Improved slip wall models using optimal finite element projections.*

Slip-based models constitute a class of wall models that allow easy implementation of the wall boundary condition and enable the possibility to model flow separation. To improve its performance, an optimal projection framework is developed to offer a unified perspective of WMLES models and a wide range of other eddy-resolving models, viz. LES and Hybrid RANS-LES. Estimates for the slip-wall model coefficient C_w computed using optimal projection of the DNS solution and Reichardt profile show a strong dependence on the numerical method and the Reynolds number based on the slip velocity and the cube root of cell volume. This slip Reynolds number-based formulation allows easy computation of C_w without requiring any iterative procedure. In an attempt to formulate a universal model, a resolution normalizer λ is introduced, which effectively parametrizes the effect of the numerical method through just a single parameter. Further corrections to the model form due to subgrid modeling errors are made by estimating C_w from the solutions of the traditional WMLES approach. The resulting slip wall model with minimal variation of the new model constant λ generalizes to different Reynolds numbers and mesh resolutions.