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Un schéma éléments finis non-conformes / volumes finis pour l'approximation en maillages non-structurés des écoulements à faible nombre de Mach

Abstract : We describe in this thesis a numerical scheme for the approximation on unstructured meshes of a system of equations coupling the « low Mach » Navier-Stokes equations with balance equations for scalar variables. The main contribution of this word is the implementation of a stable approximation of the velocity prediction discretized using nonconforming finite elements, and the design of a finite volume scheme being stable and robust towards the maximum principle for scalar balance equations. The Galerkin approximation of Navier-Stokes equations velocity prediction step is particularly sensible to convection-dominated regimes and boundary layers. Using low-order nonconforming finite elements satisfying the discrete inf-sup criterion, we developed an approximation of inertial terms for general hexahedral or tetrahedral grids. This approximation fulfills an energy inequality and enables the discrete control of kinetic energy variation by viscous dissipation. In the design of a finite volume scheme for the approximation of convection-diffusion equations, we are confronted to the necessity of managing with potentially unstructured or nonconforming grids while fulfilling a discrete maximum principle. We also proposed a new coupling of finite volume schemes for the convection-diffusion equation. All implementations of these schemes have been validated on real interest cases for the simulation of turbulent reactive flows.
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https://tel.archives-ouvertes.fr/tel-00483598
Contributor : Guillaume Ansanay-Alex <>
Submitted on : Friday, May 14, 2010 - 6:09:12 PM
Last modification on : Monday, May 17, 2010 - 8:43:13 AM
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Guillaume Ansanay-Alex. Un schéma éléments finis non-conformes / volumes finis pour l'approximation en maillages non-structurés des écoulements à faible nombre de Mach. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2009. Français. ⟨tel-00483598⟩

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