The direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime with $M{a}_t=1.2$ 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 $M{a}_t=2.0$ is performed by HGKS, which confirms the super robustness of HGKS. The coarse-graining analysis of subgrid-scale (SGS) turbulent kinetic energy $K_{sgs}$ budget is fully analyzed for constructing one-equation SGS model in the compressible large eddy simulation (LES). The exact compressible SGS turbulent kinetic energy $K_{sgs}$ transport equation is derived with density weighted filtering process. Based on the compressible $K_{sgs}$ transport equation, the coarse-graining processes are implemented on three sets of unresolved grids with the Box filter. The coarse-graining analysis of compressible $K_{sgs}$ 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 $K_{sgs}$ 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 $K_{sgs}$ budget, which provides a solid basis for compressible LES modeling of high Mach number turbulent flow.

可压缩各向同性湍流直至超音速状态的直接数值模拟（DNS） $\mathrm{中号}{\mathrm{一种}}_{Ť}=1.2$已通过高阶气体动力学方案（HGKS）进行了研究（Cao等人（2019）[8]）。在这项研究中，DNS的初始湍流马赫数更高$\mathrm{中号}{\mathrm{一种}}_{Ť}=2.0$由HGKS执行，这证实了HGKS的超强耐用性。亚网格规模（SGS）湍动能的粗粒度分析${ķ}_{sGs}$在可压缩大涡模拟（LES）中，对预算进行了全面分析，以构建一方程式SGS模型。精确可压缩的SGS湍动能${ķ}_{sGs}$输运方程是通过密度加权滤波过程得出的。基于可压缩${ķ}_{sGs}$在输运方程中，使用Box过滤器在三组未解析的网格上执行粗粒度处理。可压缩物的粗粒度分析${ķ}_{sGs}$预算显示，所有未解决的源术语在当前系统中均占主导地位。特别地，在初始声学时间标度内，SGS压力膨胀项的量级为SGS螺线管耗散项的量级。因此，不能像以前的工作那样忽略SGS压力膨胀项。可压缩SGS扩散项的精细粗粒度分析${ķ}_{sGs}$该方程还证实了波动速度三次相关项和压力-速度相关项都是主导项。当前分析提供了所有可压缩SGS项的数量级指示${ķ}_{sGs}$ 预算，这为高马赫数湍流的可压缩LES建模提供了坚实的基础。