A fast multipole method of the frequency domain FW-H equation in large-scale aeroacoustic problems

To improve the computational efficiency of the Ffowcs Williams-Hawkings (FW-H) equation for multiple source/observer points, this paper proposes a hybrid acceleration strategy combining Chebyshev interpolation and the fast multipole method (FMM). Chebyshev interpolation derives a degenerate analytical form of the free-space Green’s function, significantly reducing its computational complexity and avoiding exponential time growth with increasing points. FMM replaces direct source-observer interactions with multipole-group transfers, reducing the 2D frequency-domain solution complexity. Tests on sound propagation from point sources in moving airflow and cylinder vortex-shedding noise show the method maintains accuracy comparable to traditional approaches while achieving an acceleration of one to two orders of magnitude.