A Hybrid High-Order method for the power-law Brinkman problem with robust error estimates in all regimes
It offers a robust numerical method for fluid flow in porous media with non-Newtonian viscosity, addressing a known challenge in computational fluid dynamics.
The paper proposes a Hybrid High-Order method for the power-law Brinkman problem that works on general meshes with arbitrary approximation orders and provides robust error estimates across all regimes from Stokes to Darcy, with numerical experiments confirming the theory.
In this work we propose and analyze a new Hybrid High-Order method for the Brinkman problem for fluids with power-law viscosity. The proposed method supports general meshes and arbitrary approximation orders and is robust in all regimes, from pure (power-law) Stokes to pure Darcy. Robustness is reflected by error estimates that distinguish the contributions from Stokes- and Darcy-dominated elements as identified by an appropriate dimensionless number, and that additionally account for pre-asymptotic orders of convergence. Theoretical results are illustrated by a complete panel of numerical experiments.