A Fourier Spectral Method for Acoustic Wave Scattering by Localized Flow Inhomogeneities

To compute the acoustic wave scattered by local flow inhomogeneities like vortices, an integro-differential scheme is developed to numerically solve the Lippmann-Schwinger formulation of the linearized Euler equations in the frequency domain, achieving spectral-order accuracy and a computational complexity of [Formula: see text]. This formulation converts the aeroacoustic scattering equation into a second-order integro-differential system using the Green’s function of the Helmholtz equation. The singular convolution integrals are evaluated with the kernel truncation method, and high-order derivatives are computed using Fourier series. Validated against several aeroacoustic benchmarks, our method shows significant advantages in efficiency and accuracy, while avoiding special treatments for radiating boundary conditions. Additionally, we extend this formulation to unsteady flows, interpret the spectral broadening effect as the convolution of incident waves with the medium’s motion in the frequency domain, and offer an example for its numerical simulation.