A non-iterative domain decomposition method for the interaction between a fluid and a thick structure

TL;DR

This paper introduces a non-iterative, stable domain decomposition method for fluid-structure interaction involving thick structures, achieving optimal spatial convergence and demonstrating effectiveness through numerical tests.

Contribution

It presents a novel non-iterative partitioned approach using generalized Robin boundary conditions for moving domain fluid-structure problems, with proven stability and convergence.

Findings

Unconditionally stable for moving domain problems.

Achieves .5 order convergence in time.

Performs comparably or better than monolithic solvers.

Abstract

This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear elasticity equations. We assume that the structure is thick, i.e., described in the same dimension as the fluid. We propose a non-iterative, domain decomposition method where the fluid and the structure sub-problems are solved separately. The method is based on generalized Robin boundary conditions, which are used in both fluid and structure sub-problems. Using energy estimates, we show that the proposed method applied to a moving domain problem is unconditionally stable. We also analyze the convergence of the method and show $\mathcal{O}(\Delta t^\frac12)$ convergence in time and optimal convergence in space. Numerical examples are used to demonstrate the performance of the method. In particular, we explore the relation between the combination parameter used in the derivation of the generalized Robin boundary conditions and the accuracy of the scheme. We also compare the performance of the method to a monolithic solver.