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Asymptotic-based preconditioning technique for low Mach number flows. (English) Zbl 1010.76062
Summary: We present a comprehensive study of finite volume method for inviscid flow fields at high and low speeds. Thereby, the results of a formal single as well as multiple scale asymptotic low Mach number analysis of the Euler equations of gas dynamics are used to extend the validity of numerical methods from the simulation of compressible inviscid flow fields to the low Mach number regime. Although different strategies are applicable, we focus our view on a preconditioning technique proposed by H. Guillard and C. Viozat [Comput. Fluids 28, No. 1, 63-86 (1999; Zbl 0963.76062)]. 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. 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 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 flows.

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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