Boundary-integral-equation methods for accurate calculation of acoustic fields

Abstract

Acoustic fields near solid boundaries can be approximated by solutions of the Helmholtz equation subject to Neumann boundary conditions on the boundaries. For closed, axisymmetric geometries, the boundary-value problem can be expressed as a one-dimensional integral equation. Boundary shapes can be represented exactly in this formalism. With current code, numerical solutions can be obtained for shapes formed by rotating plane figures made up of mixtures of straight and circular line segments. Numerical solutions to the integral equation were determined by using cubic-spline approximations to the velocity potential Ψ. This procedure enabled both Ψ and the tangential acoustic velocity Ψ′ to be determined with high precision. In calculations of the fields within ducts near the orifices, with modest (∼200) numbers of boundary elements, approximate values of Ψ′ were found which were smooth over five orders of magnitude. The technique was used to calculate fields near the duct ends and to evaluate inertial and resistive end effects, for both baffled and unbaffled duct ends. The effects of rounding sharp edges has been evaluated through the use of circular-arc boundary elements. [Work supported in part by the Office of Naval Research.]