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Modèles LES invariants par groupes de symétries en écoulements turbulents anisothermes

Abstract : Since the Lie group of a given partial differential equation, represent the intrinsic physical propertiesof the equation, it gives a strong tool for modeling its physical phenomenas. The mainpurpose of this thesis, is to apply the Lie group theory, in modeling non-isothermal flows. Therefore,we calculate wall laws and more generally scaling laws for the velocity and the temperatureof a parallel flow. In fact, these scaling laws are simply self-similar solutions of the Navier-Stokesequations averaged with respect to their symmetry.The approach of the Lie group theory, leads to a class of sub-grade models which are invariantvia the symmetries of the non-isothermal Navier-Stokes equations. These models respectthe physical properties contained in these symmetries. Moreover, via this approach the heat flowmodel appears naturally in this class, without introducing the notion of the Prandlt number,which is not the case for any other existing model. From the other side, the behavior near thewall of particular models in this class, is studied. Finally, numerical tests are done in both casesof the natural convection and the mixed one.
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Submitted on : Sunday, July 3, 2011 - 5:28:12 PM
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  • HAL Id : tel-00605655, version 1



Nazir Al Sayed. Modèles LES invariants par groupes de symétries en écoulements turbulents anisothermes. Autre. Université de La Rochelle, 2011. Français. ⟨NNT : 2011LAROS325⟩. ⟨tel-00605655⟩



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