  A wall-modeled large eddy simulation approach is proposed in a Discontinuous
Galerkin (DG) setting, building on the slip-wall concept of Bae et al. (JFM'19)
and the universal scaling relationship by Pradhan and Duraisamy (JFM'23). 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 also 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 Germano identity -- performed on the
universal scaling parameter -- and is coupled with the dynamic Smagorinsky
model. A sharp modal cut-off 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 DNS, 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 modeling.
