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Theoretically based optimal large-eddy simulation

Phys. Fluids 21, 105104 (2009); doi:10.1063/1.3249754

Published 23 October 2009

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Robert D. Moser,1,2 Nicholas P. Malaya,2 Henry Chang,1 Paulo S. Zandonade,3 Prakash Vedula,4 Amitabh Bhattacharya,5 and Andreas Haselbacher6
1Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
2Department of Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
3Department of Theoretical and Applied Mechanics, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801, USA
4Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma 73019, USA
5Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
6Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA
Large eddy simulation (LES), in which the large scales of turbulence are simulated while the effects of the small scales are modeled, is an attractive approach for predicting the behavior of turbulent flows. However, there are a number of modeling and formulation challenges that need to be addressed for LES to become a robust and reliable engineering analysis tool. Optimal LES is a LES modeling approach developed to address these challenges. It requires multipoint correlation data as input to the modeling, and to date these data have been obtained from direct numerical simulations (DNSs). If optimal LES is to be generally useful, this need for DNS statistical data must be overcome. In this paper, it is shown that the Kolmogorov inertial range theory, along with an assumption of small-scale isotropy, the application of the quasinormal approximation and a mild modeling assumption regarding the three-point third-order correlation are sufficient to determine all the correlation data required for optimal LES modeling. The models resulting from these theoretically determined correlations are found to perform well in isotropic turbulence, with better high-wavenumber behavior than the dynamic Smagorinsky model. It is expected that these theory-based optimal models will be applicable to a wide range of turbulent flows, in which the small scales can be modeled as isotropic and inertial. The optimal models developed here are expressed as generalized quadratic and linear finite-volume operators. There are significant quantitative differences between these optimal LES operators and standard finite-volume operators, and these differences can be interpreted as the model of the subgrid effects. As with most other LES models, these theory-based optimal models are expected to break down near walls and other strong inhomogeneities. ©2009 American Institute of Physics
History: Received 9 December 2008; accepted 13 September 2009; published 23 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/105104/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.27.ep
    Large-eddy turbulence simulations
  • 02.70.-c
    Computational techniques; simulations
  • 47.11.Df
    Finite volume methods in fluid dynamics
  • YEAR: 2009

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ISSN:
1070-6631 (print)   1089-7666 (online)
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