A time-dependent FEM-BEM coupling method for fluid-structure interaction in 3d

TL;DR

This paper develops and analyzes a time-dependent FEM-BEM coupling method for simulating fluid-structure interaction in three dimensions, providing error estimates and demonstrating effectiveness through numerical experiments.

Contribution

It introduces a novel time-dependent FEM-BEM coupling approach for 3D fluid-structure interaction with proven error bounds and implementation insights.

Findings

The method is well-posed and stable.

Error estimates are established for the coupled scheme.

Numerical results confirm the method's accuracy and efficiency.

Abstract

We consider the well-posedness and a priori error estimates of a 3d FEM-BEM coupling method for fluid-structure interaction in the time domain. For an elastic body immersed in a fluid, the exterior linear wave equation for the fluid is reduced to an integral equation on the boundary involving the Poincar\'{e}-Steklov operator. The resulting problem is solved using a Galerkin boundary element method in the time domain, coupled to a finite element method for the Lam\'{e} equation inside the elastic body. Based on ideas from the time-independent coupling formulation, we obtain an a priori error estimate and discuss the implementation of the proposed method. Numerical experiments illustrate the performance of our scheme for model problems.