English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we intend to address the high-order gas-kinetic scheme (HGKS)in the direct numerical simulation (DNS) of compressible isotropic turbulenceup to the supersonic regime. With the consideration of robustness and accuracy,the WENO-Z scheme is adopted for spatial reconstruction in the currenthigher-order scheme. Statistical quantities are compared with the high-ordercompact finite difference scheme to determine the spatial and temporalcriterion for DNS. According to the grid and time convergence study, it can beconcluded that the minimum spatial resolution parameter $\kappa_{max} \eta_0\ge 2.71$ and the maximum temporal resolution parameter $\Deltat_{ini}/\tau_{t_0} \leq 5.58/1000$ are adequate for HGKS to resolve thecompressible isotropic turbulence, where $\kappa_{max}$ is the maximum resolvedwave number, $\Delta t_{ini}$ is the initial time step, $\eta_0$ and$\tau_{t_0}$ are the initial Kolmogorov length scale and thelarge-eddy-turnover time. Guided by such criterion, the compressible isotropicturbulence from subsonic regime $Ma_t=0.8$ to supersonic one $Ma_t=1.2$, andthe Taylor microscale Reynolds number $Re_{\lambda}$ ranging from $10$ to $72$are simulated. With the high initial turbulent Mach number, the strong randomshocklets and high expansion regions are identified, as well as the wide rangeof probability density function over local turbulence Mach number. All thoseimpose great challenge for high-order schemes. In order to constructcompressible large eddy simulation models at high turbulent Mach number, theensemble budget of turbulent kinetic energy is fully analyzed. The solenoidaldissipation rate decreases with the increasing of $Ma_t$ and $Re_{\lambda}$.Meanwhile, the dilational dissipation rate increases with the increasing of$Ma_t$, which cannot be neglected for constructing supersonic turbulence model.

Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: criterion for direct numerical simulation