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Résolution numérique des équations de Saint-Venant par la technique de projection en utilisant une méthode des volumes finis dans un maillage non structuré

Abstract : Recently, several Unstructured Finite-Volumes Methods (UFVM) have been developed to solve Navier-Stokes flows, but there do not exist so many applications of UFVM to the shallow-water problems. The principal difficulty, encountered in the applications of such models, is related to the irregular variation of bed elevation with the presence of wet/dry zones in a complex geometry. This dissertation presents the development of a 2-D numerical model, named ECOMOD-UFVM, which is based on the solving of the Saint-Venant equations by a projection technique coupled with a UFVM. The UFVM will allow a numerical modelling, which can perfectively adapt to the geometry very complex in the coastal and estuarine zones. Initially, in the framework of this thesis, a second order scheme of ULSS (Upwind Least Squares Scheme) is introduced in the code to handle the convection terms in order to prevent undesirable numerical oscillations and diffusions. Ten benchmarked test cases proposed in the existing studies were carried out: shallow water flows; dam-break flows. The results of the case-tests are satisfactory and allow us to make with confidence the passage into two real natural applications: dam-break of Malpasset (France) and flash flood in the city of Dongchuan (China). The results obtained confirm the reliability, the precision, the stability and the robustness of the developed UMVF model in solving the Saint-Venant equations, describing all kinds of flows: slow, fast and torrential on any type of the bottom: wet/dry, flat or great slopes, regular or very irregular.
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https://tel.archives-ouvertes.fr/tel-00130539
Contributor : Yu-E Shi <>
Submitted on : Friday, July 6, 2012 - 4:20:26 PM
Last modification on : Monday, April 27, 2020 - 4:26:29 PM
Long-term archiving on: : Sunday, October 7, 2012 - 2:35:11 AM

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  • HAL Id : tel-00130539, version 2

Citation

Yu-E Shi. Résolution numérique des équations de Saint-Venant par la technique de projection en utilisant une méthode des volumes finis dans un maillage non structuré. Sciences de la Terre. Université de Caen, 2006. Français. ⟨tel-00130539v2⟩

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