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

High-order gas-kinetic scheme in general curvilinear coordinate for iLES of compressible wall-bounded turbulent flows