A Sequential Discontinuous Galerkin Method for Two-Phase Flow in Deformable Porous Media

TL;DR

This paper introduces a novel sequential discontinuous Galerkin method for simulating two-phase flow in deformable porous media, demonstrating its accuracy and robustness through 3D numerical results.

Contribution

The paper develops a new numerical scheme combining interior penalty discontinuous Galerkin and sequential time-stepping for two-phase flow in poroelastic media, with proven existence of solutions.

Findings

The method accurately captures two-phase flow dynamics.

Numerical results confirm robustness in 3D simulations.

The scheme is effective for complex poroelastic problems.

Abstract

We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and the displacement. Existence of the solution is proved. Three-dimensional numerical results show the accuracy and robustness of the proposed method.