On the modeling of narrow gaps using the standard boundary element method

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes deg enerate if the objects that disturb the sound field are very thin. This pap er makes use of a standard axisymmetric Helmholtz integral equation formula tion and its boundary element method (BEM) implementation to study the beha vior of the method on two test cases: a thin rigid disk of variable thickne ss and two rigid cylinders separated by a gap of variable width. Both probl ems give rise to the same kind of degeneracy in the method, and modified fo rmulations have been proposed to overcome this difficulty. However, such te chniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range o f thicknesses/widths tractable by the otherwise unmodified standard formula tion is presented and tested. This technique is valid for both cases. The m odeling of acoustic transducers Like sound intensity probes and condenser m icrophones has motivated this work, although the proposed technique has a w ider range of applications. (C) 2001 Acoustical Society of America.