Accuracy of a low Mach number model for time-harmonic acoustics

We study the time-harmonic acoustic radiation in a fluid in flow. To go beyond the convected Helmholtz equation adapted only to potential flows, starting from the Goldstein equations, coupling exactly the acoustic waves to the hydrodynamic field, we develop a new model in which the description of the hydrodynamic phenomena is simplified. This model, initially developed for a carrier flow of low Mach number M, is proved theoretically to be accurate, associated to a low error bounded by M². Numerical experiments confirm the M² law and show that the model remains of very good quality for flow of moderate Mach numbers.