Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number

The inviscid low Mach number compressible flow developing from a plane incompressible vortex with constant density in a bounded domain is studied. A reference solution for this model flow is obtained by two-time scale asymptotic development in the zero Mach number limit. The solution can be decomposed into variations with a slow convective and a fast acoustic time scale. A selection of numerical schemes widely used to solve unsteady compressible low Mach number flows has been implemented to simulate this flow for two Mach number values, M = 0.1 and M = 0.01. The ability of the schemes to predict low Mach number flows and their behavior with the value of the Mach number have been analyzed.