Implementation of a dynamic slip wall model for large eddy simulation in the local domain-free discretization method

Abstract

Wall-modeling techniques are frequently applied in the extension of immersed boundary methods to large eddy simulation (LES) of turbulent flows. In this paper, a dynamic slip wall model is incorporated into an immersed boundary method named the local domain-free discretization (DFD) method for implicitly filtered LES, which is based on a Robin-type boundary condition and free of a priori specified tunable coefficients and also does not rely on any assumptions about the boundary layer. The present study provides a detailed description of the implementation of the dynamic slip model in the DFD framework, including the evaluation of the velocity components at an exterior dependent node via the Robin-type boundary condition and the dynamic procedure for calculating the slip length. The non-zero slip velocity in the normal direction is imposed in a new way to satisfy on average the non-penetration of the curved wall and maintain the global mass conservation in the implicitly filtered LES. To validate the present wall-modeling LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills, and the high-Reynolds-number flow past a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions are simulated, and the predicted results agree well with the referenced experimental and numerical results.