# On the stability of a loosely-coupled scheme based on a Robin interface condition for fluid-structure interaction

## TL;DR

This paper analyzes the stability of a loosely coupled fluid-structure interaction scheme using Robin interface conditions, identifying conditions for stability and optimal parameter choices through theoretical and numerical analysis.

## Contribution

It provides a stability analysis of a Robin interface-based fluid-structure interaction scheme, revealing how interface parameters affect stability and accuracy.

## Key findings

- Stability depends on interface parameter and time discretization.
- Optimal interface parameter choices improve solution accuracy.
- Numerical experiments confirm theoretical stability conditions.

## Abstract

We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface parameter in the Robin condition. In particular, for a model problem we find sufficient conditions for instability and stability of the method. In the latter case, we found a stability condition relating the time discretization parameter, the interface parameter, and the added mass effect. Numerical experiments confirm the theoretical findings and highlight optimal choices of the interface parameter that guarantee an accurate solution with respect to an implicit one.