On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Nacer Sadoun; El-Khider Si-Ahmed; Pierre Colinet; Jack Legrand

doi:10.1016/j.crme.2012.03.003

On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement

Nacer Sadoun ^1,² ; El-Khider Si-Ahmed ^1,³; Pierre Colinet ²; Jack Legrand ³

¹ Laboratoire de mécanique des fluides théorique et appliquée, faculté de physique, université des sciences et de la technologie Houari Boumediene (USTHB), BP 32, El-Alia, 16111 Alger, Algeria
² Service transferts, interfaces et procédés (TIPs), faculté des sciences appliquées/École polytechnique, université libre de Bruxelles (ULB), CP165/67, 50, avenue F.D. Roosevelt, B-1050 Bruxelles, Belgium
³ LUNAM université, université de Nantes, CNRS, GEPEA UMR-6144, BP 406, 37, boulevard de lʼUniversité, 44602 Saint-Nazaire cedex, France

Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 501-511.

Abstract
Résumé

Explicit numerical schemes obtained using variable space grid (VSGM) and boundary immobilization (BIM) methods are considered for the solution of the transient heat conduction problem with phase change. This article briefly reviews different approaches developed to track the phase change front with a particular interest to those tracking explicitly the moving boundary. The analysis shows that both methods lead to identical computational algorithm, then considers the modified numerical scheme developed by Kutluay et al. (J. Comput. Appl. Math. 81 (1997) 135–144) and proposes a refinement procedure for the scheme without any additional CPU time. Two Stefan-like problems, having exact solutions, are studied and numerical results are assessed with respect to their performances.

Les schémas numériques obtenus à partir des méthodes fixant la frontière mobile (BIM) ou adaptant le pas de discrétisation spatiale au mouvement de celle-ci (VSGM) sont appliqués au problème de conduction instationnaire avec changement de phase. Lʼarticle revoit brièvement les différentes approches développées pour le suivi dʼinterface avec une attention particulière pour celles la localisant explicitement. Lʼanalyse, qui montre que les deux schémas ne sont que deux expressions différentes dʼune même solution, porte également sur la modification apportée par Kutluay et al. (J. Comput. Appl. Math. 81 (1997) 135–144) et propose une procédure sure pour améliorer la précision de la solution. Lʼapplication de ces schémas numériques à deux exemples de problème de Stefan permet de comparer leurs performances.

Published online: 2012-05-15

DOI: 10.1016/j.crme.2012.03.003

Keywords: Stefan problem, Numerical solution, Finite differences, Variable space grid, Boundary immobilization, Accuracy refinement
Mots-clés : Problème de Stefan, Solution numérique, Différences finies, Maillage spatial variable, Immobilisation de frontière, Amélioration de la précision

Author's affiliations:

Nacer Sadoun ^{1, 2}; El-Khider Si-Ahmed ^{1, 3}; Pierre Colinet ²; Jack Legrand ³

¹ Laboratoire de mécanique des fluides théorique et appliquée, faculté de physique, université des sciences et de la technologie Houari Boumediene (USTHB), BP 32, El-Alia, 16111 Alger, Algeria
² Service transferts, interfaces et procédés (TIPs), faculté des sciences appliquées/École polytechnique, université libre de Bruxelles (ULB), CP165/67, 50, avenue F.D. Roosevelt, B-1050 Bruxelles, Belgium
³ LUNAM université, université de Nantes, CNRS, GEPEA UMR-6144, BP 406, 37, boulevard de lʼUniversité, 44602 Saint-Nazaire cedex, France

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Nacer Sadoun; El-Khider Si-Ahmed; Pierre Colinet; Jack Legrand. On the boundary immobilization and variable space grid methods for transient heat conduction problems with phase change: Discussion and refinement. Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 501-511. doi : 10.1016/j.crme.2012.03.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.03.003/

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