A BEM–FMM approach applied to the combined convected Helmholtz integral formulation for the solution of aeroacoustic problems

Abstract

Exterior and interior acoustic calculations often exploit the advantages of Boundary Element Method (BEM) numerical scheme. Due to the large dimension of dense matrices arising in real-case applications, direct matrix–vector products become prohibitive, since the computational cost of standard methods increases quadratically. In this work, the black-box Fast Multipole Method (bbFMM), based on the Chebyshev interpolation, is extended to the integral solution of the convective Helmholtz equation stabilized using the Combined Helmholtz Integral Equation Formulation (CHIEF). The CHIEF approach relies on the solution of an over-determined linear system achieved by adding a set of points internal to the scattering body. In order to handle the distribution of the CHIEF points within the body volume, a robust stochastic approach has been also developed. Moreover, an Adaptive bbFMM (AbbFMM) is presented for handling the oscillating kernels, such as those arising in the solution of the convective Helmholtz equation. The proposed approach, which has a complexity of O(NlogN), is interesting for industrial applications, especially in the aeroacoustic field.