In order to simulate multiscale problems such as turbulent flows effectively, the high-order accurate reconstruction based on minimized dispersion and controllable dissipation(MDCD) is implemented in the second-order accurate gas-kinetic scheme(GKS) to improve the accuracy and resolution. MDCD is firstly extended to non-uniform grids through the modification of dissipation and dispersion coefficients for uniform grids based on the local stretch ratio. Remarkable improvements in accuracy and resolution are achieved on general grids. Then a new scheme, MDCD-GKS is constructed, with the help of MDCD reconstruction, not only for conservative variables, but also for their gradients. MDCD-GKS shows good accuracy and efficiency in typical numerical tests.MDCD-GKS is also coupled with the improved delayed detached-eddy simulation(IDDES) hybrid model and applied in the fine simulation of turbulent flow around a cylinder, and the prediction is in good agreement with experiments when using the relatively coarse grid. The high accuracy and resolution of the developed GKS guarantee its high efficiency in practical applications.
