Fast Multipole Boundary Element Method for Aerodynamic Sound Field Analysis Based on Lighthill’s Equation

Abstract

The primary disadvantage of the aerodynamic sound field analysis based on the Lighthill’s equation using the boundary element method (BEM) is the computational time; this is mainly because contributions from numerous aerodynamic sound sources are computed at all boundary element nodes and sound-receiving points. This study proposes a fast method for computing source contributions based on the fast multipole method (FMM). Along with the fast multipole BEM, which is already in practical use as a fast BEM, the analysis is substantially accelerated. The use of a common hierarchical cell structure for grouping boundary element nodes, sound-receiving points and aerodynamic sound sources, enables coefficients of the FMM to be reused, thereby further accelerating the analysis. To deal with the increasing hierarchical level, a wideband FMM is applied. In the sound radiation analysis of a quadrupole source located in a free field, the accuracy is validated. Sound radiation from a cylinder located in a flow is analyzed as a practical problem; the accuracy and numerical settings are discussed. Finally, the proposed method is applied to a problem with more than 0.4 million degrees-of-freedom and more than 3 million aerodynamic sound sources to demonstrate its applicability to large-scale problems.