A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes/Biot problem

TL;DR

This paper introduces a hybridizable discontinuous Galerkin method for solving the coupled Navier-Stokes and Biot equations, providing stability, error estimates, and numerical validation for this complex fluid-poroelastic interaction problem.

Contribution

The paper develops a novel hybridizable discontinuous Galerkin approach for coupled Navier-Stokes/Biot equations, including stability analysis and error bounds.

Findings

Method is stable under certain data bounds

Error estimates are established for the numerical scheme

Numerical examples confirm theoretical results

Abstract

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and prove a priori error estimates. A numerical example confirms our analysis.