A Locking-free and Loosely Coupled Robin-Robin Scheme for Fluid-Poroelasticity Interaction
This addresses a computational bottleneck in simulating coupled fluid-poroelastic systems, particularly for extreme parameter regimes, though it appears incremental as an improved scheme within existing frameworks.
The authors tackled the challenge of designing robust partitioned schemes for fluid-poroelasticity interaction problems by introducing a reformulation with auxiliary variables and a fully decoupled Robin-Robin scheme. They proved unconditional stability, derived optimal-order error estimates, and demonstrated locking-robust performance in numerical experiments.
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.