A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model

TL;DR

This paper introduces a finite element method using Lagrange multipliers to simulate the interaction between a free fluid governed by Stokes equations and a poroelastic medium modeled by Biot's system, with stability analysis and numerical validation.

Contribution

It develops a novel Lagrange multiplier approach for coupling Stokes and Biot models, including stability and error analysis, and demonstrates its effectiveness through numerical experiments.

Findings

The method achieves optimal convergence rates.

Numerical experiments confirm theoretical stability.

The approach effectively models fluid-poroelastic interactions.

Abstract

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is employed to impose weakly this condition. A stability and error analysis is performed for the semi-discrete continuous-in-time and the fully discrete formulations. A series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the sensitivity of the model with respect to its parameters.