Combined integral equation formulation and null-field method for the exterior acoustic problem

Abstract

The numerical implementation of a combined integral equation and null-field method used to solve the exterior Neumann problem [D. S. Jones, Q. J. Mech. Appl. Math. XXVII, 129 (1974)] is presented here. The exterior Helmholtz integral equation is solved on the radiating or scattering surface, and the irregular frequencies are eliminated up to a given irregular frequency fM through the use of M additional null-field equations. An impedance matrix, defined on the object surface, is then obtained that can be used as an exact radiation condition in a finite-element code. The program and the numerical examples presented here are specialized to axisymmetrical problems. A purely null-field method is implemented and simple rules are defined that display its failure when applied to high aspect-ratio objects and (or) in the high-frequency range. Similar, but less restricting rules are used to specify the numerical limitations of Jones’ technique. Besides, a few theoretical considerations clarify the role played by the additional null-field equations in the elimination of the irregular frequencies and help in performing accurate high-frequency computations for surfaces such as the circular cone and the finite circular cylinder.