Annals of Mathematical Sciences and Applications

Volume 1 (2016)

Number 1

Large eddy simulation, turbulent transport and the renormalization group

Pages: 149 – 180

DOI: https://dx.doi.org/10.4310/AMSA.2016.v1.n1.a4

Authors

James Glimm (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

Bradley J. Plohr (Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A.)

Hyunkyung Lim (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

Wenlin Hu (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, U.S.A.)

David H. Sharp (Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A.)

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 numerical 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.

Keywords

LES, renormalization group, subgrid scale models

2010 Mathematics Subject Classification

76F35, 76F65, 82B28

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Published 12 April 2016