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A palette of fine-scale eddy viscosity and residual-based models for variational multiscale formulations of turbulence

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Abstract

We explore a general family of eddy viscosity models for the large-eddy simulation of turbulence within the framework of the Variational Multiscale Method. Our investigation encompasses various fine-scale eddy viscosities and coarse-scale residual-based constructs. We delineate the domain of parameter space in which physically and mathematically suitable models exist, and identify several sub-families of potentially useful models that are either entirely new or extend previously proposed ones. We also combine classical modeling ideas, that lead to turbulent kinetic energy evolution equations, with the residual-based approach to derive a new residual-driven, one-equation dynamic model.

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Notes

  1. This is still a debatable point. There is some evidence that the fine scales are being sacrificed to benefit the coarse scales, and other evidence that the fine-scale contribution improves both the coarse and fine scales.

  2. Interestingly, the residual based VMS method, which is consistent for all resolved scales, also displays this superior performance for well-resolved LES [12, 13, 28].

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Authors and Affiliations

  1. Mechanical Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, 12180, Turkey

    Assad A. Oberai

  2. Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX, 78712-1229, USA

    Thomas J. R. Hughes

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  1. Assad A. Oberai
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  2. Thomas J. R. Hughes
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Correspondence to Assad A. Oberai.

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Oberai, A.A., Hughes, T.J.R. A palette of fine-scale eddy viscosity and residual-based models for variational multiscale formulations of turbulence. Comput Mech 57, 629–635 (2016). https://doi.org/10.1007/s00466-015-1242-2

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  • DOI: https://doi.org/10.1007/s00466-015-1242-2

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