Coupled finite element/boundary element formulation for scattering from axially-symmetric objects in three dimensions

The fluid-structure interaction technique provides a paradigm for solving scattering from elastic structures embedded in an environment characterized by a Green's function, by a combination of finite and boundary element methods. In this technique, the finite element method is used to discretize the equations of motion for the structure and the Helmholtz-Kirchhoff integral with the appropriate Green's function is used to produce the discrete pressure field in the exterior medium. The two systems of equations are coupled at the surface of the structure by imposing the continuity of pressure and normal particle velocity. The present method condenses the finite element model so that finally only the boundary element problem needs to be solved. This results in a significant reduction in the number of unknowns and hence a much lower cost. In this paper, the fluid-structure interaction method is specialized to axially-symmetric objects for non-axially-symmetric loading in free space using a circumferential Fourier expansion of the fields. The specialization of the method to axially-symmetric objects results in even further significant reductions in computation. The method is validated using well-known benchmark solutions. A derivation of the method for an arbitrarily-shaped elastic structure embedded in an arbitrary environment characterized by a Green's function is given in the Appendix.