2019/05/08 by Guiyu Cao, Liang Pan, Cao, Guiyu +3 · 2 citations
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.1905.03007
openalex publication_date 2019/05/08 · openalex created_date 2019/05/16 · openalex updated_date 2026/07/28
In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime. With the consideration of robustness and accuracy, the WENO-Z scheme is adopted for spatial reconstruction in the current higher-order scheme. Statistical quantities are compared with the high-order compact finite difference scheme to determine the spatial and temporal criterion for DNS. According to the grid and time convergence study, it can be concluded that the minimum spatial resolution parameter κmax η0 ≥ 2.71 and the maximum temporal resolution parameter Δtini/τt0 ≤ 5.58/1000 are adequate for HGKS to resolve the compressible isotropic turbulence, where κmax is the maximum resolved wave number, Δtini is the initial time step, η0 and τt0 are the initial Kolmogorov length scale and the large-eddy-turnover time. Guided by such criterion, the compressible isotropic turbulence from subsonic regime Mat=0.8 to supersonic one Mat=1.2, and the Taylor microscale Reynolds number Reλ ranging from 10 to 72 are simulated. With the high initial turbulent Mach number, the strong random shocklets and high expansion regions are identified, as well as the wide range of probability density function over local turbulence Mach number. All those impose great challenge for high-order schemes. In order to construct compressible large eddy simulation models at high turbulent Mach number, the ensemble budget of turbulent kinetic energy is fully analyzed. The solenoidal dissipation rate decreases with the increasing of Mat and Reλ. Meanwhile, the dilational dissipation rate increases with the increasing of Mat, which cannot be neglected for constructing supersonic turbulence model.