Some mathematical Properties of the Low-Mach Number Model Related to the Numerical Solution of Unsteady Reactive Flows

In this paper some mathematical properties of the widely adopted model based on the low-Mach number asimpotic expansion of the Navier-Stokes equation are presented. This model is generally preferred for the numerical simulation of unsteady combustion of gas mixtures because it avoids the stiffness of the fully compressible Navier-Stokes equations when the Mach number approaches zero while taking into account the strong effects of large density variations due to the thermal expansion for the esothermic combustion reactions. However, being this model very similar to the incompressible Navier-Stokes equations, it suffers of the same closure difficulties (pressure problem), with more complications which derive from a weaker divergence constraint. Aim of this paper is to address these difficulties in a frame of mathematically well established results in order to contribute to an appropriate solution.