A polytopal method for the Brinkman problem robust in all regimes

TL;DR

This paper introduces a new discretisation method for the Brinkman problem that remains stable and accurate across all flow regimes, utilizing hybrid high-order and discrete de Rham techniques with adaptive stabilization.

Contribution

The authors develop a novel hybrid high-order discretisation method for the Brinkman problem that is robust in all regimes and supports general meshes and arbitrary approximation orders.

Findings

Error estimates valid across all regimes due to cut-off factors

Numerical validation confirms robustness and accuracy

Method supports general meshes and arbitrary approximation orders

Abstract

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across the all regimes and provide extensive numerical validation.