Multiphysics mixed finite element method with Nitsche's technique for Stokes poroelasticity problem

TL;DR

This paper introduces a novel multiphysics mixed finite element method with Nitsche's technique for solving the Stokes-poroelasticity problem, enabling stable and accurate simulations of coupled fluid-structure interactions.

Contribution

It reformulates the poroelasticity component with pseudo-pressures, and develops a loosely-coupled time-stepping method with proven stability and error estimates.

Findings

Proved existence and uniqueness of solutions.

Developed a stable, error-estimated numerical scheme.

Decoupled the complex problem into three manageable sub-problems.

Abstract

In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing two pseudo-pressures to reveal the underlying deformation and diffusion multi physical processes in the Stokes-poroelasticity problem. Then, we prove the existence and uniqueness of weak solution of the reformulated and original problem. And we use Nitsche's technique to approximate the coupling condition at the interface to propose a loosely-coupled time-stepping method -- multiphysics mixed finite element method for space variables, and we decouple the reformulated problem into three sub-problems at each time step -- a Stokes problem, a generalized Stokes problem and a mixed diffusion problem. Also, we give the stability analysis and error estimates of the loosely-coupled time-stepping method.