On the Time-Dependent Fluid-Structure Interactions

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a uid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to as a uid-structure interaction and is mathematically formulated as a time-dependent transmission problem. In this paper, we consider a typical uid-structure interaction problem by using a coupling procedure which reduces the problem to a nonlocal initial-boundary problem in the elastic body with integral equations on the interface between the domains occupied by the elastic body and the uid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform with an essential feature of which is that it works directly on data in the time domain instead in the transformed domain . Our results may be served as a mathematical foundation for treating time dependent uid-structure interaction problems by convolution quadrature coupling of FEM and BEM.