Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence II: coarse-grained analysis of compressible budget
arXiv:2005.12096
Abstract
The direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime has been investigated by high-order gas-kinetic scheme (HGKS) [{\it{Computers}} \& {\it{Fluids, 192, 2019}}]. In this study, the coarse-grained analysis of subgrid-scale (SGS) turbulent kinetic energy budget is fully analyzed for constructing one-equation SGS model in the compressible large eddy simulation (LES). The DNS on a much higher turbulent Mach number up to has been obtained by HGKS, which confirms the super robustness of HGKS. Then, the exact compressible SGS turbulent kinetic energy transport equation is derived with density weighted filtering process. Based on the compressible transport equation, the coarse-grained processes are implemented on three sets of unresolved grids with the Box filter. The coarse-grained analysis of compressible budgets shows that all unresolved source terms are dominant terms in current system. Especially, the magnitude of SGS pressure-dilation term is in the order of SGS solenoidal dissipation term within the initial acoustic time scale. Therefore, it can be concluded that the SGS pressure-dilation term cannot be neglected as the previous work. The delicate coarse-grained analysis of SGS diffusion terms in compressible equation confirms that both the fluctuation velocity triple correlation term and the pressure-velocity correlation term are dominant terms. Current coarse-grained analysis gives an indication of the order of magnitude of all SGS terms in compressible budget, which provides a solid basis for compressible LES modeling in high Mach number turbulent flow.
High-order gas-kinetic scheme, supersonic isotropic turbulence, compressible transport equation, coarse-grained budget analysis. arXiv admin note: text overlap with arXiv:1911.10966 by other authors