DNS of Decaying Compressible Turbulence Using Gas Kinetic Scheme*

We apply the gas-kinetic scheme to direct numerical simulation of decaying compressible turbulence. We compute the kinetic energy $K(t)$, dissipation rate $\varepsilon(t)$, probability density functions (PDFs) of the two-point longitudinal velocity difference, shocklet strength, and local Mach number. Our results reveal the following features of decaying compressible turbulence: (1) With the initial Taylor microscale Reynolds number $\mbox{Re}_\lambda$ fixed, increase of initial turbulent Mach number $\mbox{Ma}_{\rm t}$ leads to an increase of the dissipation rate $\varepsilon$ at the initial stage; (2) Change of $\mbox{Ma}_{\rm t}$ has little effect on $K(t)$ and the long-time asymptotics of $\varepsilon(t)$; (3) At the lower $\mbox{Ma}_{\rm t}$ ($\approx 0.1$), intermittency persists, while at the higher $\mbox{Ma}_{\rm t}$ ($\approx 0.5$), intermittency quickly dissipates, \emph{i.e.}, the PDF of the two-point longitudinal velocity difference becomes Gaussian independent of the separation distance $\delta r$; and (4) the PDF's of both shock strength and the local Mach number all appear to follow scaling laws.