Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence II: Coarse-graining analysis of compressible Ksgs budget

Abstract

The direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime with Mat=1.2 has been investigated by the high-order gas-kinetic scheme (HGKS) (Cao et al. (2019) [8]). In this study, the DNS on a much higher initial turbulent Mach number up to Mat=2.0 is performed by HGKS, which confirms the super robustness of HGKS. The coarse-graining analysis of subgrid-scale (SGS) turbulent kinetic energy Ksgs budget is fully analyzed for constructing one-equation SGS model in the compressible large eddy simulation (LES). The exact compressible SGS turbulent kinetic energy Ksgs transport equation is derived with density weighted filtering process. Based on the compressible Ksgs transport equation, the coarse-graining processes are implemented on three sets of unresolved grids with the Box filter. The coarse-graining analysis of compressible Ksgs budgets shows that all unresolved source terms are dominant in the current system. Especially, the magnitude of SGS pressure-dilation term is on the order of SGS solenoidal dissipation term within the initial acoustic time scale. Therefore, the SGS pressure-dilation term cannot be neglected as that in the previous work. The delicate coarse-graining analysis of SGS diffusion terms in compressible Ksgs equation also confirms that both the fluctuation velocity triple correlation term and the pressure-velocity correlation term are dominant terms. The current analysis provides an indication on the order of magnitude of all SGS terms in compressible Ksgs budget, which provides a solid basis for compressible LES modeling of high Mach number turbulent flow.