Comptes Rendus
Partial Differential Equations/Numerical Analysis
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]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 535-540.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.011

Aymen Laadhari 1 ; Pierre Saramito 1 ; Chaouqi Misbah 1

1 Laboratoire J. Kuntzmann, CNRS, B.P. 53, 38041 Grenoble, France
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Aymen Laadhari; Pierre Saramito; Chaouqi Misbah. Improving the mass conservation of the level set method in a finite element context. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 535-540. doi : 10.1016/j.crma.2010.03.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.011/

[1] D. Enright; R. Fedkin; J. Ferziger; I. Mitchell A hybrid particle level set method for improved interface capturing, J. Comput. Phys., Volume 183 (2002), pp. 83-116

[2] G.-S. Jiang; D. Peng Weighted ENO schemes for Hamilton–Jacobi equations, SIAM J. Sci. Comput., Volume 21 (2000), pp. 2126-2143

[3] S. Osher; R. Fedkiw The Level Set Method and Dynamic Implicit Surfaces, Springer-Verlag, New York, 2003

[4] O. Pironneau On the transport-diffusion algorithm and its applications to the Navier–Stokes equations, Numer. Math., Volume 38 (1982) no. 3, pp. 309-332

[5] P. Saramito; N. Roquet; J. Étienne, 2008 http://www-lmc.imag.fr/lmc-edp/Pierre.Saramito/rheolef (Rheolef: A finite element environment, i.e. some C++ classes and Unix commands)

[6] J. Sethian; Set Level Methods and Fast Marching Methods, Cambridge University Press, 1999

[7] M. Sussman; E. Fatemi An efficient, interface preserving level set re-distancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., Volume 20 (1998) no. 4, pp. 1165-1191

[8] S. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., Volume 31 (1979), pp. 335-362

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