Large Eddy Simulation, Turbulent Transport And The Renormalization Group

TL;DR

This paper applies the renormalization group approach to large eddy simulations, providing a systematic expansion for subgrid scale terms and addressing the nonuniqueness of solutions at infinite Reynolds numbers.

Contribution

It introduces an explicit all-orders expansion for unclosed terms in LES, linking RNG concepts to dynamic subgrid models and proposing a systematic way to determine model coefficients.

Findings

RNG-inspired expansion relates to subgrid scale models.

LES predicts unique model coefficients, breaking RNG nonuniqueness.

The approach generalizes Leonard stress for closure analysis.

Abstract

In large eddy simulations, the Reynolds averages of nonlinear terms are not directly computable in terms of the resolved variables and require a closure hypothesis or model, known as a subgrid scale term. Inspired by the renormalization group (RNG),we introduce an expansion for the unclosed terms, carried out explicitly to all orders. In leading order, this expansion defines subgrid scale unclosed terms, which we relate to the dynamic subgrid scale closure models. The expansion, which generalizes the Leonard stress for closure analysis, suggests a systematic higher order determination of the model coefficients. The RNG point of view sheds light on the nonuniqueness of the infinite Reynolds number limit. For the mixing of N species, we see an N+1 parameter family of infinite Reynolds number solutions labeled by dimensionless parameters of the limiting Euler equations, in a manner intrinsic to the RNG itself. Large eddy simulations, with their Leonard stress and dynamic subgrid models, break this nonuniqueness and predict unique model coefficients on the basis of theory. In this sense large eddy simulations go beyond the RNG methodology, which does not in general predict model coefficients.