An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Acta Materialia

Volumn 56, Issue 17, 2008, Pages 4559-4569

  Rosam, J ^a   Jimack, P K ^a   Mullis, A M ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Phase field models; Rapid solidification; Solidification

Indexed keywords

BINARY ALLOYS; CONVERGENCE OF NUMERICAL METHODS; CRYSTALLIZATION; FORECASTING; SOLIDIFICATION; UNDERCOOLING;

MULTI-GRID; NON-ISOTHERMAL; PHASE-FIELD MODELS; RAPID SOLIDIFICATION;

LINEAR EQUATIONS;

EID: 51449098186     PISSN: 13596454     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.actamat.2008.05.029     Document Type: Article

References (35)

1. Corrigan D.P., Koss M.B., LaCombe J.C., et al. Phys Rev E 60 (1999) 7217
2. Bisang U., and Bilgram J.H. Phys Rev E 54 (1996) 5309
3. Ivantsov G.P. Dokl Akad Nauk SSSR 58 (1947) 567
4. Mullins W.W., and Sekerka R.F. J Appl Phys 33 (1964) 444
5. Lipton J., Glicksman M.E., and Kurz W. Mater Sci Eng 65 (1984) 57
6. Lipton J., Glicksman M.E., and Kurz W. Metall Trans A 18 (1987) 341
7. Lipton J., Kurz W., and Trivedi R. Acta Metall 35 (1987) 957
8. Willnecker R., Herlach D.M., and Feuerbacher B. Phys Rev Lett 62 (1989) 2707
9. Huang S.C., and Glicksman M.E. Acta Metall 29 (1981) 701
10. Kessler D.A., Koplik J., and Levine H. Adv Phys 37 (1988) 255
11. Pomeau Y., and Ben-Amar M. Solids far from equilibrium (1992), Cambridge University Press 365
12. Mullis A.M., and Cochrane R.F. Acta Mater 49 (2001) 2205
13. Langer J.S. In: Grinstein G., and Mazenko G. (Eds). Directions in condensed matter physics (1986), World Science 164
14. Caginalp G. Phys Rev A 39 (1989) 5887
15. Penrose O., and Fife P.C. Physica D 43 (1990) 44
16. Kobayashi R. Physica D 63 (1993) 410
17. Wheeler A.A., Murray B.T., and Schaefer R.J. Physica D 66 (1993) 243
18. Loginova I., Amberg G., and Aagren J. Acta Mater 49 (2001) 573
19. Warren J.A., and Boettinger W.J. Acta Metall Mater 43 (1995) 689
20. Ramirez J.C., and Beckermann C. Acta Mater 53 (2005) 1721
21. Lan C.W., Chang Y.C., and Shih C.J. Acta Mater 51 (2003) 1857
22. Ramirez J.C., and Beckermann C. Phys Rev E 69 (2004) 051607
23. Karma A. Phys Rev Lett 87 (2001) 115701
24. Horvay G., and Cahn J.W. Acta Metall 9 (1961) 695
25. Aziz M.J. J Appl Phys 53 (1982) 1158
26. Rosam J. A fully implicit, fully adaptive multigrid method for multi-scale phase-field modelling. Ph.D. thesis, University of Leeds; 2007.
27. Trottenberg U., Oosterlee C., and Schüller A. Multigrid (2001), Academic Press
28. Karma A., and Rappel W.J. Phys Rev E 57 (1998) 4323
29. Echebarria B., Folch R., Karma A., and Plapp M. Phys Rev E 70 (2004) 061604
30. Provatas N., Goldenfeld N., and Dantzig J. J Comp Phys 148 (1999) 265
31. Hundsorfer W., and Verwer J.G. Numerical solution of time-dependant advection-diffusion-reaction equations (2003), Springer-Verlag
32. Rosam J., Jimack P.K., and Mullis A.M. J Comp Phys 225 (2007) 1271
33. Tong X., Beckermann C., Karma A., and Li Q. Phys Rev E 63 (2001) R49
34. Eckler K., and Herlach D.M. Mater Sci Eng A 128 (1994) 159
35. Dragnevski K.I., Cochrane R.F., and Mullis A.M. Metall Mater Trans A 35 (2004) 3211