A fast multipole boundary element method for acoustic problems in a non-uniform potential flow

This paper presents a fast multipole boundary element method (FMBEM) for acoustic problems in a non-uniform potential flow. Different from the BEM for acoustic problems in a quiescent medium, the non-uniform flow field has a dramatic effect on the propagation of sound. In the developed algorithm, only the Mach number of the flow field at infinity needs to be given, and both the non-uniform flow field and the sound field around the vibrating model are calculated by using the BEM. First, the FMBEM for the steady non-uniform potential flow is developed. The exponential expansions of the multipole translation and recurrence calculations of the solid harmonic functions are employed to accelerate the computation. The calculated physical quantity of the non-uniform flow can serve as the computational input for the subsequent sound field. Then, the boundary integral formulae for acoustic problems in non-uniform potential flows are derived. The convected Green's function is also derived by using the Taylor-Lorentz transformation and its inverse transformation. The formulae of fast multipole translations are derived in detail. Finally, several numerical experiments are performed to validate the accuracy and efficiency of the algorithm, demonstrating its capability for accurate and fast computation of large-scale sound fields in non-uniform flows.