The method of fundamental solutions for axisymmetric acoustic scattering and radiation problems

Abstract

The method of fundamental solutions (MFS) is applied to acoustic scattering and radiation for axisymmetric bodies and boundary conditions. The fundamental solution of the governing equation and its normal derivative, which are required in the formulation of the MFS, can be expressed in terms of complete elliptic integrals, which are evaluated using library software. The method is tested on several problems from the literature and the results compared with existing solutions. Numerical experiments demonstrate that the fictitious eigenfrequency problem which is encountered with the boundary element method is not present in the MFS. The method of fundamental solutions (MFS) was used to address axisymmetric acoustic scattering and radiation problems. The fundamental solutions of the governing equations involved and their normal derivatives required in the formulation of the MFS were calculated using existing library software and numerical integration. Application of the method to a number of problems from the literature yielded very good results. Further, it was found that the fictitious eigenfrequency difficulties encountered when using the boundary element method (BEM) are not present in the MFS.