Splitting schemes for a Lagrange multiplier formulation of FSI with immersed thin-walled structure: stability and convergence analysis

TL;DR

This paper introduces semi-implicit splitting schemes for fluid-structure interaction with immersed thin-walled structures, achieving stability and accuracy without solving fully coupled systems at each step.

Contribution

It proposes a novel class of semi-implicit schemes that maintain stability and accuracy while reducing computational complexity in FSI problems with thin-walled structures.

Findings

Schemes are unconditionally stable.

Error estimates are rigorously derived.

Numerical experiments confirm theoretical results.

Abstract

The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a computationally demanding coupled system at each time-step. For the case of the coupling with immersed thin-walled solids, we introduce a class of semi-implicit coupling schemes which avoids strongly coupling without compromising stability and accuracy. A priori energy and error estimates are derived. The theoretical results are illustrated through numerical experiments in an academic benchmark.