Unified wall-resolved and wall-modeled method for large-eddy simulations of compressible wall-bounded flows

We present a general strategy to unify wall-resolved and wall-modeled large-eddy simulation (LES) approaches for turbulent wall-bounded compressible flows. The proposed technique allows one to impose the proper wall stress and heat flux, preserving the no-slip and the isothermal and adiabatic conditions for the velocity and temperature fields, respectively. The approach results in a minimal intrusive algorithm that automatically switches between wall-resolved and wall-modeled LES according to the local near-wall resolution. The methodology is discussed and implemented in a flow solver based on high-order finite difference schemes, the application of which in the context of wall-modeled LES has been less explored in the available literature. Numerical simulations of canonical turbulent channel flow and spatially evolving boundary layer are performed in a wide range of Mach and Reynolds numbers. The results highlight the ability of the present method to accurately reproduce the outer layer turbulent dynamics, with a minimal influence of the near-wall grid resolution. In particular, velocity statistics and two-point spatial correlations are in good agreement with reference direct numerical simulation and wall-resolved LES, confirming the potential of the proposed approach for predictive analysis of wall-bounded flows at high-Reynolds number.