Subgrid models preserving the symmetry group of the Navier–Stokes equations

Dina Razafindralandy; Aziz Hamdouni

doi:10.1016/j.crme.2005.04.002

Subgrid models preserving the symmetry group of the Navier–Stokes equations

Presented by: Patrick Huerre

Dina Razafindralandy ¹; Aziz Hamdouni ¹

¹ LEPTAB, université de La Rochelle, avenue Michel-Crépeau, 17042 La Rochelle cedex 01, France

Comptes Rendus. Mécanique, Volume 333 (2005) no. 6, pp. 481-486.

Abstract
Résumé

In order to preserve the physical properties of the flow (scaling laws, conservation laws, …) during the simulation, a class of subgrid models respecting the symmetry group of the Navier–Stokes equations is built. The class is then refined such that models satisfy the second law of thermodynamics and are suited to take into account the inverse energy cascade. A simple model belonging to the class is tested and a better result than those provided by Smagorinsky and dynamic models is obtained.

Dans le but de respecter les propriétés physiques de l'écoulement (lois d'échelle, lois de conservation, …) lors de la simulation, on construit une classe de modèles de sous-maille conservant le groupe de symétrie des équations de Navier–Stokes. On raffine ensuite cette classe de telle sorte que les modèles satisfassent le second principe de la thermodynamique et qu'ils soient capables de prendre en compte la cascade inverse d'énergie. Un modèle simple de la classe est testé dans le cas d'un écoulement dans une chambre ventilée. Les premiers calculs donnent un résultat nettement meilleur que ceux obtenus avec le modèle de Smagorinsky et le modèle dynamique.

Received: 2005-03-10
Accepted: 2005-03-29
Published online: 2005-05-03

DOI: 10.1016/j.crme.2005.04.002

Keywords: Computational fluid mechanics, Turbulence, Subgrid models, Symmetry group
Mots-clés : Mécanique des fluides numérique, Turbulence, Modèles de sous-maille, Groupe de symétrie

Author's affiliations:

Dina Razafindralandy ¹; Aziz Hamdouni ¹

¹ LEPTAB, université de La Rochelle, avenue Michel-Crépeau, 17042 La Rochelle cedex 01, France

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     title = {Subgrid models preserving the symmetry group of the {Navier{\textendash}Stokes} equations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {481--486},
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     year = {2005},
     doi = {10.1016/j.crme.2005.04.002},
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Dina Razafindralandy; Aziz Hamdouni. Subgrid models preserving the symmetry group of the Navier–Stokes equations. Comptes Rendus. Mécanique, Volume 333 (2005) no. 6, pp. 481-486. doi : 10.1016/j.crme.2005.04.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.04.002/

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