Enriched Galerkin methods for two-phase flow in porous media with capillary pressure
For computational geoscience, this provides a more efficient numerical method for simulating two-phase flow in heterogeneous porous media.
The paper proposes an enriched Galerkin method for two-phase flow in porous media with capillary pressure, achieving local conservation with fewer degrees of freedom than discontinuous Galerkin and using entropy viscosity stabilization to avoid oscillations. Numerical examples verify the method's capabilities.
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.