The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye

TL;DR

This paper introduces a novel multiphysics model coupling fluid flow with Biot consolidation using total pressure, providing a stable finite element scheme applicable to geophysical and eye poromechanics, with detailed stability analysis and practical applications.

Contribution

A new mixed-primal finite element formulation for coupled fluid-poroelastic flow using total pressure, avoiding Lagrange multipliers and ensuring stability.

Findings

Stable finite element scheme for coupled flow and poroelasticity.

Application to geophysical flows and eye poromechanics.

Insights into interfacial flow regimes related to glaucoma.

Abstract

We consider a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element scheme is proposed solving for the pairs fluid velocity - pressure and displacement - total poroelastic pressure using Stokes-stable elements, and where the formulation does not require Lagrange multipliers to set up the usual transmission conditions on the interface. The stability and well-posedness of the continuous and semi-discrete problems are analysed in detail. Our numerical study is framed in the context of applicative problems pertaining to heterogeneous geophysical flows and to eye poromechanics. For the latter, we investigate different interfacial flow regimes in Cartesian and axisymmetric coordinates that could eventually help describe early morphologic changes associated with glaucoma development in canine species.