A new dynamic slip approach for wall-modelled large eddy simulations in a consistent discontinuous Galerkin framework

A wall-modelled large eddy simulation approach is proposed in a discontinuous Galerkin (DG) setting, building on the slip-wall concept of Bae et al. ( J. Fluid Mech. , vol. 859, 2019, pp. 400–432) and the universal scaling relationship by Pradhan and Duraisamy ( J. Fluid Mech., vol. 955, 2023, A6). The effect of the order of the DG approximation is introduced via the length scales in the formulation. The level of under-resolution is represented by a slip Reynolds number and the model attempts to incorporate the effects of the numerical discretization and the subgrid-scale model. The dynamic part of the new model is based on a modified form of the Germano identity -- performed on the universal scaling parameter -- and is coupled with the dynamic Smagorinsky model. A sharp modal cutoff filter is used as the test filter for the dynamic procedure, and the dynamic model can be easily integrated into any DG solver. Numerical experiments on channel flows show that grid independence of the statistics is achievable and predictions for the mean velocity and Reynolds stress profiles agree well with the direct numerical simulation, even with significant under-resolution. When applied to flows with separation and reattachment, the model also consistently predicts one-point statistics in the reverse flow and post-reattachment regions in good agreement with experiments. The performance of the model in accurately predicting equilibrium and separated flows using significantly under-resolved meshes can be attributed to several aspects that work synergistically: the optimal finite-element projection framework, the interplay of the scale separation and numerical discretization within the DG framework, and the consistent dynamic procedures for subgrid and wall modelling.