Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers

TL;DR

This paper introduces a stable, parameter-robust finite element scheme for fluid-structure interaction involving viscous flow and porous media, with effective preconditioners validated through test cases including brain interfacial flow.

Contribution

It develops a novel five-field mixed-primal finite element method with robustness across all material parameters, and proposes preconditioners for efficient solution of the coupled system.

Findings

Stable discretization with robust stability in all parameters

Effective preconditioners for saddle-point problems

Successful application to brain interfacial flow simulations

Abstract

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A five-field mixed-primal finite element scheme is proposed solving for Stokes velocity-pressure and Biot displacement-total pressure-fluid pressure. Adequate inf-sup conditions are derived, and one of the distinctive features of the formulation is that its stability is established robustly in all material parameters. We propose robust preconditioners for this perturbed saddle-point problem using appropriately weighted operators in fractional Sobolev and metric spaces at the interface. The performance is corroborated by several test cases, including the application to interfacial flow in the brain.