A dynamic linearized wall model for turbulent flow simulation: Towards grid convergence in wall-modeled simulations

Abstract

This paper addresses the common issue of (no-)grid convergence in wall-modeled numerical simulations and proposes a dynamic linearization technique applied to the Spalart-Allmaras wall model to achieve a proper behavior on fine grids and low-friction areas. A theoretical analysis of the numerical error committed on the shear stress balance close to the walls is performed. It shows that the error is due to the inappropriate imposition of too steep wall-normal velocity gradients that cannot be properly accounted for on the typical grids used for wall-modeled simulations. Based on this error quantification, a dedicated wall model linearization technique is proposed, following the approach developed by Tamaki, Harada and Imamura in 2017. In the proposed modified linearization method, the linearization distance is modified and adjusted dynamically. This is done according to the theoretical shear stress error estimate, in order to keep the numerical error below a user-defined threshold. The method is applied to well-referenced test cases of increasing complexity from the Turbulence Modeling Resource. Overall, the proposed wall model clearly exhibits appropriate grid convergence properties and is also able to predict accurately non-equilibrium boundary layers and flow separation using proper grid refinement.