Asymptotic based preconditioning technique for low Mach number flows

A comprehensive study of a finite volume method for inviscid flow fields at high and low speeds is presented. Thereby, the results of a formal single as well as multiple scale asymptotic low Mach number analysis [34, 45] of the Euler equations of gas dynamics are used to extend the validity of the numerical method from the simulation of compressible inviscid flow fields to the low Mach number regime. Although different strategies are applicable [28, 35, 34, 47] we focus our view to a preconditioning technique proposed by Guillard and Viozat [14]. After a brief repetition of an asymptotic analysis in the continuous context we present a finite volume approximation of the governing equations using the AUSMDV scheme [77]. To overcome the failure of the original approach in the low Mach number regime we combine the numerical flux function with a preconditioned formulation of the Lax-Friedrichs scheme. Both, a wide variety of trans-, super-, hyper-, and subsonic realistic test cases and a formal discrete asymptotic single scale analysis are employed in order to prove the validity of the derived numerical method from hypersonic to low Mach number fluid flow.