Low frequency scattering from elastic objects embedded in a waveguide by the finite element technique.

Abstract

Computation of scattering from an object in a waveguide is a challenging task because of the enormous size of the computational domain. It requires the solution of the wave equation by simultaneously satisfying the boundary conditions on the surface of the object and the boundaries of the waveguide. While the finite element solution of scattering from an object in free space can be managed by limiting the size of the computational domain by the use of infinite elements or perfectly matched layers for an object in a waveguide, the waveguide itself is part of the computational domain. Since an accurate solution requires that the computational domain be discretized at least at one‐tenth of the acoustic wavelength for a computational domain tens or hundreds of wavelength large, this results in very large systems of equations, whose solution is a daunting numerical task. To cope with the numerical complexity, in this paper we use the principles of fluid‐structure interaction to compute scattering from the object using the finite element technique and couple it to the waveguide using the Helmholtz–Kirchhoff integral, where acoustic propagation models are used to compute the environment Green’s functions. The technique is applied to buried and proud objects.