Adaptive phase-field computations of dendritic crystal growth

Journal of Crystal Growth

Volumn 174, Issue 1-4, 1997, Pages 41-53

  Braun, R J ^a   Murray, B T ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ANISOTROPY; COMPUTATIONAL METHODS; FINITE DIFFERENCE METHOD; INTERFACIAL ENERGY; MATHEMATICAL MODELS; MORPHOLOGY; PHASE TRANSITIONS; THERMODYNAMICS;

DENDRITIC CRYSTAL GROWTH; PHASE FIELD COMPUTATIONS;

CRYSTAL GROWTH;

EID: 0031547275     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0248(96)01059-7     Document Type: Article

References (33)

1. G.J. Fix, in: Free Boundary Problems: Theory and Applications, Eds. A. Fasano and M. Primicerio (Pitman, Boston, 1983) p. 580.
2. G. Caginalp, in: Applications of Field Theory to Statistical Mechanics, Ed. L. Garrido, Lecture Notes in Physics No. 216 (Springer, Berlin, 1985) p. 216.
3. J.B. Collins and H. Levine, Phys Rev. B 31 (1985) 6119.
4. G. Caginalp, Arch. Rat. Mech. Anal. 92 (1986) 205.
5. J.S. Langer, in: Directions in Condensed Matter Physics, Eds. G. Grinstein and G. Mazenko (World Scientific, Philadelphia, 1986) p. 165.
6. P.R. Harrowell and D.W. Oxtoby, J. Chem. Phys. 86 (1987) 2932.
7. J.W. Cahn and J.E. Hilliard, J. Chem. Phys. 28 (1958) 258.
8. B.I. Halperin, P.C. Hohenburg and S.-K. Ma, Phys. Rev. B 10 (1974) 139.
9. G. Caginalp and J.-T. Lin, IMA J. Appl. Math. 39 (1987) 51.
10. R. Kobayashi, Physica D 63 (1993) 410.
11. R. Kobayashi, Exp. Math. 3 (1994) 59.
12. R.J. Braun, G.B. McFadden and S.R. Coriell, Phys. Rev. E 49 (1994) 4336.
13. A.A. Wheeler, B.T. Murray and R.J. Schaefer, Physica D 66 (1993) 243.
14. B.T. Murray, W.J. Boettinger, G.B. McFadden and A.A. Wheeler, in: Heat Transfer in Melting, Solidification, and Crystal Growth, Eds. I.S. Habib and S. Thynell (ASME HTD-234, New York, 1993) p. 67.
15. A. Karma and W.-J. Rappel, Phys. Rev. E 53 (1996) 3017.
16. A.A. Wheeler, W.J. Boettinger and G.B. McFadden, Phys. Rev. A 45 (1992) 7424.
17. G. Caginalp and W. Xie, Phys. Rev. E 48 (1993) 1897.
18. J.A. Warren and W.J. Boettinger, Acta Met. Mater. 43 (1995) 689.
19. W.J. Boettinger and J.A. Warren, Met. Trans. A27 (1996) 657.
20. A. Schmidt, J. Comp. Phys. 125 (1996) 293.
21. S.-L. Wang and R.F. Sekerka, Phys. Rev. E 53 (1996) 3760.
22. S.-L. Wang and R.F. Sekerka, J. Comp. Phys. 127 (1996) 110.
23. R. Almgren and A. Almgren, in: Mathematics of Microstructure Evolution, Ed. L.-Q. Chen et al. (SIAM, Philadelphia, 1996) p. 205.
24. S.-L. Wang, R.F. Sekerka, A.A. Wheeler, B.T. Murray, S.R. Coriell, R.J. Braun and G.B. McFadden, Physica D 69 (1993) 189.
25. G.B. McFadden, A.A. Wheeler, R.J. Braun, S.R. Coriell and R.F. Sekerka, Phys. Rev. E 48 (1993) 2016.
26. G. Caginalp, Phys. Rev. A 39 (1989) 5887.
27. J.G. Blom, R.A. Trompert and J.G. Verwer, ACM TOMS 22 (1996) 302.
28. K.E. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1989) p. 410.
29. E. de Sturler and D.R. Fokkema, Preprint NR. 796, Department of Mathematics, University of Utrecht, The Netherlands, 1993; See also: R. Barrett et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994) p. 35.
30. E. de Sturler and D.R. Fokkema, Preprint NR. 796, Department of Mathematics, University of Utrecht, The Netherlands, 1993; See also: R. Barrett et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994) p. 35.
31. M.E. Glicksman and S.P. Marsh, in: Handbook of Crystal Growth, Vol. 1b, Ed. D.T.J. Hurle (North-Holland, Amsterdam, 1993) p. 1075.
32. G. Caginalp and E.A. Socolovsky, Appl. Math. Lett. 2 (1989) 117.
33. B.T. Murray, A.A. Wheeler and M.E. Glicksman, J. Crystal Growth 154 (1995) 386.