A fast multipole boundary element method for three‐dimensional acoustic problems in a subsonic uniform flow

Abstract

A fast multipole boundary element method (FMBEM) in a subsonic uniform flow is presented. It is based on the boundary integral equation (BIE) in a subsonic uniform flow. The convected Green's function complicates its multipole expansion as well as the implementation of the computer code. Although the Lorentz transformation allows the Helmholtz equation in the uniform flow to be reduced to the standard Helmholtz equation, the deformation of the domain complicates the boundary conditions and may cause the elements' distortion. In this work, the analytical evaluations of singular integrals are achieved. Then a nonsingular BIE in a subsonic uniform flow is obtained and is incorporated in building FMBEM with the plane wave multipole expansion of Green's function directly. Details on the implementation of the algorithm are described. Numerical examples including a pulsating sphere radiation problem, a multibody scattering problem and an aircraft model are performed to validate the accuracy and efficiency of the proposed method. Results show that FMBEM solutions are in good agreement with analytical solutions. The difference between the analytical moments and numerical moments is also investigated carefully in the implementation of the fast multipole method. Dramatical improvements on solution efficiency are observed by comparing the developed algorithm with the CBEM.

Installed Fan Noise Simulation of a Supersonic Business Aircraft

“…Thus, an advanced alternative to Taylor's transformation [13] could be tested only if such a formulation is highly suitable for the FMM. For example, Liu et al [14] recently published their version of the FMBEM based on the plane wave expansion of Green's function, which is generally applicable in a subsonic uniform flow.…”