A unified understanding of scale-resolving simulations and near-wall modeling of turbulent flows using optimal finite element projections

TL;DR

This paper introduces a unified framework for assessing and improving turbulence models like LES and wall modeling by using optimal finite element projections, providing new accuracy metrics and insights for model enhancement.

Contribution

It develops a unified a priori assessment framework for various turbulence models using optimal projections, and proposes improved slip-wall models based on these insights.

Findings

Optimal projections match existing a posteriori solutions.

Developed universal scaling for near-wall slip velocity.

Enhanced slip-wall models outperform existing dynamic models.

Abstract

The main objective of this work is to develop a unified framework that can be used as a lens to quantitatively assess and augment a wide range of coarse-grained models of turbulence, viz. large eddy simulations (LES), hybrid Reynolds-averaged/LES methods and wall-modeled (WM)LES. Taking a turbulent channel flow as an example, optimality is assessed in the wall-resolved limit, the hybrid RANS/LES limit and the WMLES limit, via projections at different resolutions suitable for these approaches. These optimal a priori estimates are shown to have similar characteristics to existing a posteriori solutions reported in the literature. Consistent accuracy metrics are developed for scale-resolving methods using the optimal solution as a reference, and evaluations are performed. We further characterize the slip velocity in WMLES in terms of the near-wall under-resolution and develop a universal scaling relationship. Insights from the a-priori tests are used to augment existing slip-based wall models. Various a posteriori tests reveal superior performance over the dynamic slip wall model. Guidance for the development of improved slip-wall models is provided, including a target for the dynamic procedure.