Scattering by an open sphere: Exact solution and comparison with a boundary integral method.

Abstract

The objective of the paper is to extend the variety of exact solutions in acoustic scattering configurations that may be used to validate numerical methods. The radiation of an acoustic point source located at the center of a hard sphere with a circular aperture is analyzed. In comparison with standard scattering problems, as the diffraction of a plane wave by a closed sphere, this problem adds a sharp edge. The exact solution is derived from an expansion of the pressure field on spherical Bessel functions and Legendre polynomials, and solving the linear system obtained for the coefficients. In terms of the reduced wave number ka, the truncation of the system to only 4ka coefficients insures a stable and accurate solution. A boundary integral method originally developed by Handi [Doctoral thesis, Université de Technologie de Compiègne (1982)] is used as a numerical method. Comparisons between the two sets of solutions for various wave number and aperture size show a quite good agreement, with relative differences in the far field of about 1%.