Efficient evaluation of three-dimensional Helmholtz Green's functions tailored to arbitrary rigid geometries for flow noise simulations

The Lighthill's wave equation provides an accurate characterization of the hydrodynamic noise due to interaction between a turbulent flow and obstacle, that is needed get in many industrial applications. In present study, solve expressed as boundary integral equation, we develop efficient numerical method determine three-dimensional Green's function Helmholtz presence obstacle arbitrary shape, satisfying Neumann condition. This so-called tailored useful reduce computational costs equation. first step consists deriving express thanks free space function. Then Boundary Element Method (BEM) used compute functions. Furthermore, performed second derivatives for determinations. proposed approach tested on simple geometries which analytical solutions can be determined (sphere, cylinder, half plane). order consider realistic reasonable amount time, fast BEMs are used: multipole accelerated BEM hierarchical matrix based BEM. A discussion efficiency accuracy these approaches context finally proposed.