Numerical evaluation of the compact acoustic Green's function for scattering problems

摘要

The reduction of noise generated by new and existing engineering products is becoming of increasing commercial importance. Noise prediction schemes are important tools available to help us understand and develop a means of controlling noise. Hybrid noise prediction schemes alleviate many issues associated with exclusively numerical or analytical approaches. These schemes often make use of a Green's function to compute the sound field - the Green's function representing geometrical scattering effects. Current hybrid schemes are limited to propagating noise in simple geometries for which the Green's function is known. In order to extend hybrid schemes to more general geometries, we develop here a robust semi-analytical computational method to compute Green's functions for more general geometries in both 2D and 3D. The class of Green's functions considered here can be constructed through conformal mapping of the geometry to a canonical domain. Traditionally, this would only be possible if the mapping could be expressed analytically. Here we combine the traditional algorithm with a numerical mapping procedure to allow the Green's function to be computed for more general geometries. The accuracy is assessed through application to 2D benchmark problems for which analytical solutions are known. Although we assess the accuracy and speed of the method on 2D problems only, the extension to 3D only requires an additional execution of the same computational procedure for the extra dimension with a predictable effect on these two properties. We compute a Green's function for a baffle in a 2D channel, an important geometry in vortex sound problems, and a 3D projection from the half-plane. The semi- analytical method presented here demonstrates calculation of the Green's function accurately and robustly by avoiding particular conformal transformations and the evaluation of potential models containing singularities.