A Locking-free and Loosely Coupled Robin-Robin Scheme for Fluid-Poroelasticity Interaction

TL;DR

This paper introduces a novel, locking-free, and fully decoupled numerical scheme for fluid-poroelasticity interaction problems, ensuring stability and robustness across extreme parameter regimes.

Contribution

The authors develop a new reformulation and Robin-Robin coupling scheme that achieves locking-free, unconditionally stable, and parallelizable solutions for fluid-poroelastic systems.

Findings

The scheme is unconditionally stable and provides optimal error estimates.

Numerical experiments confirm locking-robust performance.

The method allows independent, parallel solution of subproblems.

Abstract

We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related parameter regimes while preserving the physical interface coupling structure.To address this issue, we introduce two auxiliary variables and reformulate the Biot system as a four-field problem consisting of a dynamic Stokes-like system coupled with a diffusion equation. Crucially, this reformulation preserves the original interface conditions. Based on Robin-Robin transmission conditions with explicitly lagged interface data, we construct a fully decoupled scheme in which the fluid and poroelastic subproblems can be solved independently and in parallel at each time step, without sub-iterations.We prove that the resulting method is unconditionally stable and derive optimal-order error estimates in the $H^1$-norm. The analysis further shows that the scheme is robust with respect to extreme poroelastic parameters and avoids the locking effects inherent in standard formulations. Numerical experiments confirm the theoretical convergence results and demonstrate the locking-robust performance of the proposed method.