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

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 t...