Helmholtz's decomposition for Aeroacoustics using a standard Flow Solver

TL;DR

This paper provides a practical method for decomposing compressible velocity fields into vortical and acoustic components using standard flow solvers, aiding in the analysis of aeroacoustic phenomena in low Mach number flows.

Contribution

It introduces a fast, implementation-friendly Helmholtz decomposition technique applicable with common flow solvers for aeroacoustic analysis.

Findings

Clear visualization of acoustic radiation in cavity flow simulation

Validation of scalar potential Helmholtz decomposition for convex domains

Effective separation of vortical and acoustic components in simulations

Abstract

This paper is a short guideline to the decomposition of a compressible velocity into vortical and compressible structures using standard flow solvers. In particular, this is a fast solution to get an idea of the compressible fields inside your simulation, respectively acoustics for low Mach number isothermal flows. The details of the implementation are presented and the algorithm is applied to an overflown cavity with a lip. The results of the flow solver show clearly visible to acoustic radiation for the application. Finally and as previous studies showed, the use of the scalar potential formulation of Helmholtz's decomposition is valid for convex propagation domains.