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An improved reconstruction method for compressible flows with low Mach number features. (English) Zbl 1388.76188
Summary: This paper proposes a simple modification of the variable reconstruction process within finite volume schemes to allow significantly improved resolution of low Mach number perturbations for use in mixed compressible/incompressible flows. The main advantage is that the numerical method locally adapts the variable reconstruction to allow minimum dissipation of low Mach number features whilst maintaining shock capturing ability, all without modifying the formulation of the governing equations. In addition, incompressible scaling of the pressure and density variations are recovered. Numerical tests using a Godunov-type method demonstrate that the new scheme captures shock waves well, significantly improves resolution of low Mach number features and greatly reduces high wave number dissipation in the case of homogeneous decaying turbulence and Richtmyer-Meshkov mixing. In the latter case, the turbulent spectra match theoretical predictions excellently. Additional computational expense due to the proposed modification is negligible.

76M12 Finite volume methods applied to problems in fluid mechanics
76F25 Turbulent transport, mixing
76F65 Direct numerical and large eddy simulation of turbulence
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