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

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.

36 pages

References in corpus (2)

• Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue
• Coupling Stokes flow with inhomogeneous poroelasticity

Cited by in corpus (5)

• Parameter-robust methods for the Biot-Stokes interfacial coupling without Lagrange multipliers
• Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
• Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion
• Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form
• New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability