A wall-modeled large eddy simulation method with a generalized wall function for flux reconstruction solver

This study incorporates the generalized wall stress function proposed by Shih et al. into a high-order flux reconstruction (FR) solver for wall-modeled large-eddy simulation (WMLES). The wall model accounts for non-equilibrium effects induced by favorable and adverse pressure gradients in turbulent flows via the generalized wall stress formulation. Unlike previous approaches, which estimate wall shear stress based on the tangential velocity at the interface between the first and second off-wall cells in high-order discontinuous Galerkin or FR frameworks, the present model evaluates the wall shear stress at the first solution point within the wall-adjacent element. Furthermore, a no-slip wall boundary condition is enforced, in contrast to the slip condition applied in earlier studies. To achieve a balance between numerical stability and accuracy, a hybrid approach combining weak-prescribed and weak-Riemann methods is developed for computing inviscid wall fluxes. Detailed procedures for implementing the generalized wall function and treating inviscid and viscous fluxes at the wall are thoroughly described. The solver and wall model are validated in fully developed turbulent channel flows at friction Reynolds numbers 2000, 5200, and 10000. Performance of the generalized wall function is further assessed in simulations of flow over a periodic hill at Reynolds numbers of 10595 and 37000, which are characterized by strong pressure gradients. Numerical predictions show favorable agreement with experimental measurements and high-fidelity reference datasets, demonstrating the proposed WMLES approach's capability in accurately predicting non-equilibrium turbulent flows under adverse and favorable pressure gradients.