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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 535-540 (mai 2010)
Doi : 10.1016/j.crma.2010.03.011
Received : 6 January 2010 ;  accepted : 12 Mars 2010
Improving the mass conservation of the level set method in a finite element context
Amélioration de la conservation de la masse pour la méthode des fonctions de niveaux en éléments finis
 

Aymen Laadhari , Pierre Saramito , Chaouqi Misbah
Laboratoire J. Kuntzmann, CNRS, B.P. 53, 38041 Grenoble, France 

Abstract

In this Note, a new algorithm is proposed for improving the mass conservation of the level set method in the finite element context. Two kinds of Lagrange multipliers are introduced, associated respectively to the redistancing and advection equations. The first one, is located at the vicinity of the interface, while the second one is associated to a correction that is global to the domain. The performances of the proposed method are tested on the Zalesak test case, and the convergence rate versus the element mesh size are founded to be improved.

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Résumé

Dans cette Note, nous proposons un nouvel algorithme pour améliorer la conservation de la masse dans la méthode des fonctions de niveau dans un cadre éléments finis. Deux types de multiplicateurs de Lagrange sont introduits, associés respectivement à l’équation de redistanciation et à celle d’advection. Le premier est localisé au voisinage de l’interface, tandis que le second est associé à une correction globale au domaine de calcul. Les performances de la méthode proposée sont testées avec le cas test du disque de Zalesak, et nous observons que le taux de convergence par rapport au la taille des éléments du maillage est amélioré.

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