Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

摘要

The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observernlocations. Sound generation by vortex shedding is computed by a hybrid method and an accurate two-dimensionalndirect calculation, and the results are compared. The hybrid approach uses direct calculation for near-field sourcencomputations and the Ffowcs-Williams–Hawkings equation as the acoustic analogy formulation. The integrations ofnsurface dipole and volume quadrupole source terms appearing in the Ffowcs-Williams–Hawkings formulation arenaccelerated by a wideband multilevel adaptive fast multipole method. The wideband multilevel adaptive fastnmultipolemethod presented here applies a plane-wave expansion formulation for calculations in the high-frequencynregime and a partial-wave expansion formulation in the low-frequency regime. Themethod is described in detail fornthe solution of a two-dimensionalGreen’s function that incorporates convective effects. Themethod presented in thisnwork is applied to two-dimensional calculations.However, it can be easily extended to three-dimensional calculationsnof surface monopole and dipole source terms and volume quadrupole source terms. Results for acoustic fieldnsolutions obtained by the accelerated Ffowcs-Williams–Hawkings formulation are 2 orders of magnitude fasternwhen compared with the direct computation of the Ffowcs-Williams–Hawkings equation.