interior penalty discontinuous Galerkin (SWIPM). As a result of determining the degrees of freedom at the midpoint of neighboring element edges, a consistent set of pressure and velocity fields is obtained via the NCFEM. An H(div) projection based on the Raviart-Thomas (RT) element is implemented to improve the results resolution and preserve the continuity of the normal component of the velocity field. Besides, the spurious numerical oscillations of the saturation solution at the end of each time step are removed by using a novel vertex-based slope limiter, named the modified Chavent-Jaffre limiter. The accuracy and performance of the proposed numerical method are assessed by solving the Buckley-Leverett and McWhorter-Sunada benchmark problems, along with two test problems associated with highly heterogeneous porous media. The numerical results indicate that the proposed scheme has a remarkable potential to accurately capture the shock front and sharp interface zone of immiscible phases in the heterogeneous aquifers and other porous media.