| Abstract: |
| We propose a loosely coupled scheme for the incompressible fluid-fully dynamic poroelasticity interaction (FPSI) problem, which is locking-free for extreme model parameters. By introducing two new auxiliary variables, the poroelastic system is reformulated into a four-field formulation, which can be regarded as a coupling of a dynamic Stokes-like system and a diffusion system. The decoupled scheme is constructed based on Robin-Robin type coupling conditions, evaluating the right-hand side of these conditions at the previous time step. The resulting scheme is fully parallel, meaning that the fluid subsystem and poroelasticity subsystem can be solved independently and concurrently at each time step without expensive sub-iterations. Furthermore, we prove that the scheme is unconditionally stable and provide an error estimate showing that the convergence in the $H^1$ norm is optimal. The error analysis demonstrates that our scheme is robust against extreme model parameters, thereby eliminating the locking inherent in the poroelastic system. Various numerical experiments are presented to validate the stability, convergence and locking-free performance of the proposed scheme. |
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