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A Mathematical Analysis of Scale Similarity

Part of: Turbulence Hyperbolic equations and systems

Published online by Cambridge University Press:  05 December 2016

Z. J. Wang  and
Yanan Li
Z. J. Wang*
Affiliation:
Department of Aerospace Engineering, University of Kansas, 2120 Learned Hall, Lawrence, KS 66045, USA
Yanan Li*
Affiliation:
Department of Aerospace Engineering, University of Kansas, 2120 Learned Hall, Lawrence, KS 66045, USA
*
*Corresponding author. Email addresses:zjw@ku.edu (Z. J.Wang), yananli@ku.edu (Y. Li)
*Corresponding author. Email addresses:zjw@ku.edu (Z. J.Wang), yananli@ku.edu (Y. Li)
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Abstract

Scale similarity is found in many natural phenomena in the universe, from fluid dynamics to astrophysics. In large eddy simulations of turbulent flows, some sub-grid scale (SGS) models are based on scale similarity. The earliest scale similarity SGS model was developed by Bardina et al., which produced SGS stresses with good correlation to the true stresses. In the present study, we perform a mathematical analysis of scale similarity. The analysis has revealed that the ratio of the resolved stress to the SGS stress is γ2, where γ is the ratio of the second filter width to the first filter width, under the assumption of small filter width. The implications of this analysis are discussed in the context of large eddy simulation.

Keywords

Scale similaritylarge eddy simulationsub-grid scale models

MSC classification

Secondary: 35L65: Conservation laws 76F02: Fundamentals
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 1 , January 2017 , pp. 149 - 161
Copyright
Copyright © Global-Science Press 2016 

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