3D simulation of the matter transport by surface diffusion within a level-set context

Authors

  • Julien Bruchon LTDS UMR CNRS 5513
  • Daniel Pino Muñoz LTDS UMR CNRS 5513 Ecole Nationale Supérieure des Mines de Saint-Etienne Centre Sciences des Matériaux et des Structures 158 cours Fauriel F-42023 Saint-Etienne cedex 2
  • François Valdivieso PECM UMR CNRS 5146 Ecole Nationale Supérieure des Mines de Saint-Etienne Centre Sciences des Matériaux et des Structures 158 cours Fauriel F-42023 Saint-Etienne cedex 2
  • Sylvain Drapier LTDS UMR CNRS 5513 Ecole Nationale Supérieure des Mines de Saint-Etienne Centre Sciences des Matériaux et des Structures 158 cours Fauriel F-42023 Saint-Etienne cedex 2
  • Guillaume Pacquaut LTDS UMR CNRS 5513 Ecole Nationale Supérieure des Mines de Saint-Etienne Centre Sciences des Matériaux et des Structures 158 cours Fauriel F-42023 Saint-Etienne cedex 2

DOI:

https://doi.org/10.13052/EJCM.19.281-292

Keywords:

surface diffusion, level-set method, curvature, Laplace-Beltrami operator, sintering process

Abstract

Within the framework of the sintering process simulation, this paper proposes a numerical strategy for the direct simulation of the matter transport by surface diffusion. A level-set method is used to describe the topological changes which arise at the free boundary of the sintering particles. The surface velocity is found to be proportional to the surface Laplacian of the curvature, that is, proportional to the fourth-order derivative of the level-set function. Consequently, both curvature and velocity must be computed carefully and with accuracy. Finally, three-dimensional simulations are shown and investigated.

Downloads

Download data is not yet available.

References

Ashby M., “ A first report on sintering diagrams”, Acta Metall. Mater., vol. 22, n° 3, p. 275-289,

Bänsch E., Morin P., Nochetto R. H., “ A finite element method for surface diffusion: the

parametric case”, J. Comput. Phys., vol. 203, n° 1, p. 321-343, February, 2005.

Bernacki M., Chastel Y., Coupez T., Logé R., “ Level set framework for the numerical modelling

of primary recrystallization in polycrystalline materials”, Scripta Mater., vol. 58, n° 12,

p. 1129-1132, 2008.

Bouvard D., McMeeking R., “ Deformation of interparticle necks by Diffusion-Controlled

Creep”, J. Am. Ceram. Soc., vol. 79, n° 3, p. 265-672, 1996.

Bruchon J., Digonnet H., Coupez T., “ Using a signed distance function for the simulation of

metal forming processes: Formulation of the contact condition and mesh adaptation. From

a Lagrangian approach to an Eulerian approach”, Int. J. Numer. Meth. Eng., vol. 78, n° 8,

p. 980-1008, 2009a.

Bruchon J., Pacquaut G., Drapier S., Valdivieso F., “ Modélisation et simulation du transport

de matière par diffusion surfacique à l’aide d’une approche Level-Set”, Actes du 9ième

Colloque National en Calcul des Structures, Giens (Var, France), p. 517-522, May 25-29,

b.

Burger M., Hausser F., Stocker C., Voigt A., “ A level-set approach to anisotropic flows with

curvature regularization”, J. Comput. Phys., vol. 225, n° 1, p. 183-205, 2007.

Coupez T., “ Réinitialisation convective et locale des fonctions Level Set pour le mouvement de

surfaces et d’interfaces.”, Actes des Journées Activités Universitaires de Mécanique, ISBN

-9526-8123-8, La Rochelle, p. 33-41, August 31st - September 1st, 2006.

Digonnet H., Coupez T., “ Object-oriented programming for fast-and-easy development of parallel

applications in forming processes simulation”, Proceedings of the Second MIT Conference

on Computational Fluid and Solid Mechanics, 2003.

Osher S., Fedkiw F., “ Level Set Methods: An Overview and Some Recent Results”, J. Comput.

Phys., vol. 169, n° 2, p. 463-502, 2001.

Rahaman M. N., Ceramic processing and sintering, CRC Press, 2003.

Sethian J., Level Sets Methods and Fast Marching Methods, 3 edn, Cambridge Monograph on

Applied and Computational Mathematics, 1999.

Downloads

Published

2010-08-06

How to Cite

Bruchon, J. ., Muñoz, D. P. ., Valdivieso, F. ., Drapier, S. ., & Pacquaut, G. . (2010). 3D simulation of the matter transport by surface diffusion within a level-set context. European Journal of Computational Mechanics, 19(1-3), 281–292. https://doi.org/10.13052/EJCM.19.281-292

Issue

Section

Original Article