Stability and convergence analysis of the kinematically coupled scheme for fluid-structure interaction

TL;DR

This paper analyzes the stability and convergence of a loosely-coupled fluid-structure interaction scheme, demonstrating unconditional stability and optimal first-order convergence through theoretical analysis and numerical validation.

Contribution

It provides the first a priori estimates showing optimal first-order convergence for the kinematically coupled scheme in fluid-structure interaction problems.

Findings

Unconditional stability of the scheme is proven.

Optimal first-order convergence in time is established.

Numerical examples support theoretical results.

Abstract

In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, for interaction between an incompressible viscous fluid and a thin structure. We consider a benchmark problem where the structure is modeled using the linearly elastic Koiter membrane model and the coupling between the fluid and structure is linear. We derive the energy estimates associated with the unconditional stability and, for the first time, present a priori estimates showing optimal, first-order in time, convergence. The theoretical stability and convergence results are supported with numerical examples.