A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure

TL;DR

This paper introduces a fully-coupled discontinuous Galerkin method for simulating two-phase flow in porous media with discontinuous capillary pressure, demonstrating high accuracy, robustness, and scalability for large-scale 3D problems.

Contribution

The paper presents a novel fully-coupled DG scheme for two-phase flow with discontinuous capillary pressure, improving accuracy and computational efficiency over existing methods.

Findings

Method is accurate and robust across test problems.

No post-processing needed for velocity field, unlike decoupled schemes.

Scales efficiently to large 3D problems with up to 100 million degrees of freedom.

Abstract

In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential / capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes the resulting systems of nonlinear algebraic equations are solved with Newton's method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust and efficient. In particular no post-processing of the DG velocity field is necessary in contrast to results reported by several authors for decoupled schemes. Moreover, the solver scales well in parallel and three-dimensional problems with up to nearly 100 million degrees of freedom per time step have been computed on 1000 processors.