  The performance of high-order gas-kinetic scheme (HGKS) has been investigated
for the direct numerical simulation (DNS) of isotropic compressible turbulence
up to the supersonic regime. Due to the multi-scale nature and coupled
temporal-spatial evolution process, HGKS provides a valid tool for the
numerical simulation of compressible turbulent flow. Based on the domain
decomposition and message passing interface (MPI), a parallel HGKS code is
developed for large-scale computation in this paper. The standard tests from
the nearly incompressible flow to the supersonic one, including Taylor-Green
vortex problem, turbulent channel flow and isotropic compressible turbulence,
are presented to validate the parallel scalability, efficiency, accuracy and
robustness of parallel implementation. The performance of HGKS for the nearly
incompressible turbulence is comparable with the high-order finite difference
scheme, including the resolution of flow structure and efficiency of
computation. Based on the accuracy of the numerical solution, the numerical
dissipation of the scheme in the turbulence simulation is quantitatively
evaluated. As a mesoscopic method, HGKS performs better than both lattice
Boltzmann method (LBM) and discrete unified gas-kinetic scheme (DUGKS), due to
its high-order accuracy. Meanwhile, based on the kinetic formulation HGKS shows
advantage for supersonic turbulent flow simulation with its accuracy and
robustness. The current work demonstrates the capability of HGKS as a powerful
DNS tool from the low speed to supersonic turbulence study, which is less
reported under the framework of finite volume scheme.
