Geometric Multigrid for Darcy and Brinkman models of flows in highly heterogeneous porous media: A numerical study

TL;DR

This paper demonstrates the effectiveness of geometric multigrid methods combined with divergence-conforming discontinuous Galerkin techniques for simulating Darcy and Brinkman flows in highly heterogeneous porous media, showing robustness across mesh sizes and permeability contrasts.

Contribution

It introduces a novel multigrid approach tailored for Darcy and Brinkman models using divergence-conforming DG methods with patch-based smoothers, enhancing robustness in complex media.

Findings

Method is robust to mesh size variations.

Method handles high permeability contrast effectively.

Benchmark results confirm numerical stability.

Abstract

We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous Galerkin methods and overlapping, patch based domain decomposition smoothers. We show in benchmark experiments that the method is robust with respect to mesh size and contrast of permeability for highly heterogeneous media.