Homogenization of immiscible compressible two--phase flow in random porous media

TL;DR

This paper develops a homogenized macroscopic model for immiscible compressible two-phase flow in random porous media, proving convergence of solutions using stochastic two-scale convergence techniques.

Contribution

It introduces a novel homogenization approach for two-phase flow in random media using stochastic two-scale convergence and provides rigorous convergence proofs.

Findings

Derived the effective macroscopic problem for two-phase flow.

Proved convergence of solutions in the homogenization process.

Utilized stochastic two-scale convergence techniques.

Abstract

The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of solutions. Our approach relies on stochastic two-scale convergence techniques, the realization-wise notion of stochastic two-scale convergence being used. Also, we exploit various a priori estimates as well as monotonicity and compactness arguments.