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Symmetry 2010, 2(2), 848-867; doi:10.3390/sym2020848

The Symmetry Group of the Non-Isothermal Navier–Stokes Equations and Turbulence Modelling

LEPTIAB, Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France
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Received: 10 December 2009 / Revised: 18 March 2010 / Accepted: 12 April 2010 / Published: 16 April 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract

In this work, the non-isothermal Navier–Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulence models are analyzed with the symmetries of the equations. A class of turbulence models which preserve the physical properties contained in the symmetry group is built. The proposed turbulence models are applied to an illustrative example of natural convection in a differentially heated cavity, and the results are presented.
Keywords: symmetry; invariance; turbulence; large-eddy simulation; convection symmetry; invariance; turbulence; large-eddy simulation; convection
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Al Sayed, N.; Hamdouni, A.; Liberge, E.; Razafindralandy, D. The Symmetry Group of the Non-Isothermal Navier–Stokes Equations and Turbulence Modelling. Symmetry 2010, 2, 848-867.

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