An enriched finite element algorithm for the implicit simulation of the Stefan problem

Eric Feulvarch; Jean-Christophe Roux; Jean-Michel Bergheau

doi:10.1016/j.crme.2011.07.001

An enriched finite element algorithm for the implicit simulation of the Stefan problem

Eric Feulvarch ¹ ; Jean-Christophe Roux ²; Jean-Michel Bergheau ¹

¹ Univ Lyon, ENISE, UMR 5513, LTDS, 58, rue Jean Parot, 42023 Saint-Etienne cedex 2, France
² Univ Lyon, ENISE, EA 3719, DIPI, 58, rue Jean Parot, 42023 Saint-Etienne cedex 2, France

Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 649-654.

Abstract
Résumé

An implicit enriched finite element algorithm is proposed to simulate heat transfer involving isothermal phase changes. This technique is based on a mixed variational formulation discretized by means of an enriched finite element approximation of the enthalpy in space. The interface is implicitly described without coupling with an interface-capturing technique. The time integration is carried out with an implicit (backward) Euler algorithm in time. Two examples in 1D and 2D clearly evidence the efficiency of the method developed.

Un algorithme implicite de type éléments finis enrichis est proposé pour simuler des transferts de chaleur avec des changements de phase isothermes. Cette technique repose sur une formulation variationnelle mixte, discrétisée au moyen dʼune approximation de lʼenthalpie par éléments finis enrichis. Lʼinterface est décrite de manière implicite sans couplage avec une technique spécifique de capture dʼinterface. Lʼintégration temporelle est réalisée par un algorithme dʼEuler purement implicite en temps. Deux exemples 1D et 2D mettent clairement en évidence lʼefficacité de la méthode développée.

Received: 2011-05-14
Accepted: 2011-07-04
Published online: 2011-08-05

DOI: 10.1016/j.crme.2011.07.001

Keywords: Computational solid mechanics, Enriched finite element, Implicit time integration, Stefan problem, Isothermal phase changes
Mots-clés : Mécanique des solides numérique, Éléments finis enrichis, Intégration temporelle implicite, Problème de Stefan, Changements de phase isothermes

Author's affiliations:

Eric Feulvarch ¹; Jean-Christophe Roux ²; Jean-Michel Bergheau ¹

¹ Univ Lyon, ENISE, UMR 5513, LTDS, 58, rue Jean Parot, 42023 Saint-Etienne cedex 2, France
² Univ Lyon, ENISE, EA 3719, DIPI, 58, rue Jean Parot, 42023 Saint-Etienne cedex 2, France

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     author = {Eric Feulvarch and Jean-Christophe Roux and Jean-Michel Bergheau},
     title = {An enriched finite element algorithm for the implicit simulation of the {Stefan} problem},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {649--654},
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     volume = {339},
     number = {10},
     year = {2011},
     doi = {10.1016/j.crme.2011.07.001},
     language = {en},
}

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Eric Feulvarch; Jean-Christophe Roux; Jean-Michel Bergheau. An enriched finite element algorithm for the implicit simulation of the Stefan problem. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 649-654. doi : 10.1016/j.crme.2011.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.07.001/

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