A low Mach correction able to deal with low Mach acoustics

Highlights: • Usual low Mach fixes do not accurately compute acoustics in low Mach number flows. • Origins of this wrong behaviour for acoustics computation are studied • A finite volume scheme is developed for acoustics in low Mach number flows. • The scheme is proved to be accurate for both stationary and unstationary problems. -- Abstract: This article deals with acoustic computations in low Mach number flows with density based solvers. For ensuring a good resolution of the low Mach number base flow, a scheme able to deal with stationary low Mach number flows is necessary. Previously proposed low Mach number fixes are tested with acoustic computations. Numerical results prove that they are not accurate for acoustic computations. The issues raised with acoustic computations with low Mach number fixes are discussed, and a new scheme is developed, in order to be accurate not only for steady low Mach number flows, but also for acoustic computations. Numerical tests show the improvement of the proposed scheme with respect to the state of the art.