A Fully Parallelizable Loosely Coupled Scheme for Fluid-Poroelastic Structure Interaction Problems

TL;DR

This paper introduces a fully parallelizable, loosely coupled numerical scheme for fluid-poroelastic structure interaction problems, enabling efficient, stable, and accurate simulations without sub-iterations, applicable to complex real-world scenarios.

Contribution

The paper presents the first fully parallelizable, unconditionally stable scheme for the nonlinear Navier-Stokes-Biot system that avoids sub-iterations and demonstrates first-order temporal accuracy.

Findings

Scheme is unconditionally stable without time step restrictions.

Achieves first-order accuracy in time.

Effective for 2D and 3D real-world applications.

Abstract

We investigate the fluid-poroelastic structure interaction problem in a moving domain, governed by Navier-Stokes-Biot (NSBiot) system. First, we propose a fully parallelizable, loosely coupled scheme to solve the coupled system. At each time step, the solution from the previous time step is used to approximate the coupling conditions at the interface, allowing the original coupled problem to be fully decoupled into seperate fluid and structure subproblems, which are solved in parallel. Since our approach utilizes a loosely coupled scheme, no sub-iterations are required at each time step. Next, we conduct the energy estimates of this splitting method for the linearized problem (Stokes-Biot system), which demonstrates that the scheme is unconditionally stable without any restriction of the time step size from the physical parameters. Furthermore, we illustrate the first-order accuracy in time through two benchmark problems. Finally, to demonstrate that the proposed method maintains its excellent stability properties also for the nonlinear NSBiot system, we present numerical results for both $2D$ and $3D$ NSBiot problems related to real-world physical applications.