W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Phase-Field Simulation of Solidification, Annual Review of Materials Research, vol.32, issue.1, pp.163-194, 2002.
DOI : 10.1146/annurev.matsci.32.101901.155803

I. Steinbach, Why Solidification? Why Phase-Field?, JOM, vol.57, issue.9, pp.1096-1102, 2013.
DOI : 10.1080/14786435.2012.717726

A. Choudhury, K. Reuther, E. Wesner, A. August, B. Nestler et al., Comparison of phase-field and cellular automaton models for dendritic solidification in Al???Cu alloy, Computational Materials Science, vol.55, pp.263-268, 2012.
DOI : 10.1016/j.commatsci.2011.12.019

T. Takaki, T. Shimokawabe, M. Ohno, A. Yamanaka, and T. Aoki, Unexpected selection of growing dendrites by very-large-scale phase-field simulation, Journal of Crystal Growth, vol.382, pp.21-25, 2013.
DOI : 10.1016/j.jcrysgro.2013.07.028

C. Gandin, T. Carozzani, H. Digonnet, S. Chen, and G. Guillemot, Direct Modeling of Structures and Segregations Up to Industrial Casting Scales, JOM, vol.50, issue.9, pp.1122-1130, 2013.
DOI : 10.1016/S1359-6454(01)00376-7

URL : https://hal.archives-ouvertes.fr/hal-00850850

J. Ni and C. Beckermann, A volume-averaged two-phase model for transport phenomena during solidification, Metallurgical Transactions B, vol.21, issue.3, pp.349-361, 1991.
DOI : 10.1007/BF02671947

C. Y. Wang and C. Beckermann, Equiaxed dendritic solidification with convection: Part I. Multiscale/multiphase modeling, Metallurgical and Materials Transactions A, vol.173, issue.9, pp.2754-2764, 1996.
DOI : 10.1016/0921-5093(93)90195-K

M. Wu, A. Fjeld, and A. Ludwig, Modelling mixed columnar-equiaxed solidification with melt convection and grain sedimentation ??? Part I: Model description, Computational Materials Science, vol.50, issue.1, pp.32-42, 2010.
DOI : 10.1016/j.commatsci.2010.07.005

I. Steinbach, C. Beckermann, B. Kauerauf, Q. Li, and J. Guo, Three-dimensional modeling of equiaxed dendritic growth on a mesoscopic scale, Acta Materialia, vol.47, issue.3, pp.971-982, 1999.
DOI : 10.1016/S1359-6454(98)00380-2

I. Steinbach, H. Diepers, and C. Beckermann, Transient growth and interaction of equiaxed dendrites, Journal of Crystal Growth, vol.275, issue.3-4, pp.624-638, 2005.
DOI : 10.1016/j.jcrysgro.2004.12.041

P. Delaleau, C. Beckermann, R. H. Mathiesen, and L. Arnberg, Mesoscopic Simulation of Dendritic Growth Observed in X-ray Video Microscopy During Directional Solidification of Al???Cu Alloys, ISIJ International, vol.50, issue.12, pp.1886-1894, 2010.
DOI : 10.2355/isijinternational.50.1886

A. J. Melendez and C. Beckermann, Measurements of dendrite tip growth and sidebranching in succinonitrile???acetone alloys, Journal of Crystal Growth, vol.340, issue.1, pp.175-189, 2012.
DOI : 10.1016/j.jcrysgro.2011.12.010

Q. Li and C. Beckermann, Scaling behavior of three-dimensional dendrites, Physical Review E, vol.24, issue.3, pp.3176-3188, 1998.
DOI : 10.1007/BF02659502

M. E. Glicksman, E. Winsa, R. C. Hahn, T. A. Lograsso, S. H. Tirmizi et al., Isothermal dendritic growth??? a proposed microgravity experiment, Metallurgical Transactions A, vol.36, issue.no. 8, pp.1945-1953, 1988.
DOI : 10.1007/BF02644687

