A discontinuous Galerkin method for wall-modeled large-eddy simulations

We develop an augmented discontinuous Galerkin method for wall-modeled large-eddy simulations. This method is motivated by the enrichment method that has been formulated for finite-element method, by statistically augmenting the variational solution of the near-wall element with a simple wall function to model the effects of the unresolved momentum-carrying near-wall eddies on the resolved scales. An explicit model is employed to model the subgrid-scale stresses. It is shown that this approach improves the solution accuracy on significantly underresolved grids and reduces spurious oscillations that occur in the presence of strong wall gradients on coarse grids with high-order DG methods. The proposed method is applied in low-Mach-number plane channel flows over a range of Reynolds numbers to examine effects of mesh resolution, polynomial order, solution-augmentation, and the SGS closure on the model performance. The results show that the proposed approach reproduces the log-law profile for different flow conditions, even at extreme Reynolds numbers, and yields improved predictions with increasing polynomial order. In addition, the capability of the present DG-based WMLES framework for computations of complex flows is demonstrated in LES of a shock-induced boundary-layer separation for the transonic bump experiment by Bachalo & Johnson (AIAA J., 24, 1986).