Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media

TL;DR

This paper develops and analyzes a discontinuous Galerkin method for simulating incompressible three-phase flow in porous media, demonstrating its well-posedness, convergence, and validating the theoretical error estimates through numerical experiments.

Contribution

It introduces a novel discontinuous Galerkin approach with a first order time extrapolation for three-phase flow, providing rigorous analysis and validation.

Findings

The method is well-posed and converges with first order.

Numerical results confirm the theoretical error estimates.

The approach effectively solves the three-phase flow equations sequentially.

Abstract

This paper presents and analyzes a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. We use a first order time extrapolation which allows us to solve the equations implicitly and sequentially. We show that the discrete problem is well-posed, and obtain a priori error estimates. Our numerical results validate the theoretical results, i.e. the algorithm converges with first order.