A hybridizable discontinuous Galerkin method for two-phase flow in heterogeneous porous media

TL;DR

This paper introduces a high-order hybridizable discontinuous Galerkin method for simulating two-phase flow in heterogeneous porous media, improving efficiency and accuracy over traditional methods.

Contribution

The paper develops a novel HDG-based semi-implicit approach that reduces globally coupled degrees of freedom and maintains mass conservation in two-phase flow simulations.

Findings

Method achieves high accuracy and robustness.

Numerical examples verify convergence and effectiveness.

Significant reduction in degrees of freedom compared to standard methods.

Abstract

We present a new method for simulating incompressible immiscible two-phase flow in porous media. The semi-implicit method decouples the wetting phase pressure and saturation equations. The equations are discretized using a hybridizable discontinuous Galerkin (HDG) method. The proposed method is of high order, conserves global/local mass balance, and the number of globally coupled degrees of freedom is significantly reduced compared to standard interior penalty discontinuous Galerkin methods. Several numerical examples illustrate the accuracy and robustness of the method. These examples include verification of convergence rates by manufactured solutions, common 1D benchmarks and realistic discontinuous permeability fields.