Comptes Rendus
no. 6
Numerical Analysis
Computation of the normal vector to a free surface by a finite element – finite volume mixed method
[Calcul du vecteur normal à une surface libre par une méthode mixte d'éléments finis – volumes finis]

Présenté par : Philippe G. Ciarlet

Alexandre Caboussat1 ; Roland Glowinski1, 2 ; James M. Sicilian3
1 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
2 Laboratoire J.L. Lions, Université P. et M. Curie, 4, place Jussieu, 75005 Paris, France
3 CCS-2, Methods for Adv. Sci. Simulations, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 431-436.

Dans la plupart des schémas de type volume finis pour des problèmes de surface libre, la reconstruction de l'interface et le calcul des effets de tension de surface nécessitent une approximation précise du vecteur normal à l'interface. Nous présentons une méthode numérique pour le calcul du vecteur normal, basée sur une approche de type éléments finis. Nous interpolons la fraction liquide de la grille volumes finis sur un maillage emboité de type éléments finis à l'aide de projections. Nous obtenons des estimations d'erreurs a priori et l'efficacité de la méthode est confirmée par les résultats d'essais numériques.

In volume tracking finite volume schemes for free surface flows, the reconstruction of the interface and the computation of surface tension effects require an accurate approximation of the normal vector to the interface. A numerical method for the computation of the normal vector is presented here, based on a finite element approach. We use projections to interpolate the volume fraction of liquid between the finite volume mesh and a nested finite element mesh. Error estimates are obtained and numerical results show the efficiency and flexibility of the approach discussed here.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.08.010
Alexandre Caboussat 1 ; Roland Glowinski 1, 2 ; James M. Sicilian 3

1 Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA
2 Laboratoire J.L. Lions, Université P. et M. Curie, 4, place Jussieu, 75005 Paris, France
3 CCS-2, Methods for Adv. Sci. Simulations, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 
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     author = {Alexandre Caboussat and Roland Glowinski and James M. Sicilian},
     title = {Computation of the normal vector to a free surface by a finite element {\textendash} finite volume mixed method},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {431--436},
     publisher = {Elsevier},
     volume = {343},
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     year = {2006},
     doi = {10.1016/j.crma.2006.08.010},
     language = {en},
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Alexandre Caboussat; Roland Glowinski; James M. Sicilian. Computation of the normal vector to a free surface by a finite element – finite volume mixed method. Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 431-436. doi : 10.1016/j.crma.2006.08.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.08.010/

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