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Résolution des équations de Saint Venant avec transport de polluant par un schéma éléments finis et un schéma volumes finis

Résolution des équations de Saint Venant avec transport de polluant par un schéma éléments finis et un schéma volumes finis

          
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About the Book

Thèse de Doctorat de l'année 2006 dans le domaine Ingénierie - Génie Mécanique, langue: Français, résumé Dans ce travail nous avons modélisé numériquement les équations de Saint Venant qui régissent les écoulements en eau peu profonde, couplées à l'équation de diffusion d'un polluant. Nous avons utilisé deux techniques de calcul numérique parmi les plus efficaces, la méthode des éléments finis et la méthode des volumes finis. En éléments finis nous utilisons le schéma de Taylor-Galerkin qui est un schéma centré de deuxième ordre dans l'espace et dans le temps. La solution est calculée par ce schéma en deux étapes, la première utilise une approximation constante par élément et la seconde une approximation linéaire. Nous obtenons un schéma conservatif, précis et simple à programmer; néanmoins il génère des oscillations aux voisinages des gradients importants. Cet handicap est résolu par l'introduction d'un modèle de diffusion numérique du à MacCormak. Cette dissipation a pour caractéristique de n'agir que dans les régions à forts gradients et d'être inactive dans les régions lisses. Le deuxième schéma est issu de la méthode des volumes finis et il est dû à Roe. On y utilise un maillage de type éléments finis non-structuré (cell-centered) ou les grandeurs physiques sont évaluées aux centres des cercles circonscrits aux triangles. La partie hyperbolique du système d'équations est approximée par un solveur de Riemann, puis le flux numérique est corrigé de façon à garantir l'entropie de la solution. Afin d'augmenter la précision du schéma dans l'espace à l'ordre deux, la technique MUSCL est utilisée. Quant à la discrétisation du temps, elle est effectuée par le schéma de Runge Kutta à l'ordre deux. La validition des deux méthodes est démontrée sur le test du ressaut hydraulique dont la solution théorique est connue. Ensuite, des comparaisons sont effectuées sur une série d'exemples d'écoulements à surface libre. Les deux schémas se révèlent être puissants, préc


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Product Details
  • ISBN-13: 9783346345462
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Height: 210 mm
  • No of Pages: 142
  • Spine Width: 8 mm
  • Width: 148 mm
  • ISBN-10: 3346345467
  • Publisher Date: 09 Apr 2021
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Weight: 195 gr


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