Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow

TL;DR

This paper introduces a stable, accurate, and bound-preserving discontinuous Galerkin method for simulating incompressible two-phase flow in porous media, effectively handling gravity, capillarity, and heterogeneity.

Contribution

It develops a fully implicit DG scheme with flux and slope limiters that ensures maximum principle satisfaction and local mass conservation in complex flow simulations.

Findings

The method accurately captures flow dynamics in benchmark tests.

Solutions satisfy maximum principle constraints.

The scheme conserves mass locally in simulations.

Abstract

This paper proposes a fully implicit numerical scheme for immiscible incompressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The objective is to develop a fully implicit stable discontinuous Galerkin (DG) solver for this system that is accurate, bound-preserving, and locally mass conservative. To achieve this, we augment our DG formulation with post-processing flux and slope limiters. The proposed framework is applied to several benchmark problems and the discrete solutions are shown to be accurate, to satisfy the maximum principle and local mass conservation.