Comptes Rendus
An enriched finite element algorithm for the implicit simulation of the Stefan problem
Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 649-654.

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:
Accepted:
Published online:
DOI: 10.1016/j.crme.2011.07.001
Keywords: Computational solid mechanics, Enriched finite element, Implicit time integration, Stefan problem, Isothermal phase changes
Mot clés : Mécanique des solides numérique, Éléments finis enrichis, Intégration temporelle implicite, Problème de Stefan, Changements de phase isothermes

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
@article{CRMECA_2011__339_10_649_0,
     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},
     publisher = {Elsevier},
     volume = {339},
     number = {10},
     year = {2011},
     doi = {10.1016/j.crme.2011.07.001},
     language = {en},
}
TY  - JOUR
AU  - Eric Feulvarch
AU  - Jean-Christophe Roux
AU  - Jean-Michel Bergheau
TI  - An enriched finite element algorithm for the implicit simulation of the Stefan problem
JO  - Comptes Rendus. Mécanique
PY  - 2011
SP  - 649
EP  - 654
VL  - 339
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2011.07.001
LA  - en
ID  - CRMECA_2011__339_10_649_0
ER  - 
%0 Journal Article
%A Eric Feulvarch
%A Jean-Christophe Roux
%A Jean-Michel Bergheau
%T An enriched finite element algorithm for the implicit simulation of the Stefan problem
%J Comptes Rendus. Mécanique
%D 2011
%P 649-654
%V 339
%N 10
%I Elsevier
%R 10.1016/j.crme.2011.07.001
%G en
%F CRMECA_2011__339_10_649_0
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/

[1] V.R. Voller An overview of numerical methods for phase change problems, Advances in Numerical Heat Transfer, Volume 1 (1996), pp. 341-375

[2] E. Feulvarch; J.M. Bergheau; J.B. Leblond An implicit finite element algorithm for the simulation of diffusion with phase changes in solids, International Journal for Numerical Methods in Engineering, Volume 78 (2009), pp. 1492-1512

[3] G. Comini; S. Del Guidice; R.W. Lewis; O.C. Zienkiewicz Finite element solution of nonlinear heat conduction problems with special reference to phase change, International Journal for Numerical Methods in Engineering, Volume 8 (1974), pp. 613-624

[4] K. Morgan; R.W. Lewis; O.C. Zienkiewicz An improved algorithm for heat conduction problems with phase change, International Journal for Numerical Methods in Engineering, Volume 12 (1978), pp. 1191-1195

[5] R. Lewis; P. Roberts Finite element simulation of solidification problems, Applied Scientific Research, Volume 44 (1987), pp. 61-92

[6] E. Feulvarch; J.M. Bergheau An implicit fixed-grid method for the finite-element analysis of heat transfer involving phase changes, Numerical Heat Transfer, Part B: Fundamentals, Volume 51 (2007), pp. 585-610

[7] J. Chessa; P. Smolinski; T. Belytschko The extended finite element method for solidification problems, International Journal for Numerical Methods in Engineering, Volume 53 (2002), pp. 1959-1977

[8] R. Merle; J. Dolbow Solving thermal and phase change problems with the extended finite element method, Computational Mechanics, Volume 28 (2002), pp. 339-350

[9] H. Ji; D. Chopp; J.E. Dolbow A hybrid extended finite element/level set method for modeling phase transformations, International Journal for Numerical Methods in Engineering, Volume 54 (2002), pp. 1209-1233

[10] H. Carslaw; J. Jaeger Conduction of Heat in Solids, Clarendon Press, Oxford, UK, 1959

Cited by Sources:

Comments - Policy