J. C. Lacombe, M. B. Koss, V. E. Fradkov, and M. E. Glicksman, Three-dimensional dendrite-tip morphology, Physical Review E, vol.3, issue.3, pp.2778-2786, 1995.
DOI : 10.1080/10586458.1994.10504577

R. H. Mathiesen and L. Arnberg, X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al???30wt%Cu alloy, Acta Materialia, vol.53, issue.4, pp.947-956, 2005.
DOI : 10.1016/j.actamat.2004.10.050

R. H. Mathiesen, L. Arnberg, P. Bleuet, and A. Somogyi, Crystal fragmentation and columnar-to-equiaxed transitions in Al-Cu studied by synchrotron X-ray video microscopy, Metallurgical and Materials Transactions A, vol.27, issue.306, pp.2515-2524, 2006.
DOI : 10.1016/S0921-5093(00)01553-7

J. Lipton, M. E. Glicksman, and W. Kurz, Equiaxed dendrite growth in alloys at small supercooling, Metallurgical Transactions A, vol.29, issue.2, pp.341-345, 1987.
DOI : 10.1016/0001-6160(81)90082-1

B. Cantor and A. Vogel, Dendritic solidification and fluid flow, Journal of Crystal Growth, vol.41, issue.1, pp.109-123, 1977.
DOI : 10.1016/0022-0248(77)90104-X

Y. Sun and C. Beckermann, Sharp interface tracking using the phase-field equation, Journal of Computational Physics, vol.220, issue.2, pp.626-653, 2007.
DOI : 10.1016/j.jcp.2006.05.025

C. Beckermann and R. Viskanta, Mathematical Modeling of Transport Phenomena During Alloy Solidification, Applied Mechanics Reviews, vol.46, issue.1, pp.1-27, 1993.
DOI : 10.1115/1.3120318

M. Zalo?nik and H. Combeau, An operator splitting scheme for coupling macroscopic transport and grain growth in a two-phase multiscale solidification model: Part I ??? Model and solution scheme, Computational Materials Science, vol.48, issue.1, pp.1-10, 2010.
DOI : 10.1016/j.commatsci.2009.04.036

G. M. Treece, R. W. Prager, and A. H. Gee, Regularised marching tetrahedra: improved iso-surface extraction, Computers & Graphics, vol.23, issue.4, pp.583-598, 1998.
DOI : 10.1016/S0097-8493(99)00076-X

P. J. Roache, QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS, Annual Review of Fluid Mechanics, vol.29, issue.1, pp.123-160, 1997.
DOI : 10.1146/annurev.fluid.29.1.123

M. B. Koss, J. C. Lacombe, L. A. Tennenhouse, M. E. Glicksman, and E. A. Winsa, Dendritic Growth tip velocities and radii of curvature in microgravity, Metallurgical and Materials Transactions A, vol.194, issue.1, pp.3177-3190, 1999.
DOI : 10.2355/isijinternational.35.604

Q. Li and C. Beckermann, Modeling of free dendritic growth of succinonitrile???acetone alloys with thermosolutal melt convection, Journal of Crystal Growth, vol.236, issue.1-3, pp.482-498, 2002.
DOI : 10.1016/S0022-0248(01)02390-9

C. Y. Wang and C. Beckermann, A unified solute diffusion model for columnar and equiaxed dendritic alloy solidification, Materials Science and Engineering: A, vol.171, issue.1-2, pp.199-211, 1993.
DOI : 10.1016/0921-5093(93)90407-6

B. Appolaire, H. Combeau, and G. Lesoult, Modeling of equiaxed growth in multicomponent alloys accounting for convection and for the globular/dendritic morphological transition, Materials Science and Engineering: A, vol.487, issue.1-2, pp.33-45, 2008.
DOI : 10.1016/j.msea.2007.11.030

H. Combeau, M. Zalo?nik, S. Hans, and P. Richy, Prediction of Macrosegregation in Steel Ingots: Influence of the Motion and the Morphology of Equiaxed Grains, Metallurgical and Materials Transactions B, vol.47, issue.4, pp.289-304, 2009.
DOI : 10.1007/s11663-008-9178-y