  In this paper, a high-order gas-kinetic scheme in general curvilinear
coordinate (HGKS-cur) is developed for the numerical simulation of compressible
turbulence. Based on the coordinate transformation, the Bhatnagar-Gross-Krook
(BGK) equation is transformed from physical space to computational space. To
deal with the general mesh given by discretized points, the geometrical metrics
need to be constructed by the dimension-by-dimension Lagrangian interpolation.
The multidimensional weighted essentially non-oscillatory (WENO) reconstruction
is adopted in the computational domain for spatial accuracy, where the
reconstructed variables are the cell averaged Jacobian and the
Jacobian-weighted conservative variables. The two-stage fourth-order method,
which was developed for spatial-temporal coupled flow solvers, is used for
temporal discretization. The numerical examples for inviscid and laminar flows
validate the accuracy and geometrical conservation law of HGKS-cur. As a direct
application, HGKS-cur is implemented for the implicit large eddy simulation
(iLES) in compressible wall-bounded turbulent flows, including the compressible
turbulent channel flow and compressible turbulent flow over periodic hills. The
iLES results with HGKS-cur are in good agreement with the refereed spectral
methods and high-order finite volume methods. The performance of HGKS-cur
demonstrates its capability as a powerful tool for the numerical simulation of
compressible wall-bounded turbulent flows and massively separated flows.
