A Stable Loosely-Coupled Dirichlet-Neumann Scheme for Fluid-Structure Interaction with Large Added Mass

TL;DR

This paper introduces a new stable loosely-coupled Dirichlet-Neumann scheme for fluid-structure interaction problems with large added mass, improving stability and convergence over existing methods through a novel partitioning strategy and theoretical analysis.

Contribution

The paper develops a new strongly-coupled partitioning strategy and derives a stable loosely-coupled scheme for FSI with large added mass, supported by convergence and stability analysis.

Findings

The new SC scheme shows enhanced convergence over standard methods.

The LC scheme is conditionally stable in large added mass regimes.

Numerical experiments confirm the theoretical stability and effectiveness.

Abstract

Solving fluid-structure interaction (FSI) problems when the densities are similar (large added mass), such as in hemodynamics, is challenging since the stability and convergence of the adopted numerical scheme could be compromised. In particular, while loosely coupled (LC) partitioned approaches are appealing due to their computational efficiency, the stability issues arising in high added mass regimes limit their applicability. In this work, we present a new strongly-coupled (SC) partitioning strategy for the solution of the FSI problem, from which we derive a stable LC scheme based on Dirichlet and Neumann interface conditions. We analyse the convergence of the new SC scheme on a benchmark problem, demonstrating enhanced behaviour over the standard DN method for specific ranges of a parameter $\alpha$, without additional relaxation. Building on this, we introduce a new LC scheme by performing a single iteration per time step. Stability analysis on a benchmark problem proves that the proposed LC scheme is conditionally stable in large added mass regimes, under a constraint on a parameter $\alpha$. Numerical experiments in large added mass settings confirm the theoretical results, demonstrating the effectiveness and applicability of the proposed schemes.