Phase-field model for the isothermal solidification process of a binary alloy

Computer Assisted Mechanics and Engineering Sciences

Volumn 7, Issue 3, 2000, Pages 279-288

  Kessler, Daniel ^a   Krüger, Olivier ^a   Rappaz, Jacques ^a   Scheid, Jean François ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BINARY ALLOYS; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; FREE ENERGY; INTEGRAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SOLIDIFICATION; THEOREM PROVING;

LIPSCHITZ CONDITIONS; PHASE FIELD MODEL;

COMPUTER SIMULATION;

EID: 0342409419     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

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2. G. Caginalp. An analysis of a phase-field model for free boundary, Arch. Rational Mech. Anal., 92: 205-245, 1986.
3. J.W. Cahn, J.E. Hilliard. Free energy of a uniform system. I. Interfacial free energy, J. Chem. Phys., 28(2): 258-267, 1958.
4. D. Kessler. Sharp-interface limits of a thermodynamically consistent solutal phase-field model, in preparation.
5. D. Kessler, O. Krüger, J.F. Scheid. Construction d'un modèle de champ-de-phase à température homogène pour la solidification d'un alliage binaire. Internal report DMA-EPFL, 1998.
6. D. Kessler, J.F. Scheid. An error estimate of a finite element method for a isothermal phase-field model for solidification of binary alloy, in preparation.
7. O. Krüger. Modélisation et analyse numérique de problěmes de réaction-diffusion provenant de la solidification d'alliages binaires, PhD Thesis. EPFL 1999.
8. O. Penrose, P.C. Fife. Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D, 43: 44-62, 1990.
9. J. Rappaz, J.F. Scheid. Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy, to appear in Math. Methods Appl. Sci.
10. A. Visintin. Models of phase transitions, PNLDE 28, Birkhaüser, 1996.
11. J.A. Warren, W.J. Boettinger. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field model, Acta metall. mater., 43(2): 689-703 (1995).
12. A.A. Wheeler, W.J. Boettinger, G.B. McFadden. Phase-field model for isothermal phase transitions in binary alloys, Phys. Rev. A, 45(10): 7424-7439 (1992).