Flux Reconstruction Implementation of an Algebraic Wall Model for Large-Eddy Simulation

In the present study, an algebraic equilibrium wall model is implemented and tested for a large-eddy simulation (LES) solver based on the flux reconstruction (FR) method. One of the objectives of the present paper is to verify the main results of Frère et al. (“Application of Wall Models to Discontinuous Galerkin LES,” Physics of Fluids, Vol. 29, No. 8, 2017, Paper 085111) under the FR framework. In addition, the influence of the mesh growth ratio in the wall-normal direction and the mesh resolutions in the wall-parallel directions are investigated, as well as the size of the first element in the wall-normal direction. In the present wall model, the wall shear stress is computed according to the wall tangential velocity at the interface between the first and second cells from the wall. The stress is then used to update the solution unknowns. Various strategies are evaluated using a turbulent channel flow at a high Reynolds number. A comparison between a wall-modeled LES and implicit LES (ILES) without a wall model on a coarse mesh shows that the wall-modeled approach produces better results than the ILES. The wall model is then evaluated with the two-dimensional periodic hill problem to assess its capability of capturing flow separation and reattachment. The equilibrium wall model fails to capture turbulent flow separation and reattachment, indicating the need for nonequilibrium wall models for such problems.