An analytical solution versus half space BEM formulation for acoustic radiation and scattering from a rigid sphere

Abstract

A half space problem in acoustics is described by introducing an infinite plane boundary that reflects the wave coming into the plane. A numerical solution using Boundary Element Method (BEM) has been known which is formulated using a modified Green's function in the Helmholtz Integral Formulation, which eliminates the discretization over the infinite plane. Hence, the discretization are confined to the body or obstacle in question only. This feature constitutes the main advantage of the BEM formulation for half space problems. However, no general analytical solution is available to verify the BEM results for half space problems. This paper is aimed to propose an analytical solution for the BEM to compare with, hence to verify the BEM calculation. This analytical approach is currently developed for a half space problem involving radiation and scattering of acoustic waves from a rigid sphere. The image of sphere as well as the image of the field point are defined with respect to the infinite plane. Then, an ad hoc solution is assumed involving a constant and the distance from the center of the sphere to the field point and the distance from the center of the image of the sphere to the field point. The constant is determined by imposing the boundary conditions. Test cases were run with several configuration involving the location of field points and the sphere. Comparison of the analytical solution with BEM calculations shows a good agreement between the two results..