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Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes 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 the industrial context of inertial confinement fusion. (author)
Authors:
Publication Date:
Apr 15, 2006
Product Type:
Thesis/Dissertation
Report Number:
FRNC-TH-6911
Resource Relation:
Other Information: TH: These mathematiques; 75 refs.; Also available from SCD Universite d'Orleans- BP 6749, 45067 - Orleans cedex 2 (France)
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOLTZMANN EQUATION; DISCRETE ORDINATE METHOD; FINITE ELEMENT METHOD; MARKOV PROCESS; MESH GENERATION; NEUTRON TRANSPORT THEORY; VARIATIONAL METHODS
OSTI ID:
20873602
Research Organizations:
Orleans Univ., 45 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR0604919041616
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
223 pages
Announcement Date:
Jun 06, 2007

Citation Formats

Cartier, J. Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport. France: N. p., 2006. Web.
Cartier, J. Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport. France.
Cartier, J. 2006. "Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport." France.
@misc{etde_20873602,
title = {Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport}
author = {Cartier, J}
abstractNote = {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 the industrial context of inertial confinement fusion. (author)}
place = {France}
year = {2006}
month = {Apr}
}