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

TL;DR

This paper introduces an enriched Galerkin method for simulating two-phase flow in porous media, combining local conservation, fewer degrees of freedom, and stabilization techniques for improved accuracy and efficiency.

Contribution

The paper develops an enriched Galerkin approach with entropy viscosity stabilization and adaptive mesh refinement for two-phase flow, enhancing computational efficiency and accuracy over existing methods.

Findings

EG methods are locally conservative and computationally efficient.

Entropy viscosity stabilization prevents non-physical oscillations.

Numerical examples demonstrate the method's effectiveness across various conditions.

Abstract

In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase pressure saturation system with capillary pressure in heterogeneous porous media. The EG methods are locally conservative, have fewer degrees of freedom compared to discontinuous Galerkin (DG), and have an efficient pressure solver. To avoid non-physical oscillations, an entropy viscosity stabilization method is employed for high order saturation approximations. Entropy residuals are applied for dynamic mesh adaptivity to reduce the computational cost for larger computational domains. The iterative and sequential IMplicit Pressure and Explicit Saturation (IMPES) algorithms are treated in time. Numerical examples with different relative permeabilities and capillary pressures are included to verify and to demonstrate the capabilities of EG.