A boundary element method for acoustic radiation valid for all wavenumbers

Abstract

A boundary element method for solving the exterior acoustic radiation problem that is valid for all wavenumbers has been developed. The new formulation derives from the earlier work of Burton and Miller [Proc. R. Soc. London Ser. A 323, 201–210 (1971)], which uses a linear combination of the Helmholtz integral equation and its gradient to overcome the uniqueness problem. A main feature of this formulation is the absence of integral singularities. By restricting the field points of the kernels of the integrals to interior regions well away from radiating boundaries, the usual complication of dealing with singular kernels is circumvented. The new formulation has been named CHI, for coupled Helmholtz integrals. A corresponding computer program, CHI 4.35, can be used to compute the surface acoustic pressure on an arbitrary body for a given specified surface normal velocity. Results generated with CHI 4.35 are presented for the spherical monopole and dipole, along with results for parametric studies on the accuracy of the results. A useful feature of this work is that the computations have been implemented on a personal computer that presents the results in a graphical format.