The multiple pressure variables method for fluid dynamics and aeroacoustics at low Mach numbers

Abstract

The incompressible limit of a compressible fluid, when the Mach number tends to zero, is a singular limit due to the fact that the governing equations change their type. The propagation rate of the pressure waves become infinite. Based on asymptotic results the multiple pressure variables (MPV-) method is reviewed as it may be used for the construction of numerical methods in this low Mach number regime. The MPV-schemes formally converge to incompressible methods, if the Mach number tends to zero. The insight into the behavior in the incompressible limit is used to introduce a perturbation method to calculate the noise generation and propagation in the flow region. In this approach the fluid flow is calculated by an incompressible method. The introduction of a perturbation about this incompressible solution leads to a system describing the generation and propagation of the compressible corrections to the incompressible flow field. The wave propagation model are the linearized Euler equations and the noise generation is given by source terms for these equations. This relates very well to the EIF-approach (Expansion about Incompressible Flow) as proposed by Hardin and Pope. The new part is a scaling motivated by the MPV-method and M = 0 limit. By that a linearization is introduced and the most important terms in the sources can easily be identified. For a simple one- dimensional problem with compression from the boundary the perturbation method is validated. Numerical results are also presented for the noise generation by a rotating vortex pair and for the applied problem of the noise generation of a plane jet.