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Contribution à l'étude mathématique et numérique de la simulation des grandes échelles

Abstract : Transformations which preserve the set of the solutions of Navier-Stokes equations (NS) are called symmetries of NS. They form a Lie group called the symmetry group of NS. This group plays an important role in the description of the physics of the equations (conservation law, wall law, ...) and turbulence models should remain invariant under the action of this group. In the first part of the thesis, an analysis of some standard models from the point of view of symmetries is carried out. Next, a class of subgrid models which, on the one hand, respect the symmetry group of NS and, on the other hand, conform to the second law of thermodynamics is built. A simple model of the class is then numerically tested and validated. The analysis and construction of models are extended to the case of thermal convection. In the second part of the thesis, the possibility of integrating LES (large eddy simulation) in an algorithm belonging to the family of MAN (asymptotic numerical method) is explored. MAN is a perturbation technique which consists in computing a solution as a formal series. A first algorithm associating MAN and LES and using a technique of homotopy is built and tested. Because of the limits of this first algorithm, the use of an other algorithm based on a time series development is studied. To increase the range of validity of the series, or to extract an analytic solution from this series when it diverges, the Borel resummation method is proposed. This method is applied to reduced models obtained from Navier-Stokes equations.
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Contributor : Dina Razafindralandy Connect in order to contact the contributor
Submitted on : Friday, July 15, 2005 - 5:50:08 AM
Last modification on : Friday, June 3, 2022 - 10:24:27 AM
Long-term archiving on: : Friday, April 2, 2010 - 10:07:07 PM


  • HAL Id : tel-00009762, version 1


Dina Razafindralandy. Contribution à l'étude mathématique et numérique de la simulation des grandes échelles. Mécanique []. Université de la Rochelle, 2005. Français. ⟨tel-00009762⟩



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