Gas-kinetic schemes for direct numerical simulations of compressible homogeneous turbulence.

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Re(lambda)=72.0 and the turbulence Mach number Ma(t) between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K(t), the dissipation rate epsilon(t), the skewness S(u)(t), and the flatness F(u)(t) of the velocity field u(x,t). We assess the effects on the turbulence statistics due to the approximations made in the treatment of fluxes, the flux limiter, the accuracy of the interpolation, and the bulk viscosity. Our results show that the GKS is adequate for DNS of compressible homogeneous turbulence as far as the low-order turbulence statistics are concerned.