A hybrid multilevel fast multipole and equivalent source method for aeroacoustic scattering prediction

Abstract

A hybrid multilevel fast multipole and equivalent source method (FM-ESM) has been developed for efficient aeroacoustic scattering prediction, which is distinguished by its application of the equivalent source concept across all fast multipole stages, including particle-to-multipole, multipole-to-multipole, multipole-to-local, local-to-local, local-to-particle, and particle-to-particle translations. The capability of the method for scattering predictions in two and three dimensions with different flow conditions is demonstrated through an analytical solution utilizing an image source method. Furthermore, the flexibility to reduce the number of equivalent sources is explored during particle-to-multipole and particle-to-particle translations, where the mismatch between equivalent sources and collocation points results in an over-determined system. To iteratively invert the resulting rectangular matrix, a variant of the generalized minimal residual algorithm known as the BA-GMRES method is utilized, accompanied by a specified pre-conditioner. A fast multipole boundary element method is included for reference under the same framework. Through examinations of cylindrical and spherical scattering, it is observed that FM-ESM, with fewer sources, efficiently yields accurate results in cases involving fictitious resonant frequencies. The method’s applicability to large-scale problems makes it a complementary choice for aeroacoustic scattering prediction.