Skip to Main content Skip to Navigation
Theses

Résolution de l'équation du transport par une méthode d'éléments finis mixtes-hybrides et approximation par la diffusion de problèmes de transport

Abstract : This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations.
First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme.
We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion
limit (when the mean free path is small in comparison with the characteristic length of the physical domain).
We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate
our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one
consists in modelling and simulating radiative transfer phenomenon in case of industrial context of inertial confinment fusion.
Complete list of metadatas

Cited literature [69 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00092407
Contributor : Julien Cartier <>
Submitted on : Saturday, September 9, 2006 - 6:36:12 PM
Last modification on : Thursday, March 5, 2020 - 6:49:20 PM
Document(s) archivé(s) le : Monday, April 5, 2010 - 10:48:28 PM

Identifiers

  • HAL Id : tel-00092407, version 1

Citation

Julien Cartier. Résolution de l'équation du transport par une méthode d'éléments finis mixtes-hybrides et approximation par la diffusion de problèmes de transport. Mathématiques [math]. Université d'Orléans, 2006. Français. ⟨tel-00092407⟩

Share

Metrics

Record views

1370

Files downloads

20366