# Modèle hydrostatique pour les écoulements à surface libre tridimensionnels et schémas numériques

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : This PhD thesis aims to deepen the analysis of the equations governing the three-dimensional free surface flows.
On one hand we present a new weak formulation of the hydrostatic problem leading to a well-posed time-discrete problem. This problem is analysed mathematically and its resolution is implemented into the
Telemac-$3$D system, developed at the Laboratoire National d'Hydraulique et Environnement (LNHE), edf. Some numerical results are shown.
On the other hand, we study the ALE interpretation of the sigma transformation method for the vertical discretization of three-dimensional domains. Especially we propose a generalization allowing to improve the representation of stratifications in a flow.
Finally, we introduce an ALE-MURD scheme for the linear advection problem posed on moving domains. A particular constraint must be satisfied for the scheme to be conservative when the domain moves. We show how to ensure this constraint in the particular case where the domain is three-dimensional and only moves in the vertical direction. This result is illustrated numerically in the framework of the
three-dimensional free surface flow problem.
Keywords :
Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00180003
Contributor : Decoene Astrid <>
Submitted on : Wednesday, October 17, 2007 - 2:08:34 PM
Last modification on : Thursday, December 10, 2020 - 10:50:32 AM
Long-term archiving on: : Sunday, April 11, 2010 - 9:49:42 PM

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• HAL Id : tel-00180003, version 1

### Citation

Astrid Decoene. Modèle hydrostatique pour les écoulements à surface libre tridimensionnels et schémas numériques. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI; Laboratoire Jacques-Louis Lions, 2006. Français. ⟨tel-00180003⟩

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