Identification de modèles et de paramètres pour la méthode de Boltzmann sur réseau.

Abstract : This thesis is composed of three parts. Firstly a study of Lattice
Boltzmann scheme (LBE) is performed. Then Adjoint Lattice Boltzmann
scheme (ALBE) is introduced for parameters identification. Finally a new Lattice Boltzmann scheme (BRB) is proposed to model Bérenger's Perfectly Matched Layer (PML) method.

The first part introduces and analyzes the LBE method.

The second part describes a variational approach for parameters
identification adapted to LBE. A time discrete adjoint method is developed. At first the ALBE method is applied to Stokes' problem and
then to a nonlinear problem. Good results have been obtained in the cases of one or tow unknown parameters.

Finally the third part describes an adaptation of PML for LBE. The LB
scheme is obtained with 9 discrete velocities. An analysis of reflected
waves between two one dimensional LB media is performed. It provides us an equivalent for the Fresnel formula for LBE interface. That gives us same ideas to modify the LB scheme at the interface to vanish reflected waves. In the two dimensional case, the same analysis of reflected waves shows the existence of Knudsen modes and transverse waves, which make the analysis more difficult.
Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00207541
Contributor : Mohamed Mahdi Tekitek <>
Submitted on : Thursday, January 17, 2008 - 4:31:18 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on : Tuesday, April 13, 2010 - 7:00:38 PM

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Mohamed Mahdi Tekitek. Identification de modèles et de paramètres pour la méthode de Boltzmann sur réseau.. Mathématiques [math]. Université Paris Sud - Paris XI, 2007. Français. ⟨tel-00207541⟩

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