A new dynamic slip approach for wall-modeled Large Eddy Simulations in a Consistent Discontinuous Galerkin Framework

TL;DR

This paper introduces a novel dynamic slip wall model for wall-modeled Large Eddy Simulations within a Discontinuous Galerkin framework, effectively capturing flow features even under significant under-resolution.

Contribution

It develops a new dynamic slip wall model that incorporates DG approximation order, discretization effects, and subgrid-scale modeling, enhancing accuracy in under-resolved turbulent flow simulations.

Findings

Achieves grid-independent statistics in channel flows.

Accurately predicts mean velocity and Reynolds stress profiles.

Successfully models separated flows with under-resolved meshes.

Abstract

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 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 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 modeling.