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Contribution à la modélisation mathématique et numérique pour des modèles d'écoulement non-linéaires dispersifs en eaux peu profondes

Abstract : This work focuses on the modeling and mathematical analysis of asymptotic models used in oceanography describing long wave propagation.This thesis aims to derive and justify new asymptotic models taking into account the variation in topography and cross-section.To do so, several hypotheses are formulated on water depth and cross-sectional deformations. The first part of this thesis is to put the problem into equations, and to find asymptotic models and study them mathematically, see the linear analysis of dispersion and shoaling.In the second part, a one-dimensional model of section-averaged long waves is developed. Three-dimensional equations of motion of non-viscous and incompressible fluids are first integrated over a cross-section of the channel, resulting in the SGN-type equations. Therefore, the new model is adequate to describe fully non-linear and weakly dispersive waves along a channel of an arbitrary and non-uniform cross-section. Specifically, the new model extends the Saint-Venant model to cross-section mean and generalizes the Serre-Green-Naghdi equations to any cross-section.This new model has been reformulated in a way more appropriate for numerical resolution by maintaining the same order of accuracy as the original and improving its propertiesof dispersion. Finally, we present some numerical simulations to study the influence of the change of section on the propagation of a solitary wave.The last part of this thesis is devoted to the numerical simulation of the SGN model with a new reformulation.
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https://tel.archives-ouvertes.fr/tel-03170340
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Submitted on : Tuesday, March 16, 2021 - 10:19:08 AM
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  • HAL Id : tel-03170340, version 1

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Debyaoui Mohamed Ali. Contribution à la modélisation mathématique et numérique pour des modèles d'écoulement non-linéaires dispersifs en eaux peu profondes. Equations aux dérivées partielles [math.AP]. Université de Toulon; Université de Sfax. Faculté des sciences, 2020. Français. ⟨NNT : 2020TOUL0002⟩. ⟨tel-03170340⟩

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