Comptes Rendus
Finite element solution for diffusion–convection problems with isothermal phase changes
Comptes Rendus. Mécanique, Volume 340 (2012) no. 7, pp. 512-517.

A finite element algorithm is proposed to simulate steady-state diffusion–convection problems with isothermal phase changes. This technique is based on an enthalpic approach discretized by means of a finite element approximation of the enthalpy including the latent heat of transformation. The interface of phase changes is implicitly described without coupling with an interface-capturing technique. An example clearly shows the efficiency of the method developed.

Un algorithme éléments finis est proposé pour simuler les problèmes de diffusion–convection avec des changements de phase isothermes. Cette technique repose sur une approche en enthalpie, discrétisée au moyen dʼune approximation éléments finis de lʼenthalpie intégrant la chaleur latente de transformation. Lʼinterface est décrite de manière implicite sans couplage avec une technique spécifique de capture dʼinterface. Un exemple met clairement en évidence lʼefficacité de la méthode développée.

Published online:
DOI: 10.1016/j.crme.2012.03.009
Keywords: Convection, Enriched finite element, Stefan problem, Isothermal phase changes
Mot clés : Convection, Éléments finis enrichis, 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
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Eric Feulvarch; Jean-Christophe Roux; Jean-Michel Bergheau. Finite element solution for diffusion–convection problems with isothermal phase changes. Comptes Rendus. Mécanique, Volume 340 (2012) no. 7, pp. 512-517. doi : 10.1016/j.crme.2012.03.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.03.009/

[1] J.-M. Bergheau, G. Mangialenti, F. Boitout, Contribution of numerical simulation to the analysis of heat treatment and surface hardening processes, in: Proc. of Heat Treatʼ98, 18th ASM Heat Treating Society Conference and Exposition, Rosemont, Illinois, USA, 12–15 October 1998.

[2] M. El Ganaoui; P. Bontoux; D. Morvan Localisation dʼun front de solidification en interaction avec un bain fondu instationnaire, C. R. Acad. Sci. Paris, Sér. IIb, Volume 327 (1999), pp. 41-48

[3] M. El Ganaoui; A. Lamazouade; P. Bontoux; D. Morvan Computational solution for fluid flow under solid/liquid phase change conditions, Int. J. Comput. Fluids, Volume 31 (2002) no. 4–7, pp. 539-556

[4] Y. Ruan; B.Q. Li; J.C. Liu A finite element method for steady-state conduction–advection phase change problems, Finite Elem. Anal. Des., Volume 19 (1995), pp. 153-168

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

[6] E. Feulvarch; J.M. Bergheau; J.B. Leblond An implicit finite element algorithm for the simulation of diffusion with phase changes in solids, Int. J. Numer. Meth. Eng., Volume 78 (2009), pp. 1492-1512

[7] 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, Int. J. Numer. Meth. Eng., Volume 8 (1974), pp. 613-624

[8] K. Morgan; R.W. Lewis; O.C. Zienkiewicz An improved algorithm for heat conduction problems with phase change, Int. J. Numer. Meth. Eng., Volume 12 (1978), pp. 1191-1195

[9] R. Lewis; P. Roberts Finite element simulation of solidification problems, Appl. Sci. Res., Volume 44 (1987), pp. 61-92

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

[11] E. Feulvarch; J.C. Roux; J.M. Bergheau An enriched finite element algorithm for the implicit simulation of the Stefan problem, C. R. Mecanique, Volume 339 (2011), pp. 649-654

[12] J.M. Bergheau; R. Fortunier Finite Element Simulation of Heat Transfer, ISTE–Wiley, 2008 (ISBN: 978-1-84821-053-0)

[13] F. Brezzi; P. Houston; D. Marini; E. Suli Modeling subgrid viscosity for advection–diffusion problems, Comput. Meth. Appl. Mech. Eng., Volume 190 (2000), pp. 1601-1610

[14] J.-L. Guermond Subgrid stabilization of Galerkin approximations of linear monotone operators, IMA J. Numer. Anal., Volume 21 (2001), pp. 165-197

[15] F. Brezzi; L.D. Marini; A. Russo On the choice of a stabilizing subgrid for convection–diffusion problems, Comput. Meth. Appl. Mech. Eng., Volume 197 (2005), pp. 127-148

[16] A.N. Brooks; T.J.R. Hughes Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations, Comput. Meth. Appl. Mech. Eng., Volume 32 (1982), pp. 199-259

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