Boundary integral equation methods for the two dimensional fluid-solid interaction problem

TL;DR

This paper develops boundary integral equation methods for efficiently solving two-dimensional fluid-solid interaction problems, including new regularization techniques for hypersingular operators, with theoretical proofs and numerical validation.

Contribution

It introduces a novel regularization approach for hypersingular boundary integral operators in fluid-solid interaction problems, along with existence and uniqueness results.

Findings

The regularization method effectively handles hypersingular kernels.

Theoretical results are confirmed by numerical examples.

Boundary integral formulations are proven to be well-posed.

Abstract

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect approaches. Existence and uniqueness results for variational solutions of boundary integral equations equations are established. Since in all these boundary variational formulations, the hypersingular boundary integral operator associated with the time-harmonic Navier equation is a dominated integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a wealkly singular kernel. Numerical examples are presented to verify and validate the theoretical results.