Extension of the local domain-free discretization method to large eddy simulation of compressible flows

Most of the flow problems encountered in practical engineering are wall-bounded turbulent flows at high Reynolds numbers. Wall-modeled large eddy simulation (WMLES) is one of the most viable approaches for predicting these realistic flows. Immersed boundary (IB) approach is an efficient computational technique to solve flow problems involving complex and/or moving geometries. This work extends a sharp-interface IB method, named the local domain-free discretion (DFD), to WMLES of compressible flows at high Reynolds numbers. An equilibrium wall model based on solving the simplified compressible turbulent boundary layer equations is utilized to alleviate the requirement of high near-wall mesh resolution. In conjunction with the approximate boundary conditions prescribed by the modeled wall shear stress and wall heat flux, the tangential velocity and temperature at an exterior dependent node are evaluated. Then, the closure of the discrete form of governing equations at an interior node in the immediate vicinity of the immersed wall is accomplished. A simple non-equilibrium correction of the wall shear stress provided by the equilibrium wall model is introduced explicitly. The WMLES/DFD method is applied to a supersonic zero-pressure-gradient turbulent boundary layer flow, a shock wave/flat-plate boundary layer interaction, a supersonic compression ramp flow and high-speed turbulent Couette flows with various thermal boundary conditions. The influence of grid resolution is investigated in the simulation of zero-pressure-gradient turbulent boundary layer flow. By comparing the computed results with the referenced experimental data and/or numerical results, the accuracy and ability of the WMLES/DFD method to simulate compressible turbulent flows are verified.