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ÉDITIONS UNIVERSITAIRES EUROPÉENNES Étude numérique de quelques problèmes issus de la mécanique des fluide: Ondes solitaires et tsunami

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Description

Ce livre est consacrée à l'étude mathématique et numérique de deux problèmes issus de la mécanique des fluides: le premier modélise la propagation transocéanique d'un tsunami et le second détermine les solitons qui sont des solutions de l'équation Korteweg de Vries KdV. Concernant le premier problème, nous considérons le cas d'un fluide parfait et celui d'un fluide de faible viscosité en intégrant une dispersion numérique. Pour cela, nous adoptons la technique des différences finies combinée avec la méthode des directions alternées implicites DAI. Ensuite, nous étudions la stabilité et la convergence de la solution. Pour le second, nous introduisons les variables de distorsion et "inverse scattering method" afin d'amener l'équation KdV à une équation aux dérivées ordinaires EDO appelée Sturm-Liouville. Aussi, nous utilisons l'algorithme de Runge-Kutta-4 pour calculer les valeurs propres et les fonctions propres associées au problème de Sturm-Liouville. Des simulations numériques sont présentées à la fin de chaque chapitre pour valider l'aspect théorique. Mots-clés: Dispersion numérique; Équations de Boussinesq; Équation de KdV; Équation de Sturm-Liouville; Méth

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
11 December 2018
Listed Since
08 January 2019

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