Green's functions in computational aeroacoustics

Abstract

The theory of Green's functions for the wave and Helmholtz equations is examined with particular attention to their use in aeroacoustics for the extrapolation of acoustic wavefields from numerical flow simulations. In a new synthesis that permits straightforward generalization of previously published results, spatial and temporal windowing functions are employed to provide equivalent-source expressions to account for both initial and boundary conditions. Detailed results describe the transformation of both source terms and Green's functions to take account of uniform subsonic mean flow, and expressions are given for free-field Green's functions, both with and without flow, in time, frequency and wavenumber domains. Aworked example illustrates the non-uniqueness of the Green's function for a simple one-dimensional bounded problem.