Abstract: In adaptive Cartesian mesh turbulence simulation, the number of grids increases exponentially with Reynolds number, resulting in the "disaster" of grid number. The wall function is one of the effective solutions, which can reduce the scale of the first layer grid by 1-2 orders of magnitude. However, due to the non-body fitted characteristics of Cartesian grids, the realization of the wall function and its matching with different turbulence models are key. In order to solve this problem, starting from the classical Spalding wall function, an explicit assignment of initial value was adopted to solve the problem of sensitive initial value iterative solution of wall friction velocity and non-smooth velocity of layered wall function. Based on the wall condition of constant shear stress, the tangential velocity and turbulent viscosity coefficient of multi-layer ghost cell were constructed, and the wall function method was implemented in Cartesian grid. Using the structure ensemble theory and through the DNS data calibration, the relation formula of turbulent kinetic energy was constructed, which changes with turbulent viscosity ratio and wall function, and achieves KDO matching of turbulence model. Taking flat T3b, turbulent bump and transonic flow around NACA0012 airfoil as examples, the commonly used SST, SA turbulence model wall function methods were analyzed. The results show that the wall function method of KDO turbulence model is accurate, reliable, and has great application value because of its simple form and relatively small computation cost.