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

Abstract

The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observer locations. Sound generation by vortex shedding is computed by a hybrid method and an accurate two-dimensional direct calculation, and the results are compared. The hybrid approach uses direct calculation for near-field source computations and the Ffowcs-Williams―Hawkings equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the Ffowcs-Williams―Hawkings formulation are accelerated by a wideband multilevel adaptive fast multipole method. The wideband multilevel adaptive fast multipole method presented here applies a plane-wave expansion formulation for calculations in the high-frequency regime and a partial-wave expansion formulation in the low-frequency regime. The method is described in detail for the solution of a two-dimensional Green's function that incorporates convective effects. The method presented in this work is applied to two-dimensional calculations. However, it can be easily extended to three-dimensional calculations of surface monopole and dipole source terms and volume quadrupole source terms. Results for acoustic field solutions obtained by the accelerated Ffowcs-Williams―Hawkings formulation are 2 orders of magnitude faster when compared with the direct computation of the Ffowcs-Williams―Hawkings equation.