Boundary integral equation methods for the two dimensional fluid-solid interaction problem
Provides rigorous mathematical foundations for boundary integral methods in fluid-solid interaction, but is incremental for specialists in computational acoustics and elasticity.
The paper develops boundary integral equation methods for 2D fluid-solid interaction, establishing existence and uniqueness of variational solutions and introducing a regularization for the hypersingular Navier operator. Numerical examples validate the theoretical results.
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.