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In this paper, we propose an enriched Galerkin (EG) approximation for atwo-phase pressure saturation system with capillary pressure in heterogeneousporous media. The EG methods are locally conservative, have fewer degrees offreedom compared to discontinuous Galerkin (DG), and have an efficient pressuresolver. To avoid non-physical oscillations, an entropy viscosity stabilizationmethod is employed for high order saturation approximations. Entropy residualsare applied for dynamic mesh adaptivity to reduce the computational cost forlarger computational domains. The iterative and sequential IMplicit Pressureand Explicit Saturation (IMPES) algorithms are treated in time. Numericalexamples with different relative permeabilities and capillary pressures areincluded to verify and to demonstrate the capabilities of EG.

Enriched Galerkin methods for two-phase flow in porous media with capillary pressure