An improved slip-wall model for large eddy simulation and its implementation in the local domain-free discretization method

In this paper, a slip-wall model for large eddy simulation (LES) is improved and implemented in an immersed boundary method named the local domain-free discretization (DFD) method. Considering that the matching location may be in the viscous sublayer, the physics-based interpretation of a Robin-type wall closure is complemented. Then, the slip-wall wall model is improved, in which the slip length is redefined and the Robin boundary condition is imposed at the solid wall. The improved slip-wall model is implemented in the local DFD method to evaluated the tangential velocity at an exterior dependent node, and then the requirement on high resolution of boundary layers can be alleviated. The non-equilibrium effects are accounted for by adding an explicit correction to the wall shear stress. In order to validate the present wall-modeled LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills and the flows over a NACA 4412 airfoil at a high Reynolds number are simulated. The predicted results agree well with the referenced experimental data and numerical results. Especially, the results of the separated flow over the airfoil at a near-stall condition demonstrate the performance of the present wall-modeled LES/DFD method for complex flows.