A front-tracking method for dendritic solidification

Journal of Computational Physics

Volumn 123, Issue 1, 1996, Pages 127-148

  Juric, Damir ^a   Tryggvason, GRÉTAR ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PHASE INTERFACES; SOLIDIFICATION; SPECIFIC HEAT;

DENDRITIC SOLIDIFICATION; FINITE DIFFERENCE APPROXIMATIONS; FRONT TRACKING METHOD; HEAT EQUATION; LIQUID/SOLID INTERFACE; PURE SUBSTANCES; SOLID PHASIS; SOLID-PHASE; TIME DEPENDENT; TWO-DIMENSIONAL;

FINITE DIFFERENCE METHOD;

EID: 0029684784     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0011     Document Type: Article

References (86)

1. 1. H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959), p. 294.
2. 2. H. G. Landau, Q. Appl. Math. 8, 81 (1950).
3. 3. M. E. Rose, Math. Comput. 14, 249 (1960).
4. 4. V. R. Voller, M. Cross, and P. Walton, in Numerical Methods in Thermal Problems, edited by R. W. Lewis and K. Morgan (Pineridge Press, Swansea, 1979), p. 172.
5. 5. V. R. Voller and M. Cross, Int. J. Heat Mass Transfer 24, 545 (1981).
6. 6. C. R. Swaminathan and V. R. Voller, Int. J. Numer. Methods. Heat Fluid Flow 3, 233 (1993).
7. 7. G. Comini, C. Nonino, and O. Saro, in Advanced Computational Methods in Heat Transfer. Vol. 3. Phase Change and Combustion Simulation, edited by L. C. Wrobel, C. A. Brebbia, and A. J. Nowak (Springer-Verlag, Berlin, 1990), p. 3.
8. 8. V. R. Voller and C. R. Swaminathan, Int. J. Numer. Methods. Eng. 30, 875 (1990).
9. 9. V. R. Voller and C. R. Swaminathan, Numer. Heat Transfer, Part B 19, 175 (1991).
10. 10. J. Crank and R.D. Phahle, Bull. J. Inst. Math. Appl. 9, 12 (1973).
11. 11. A. N. Alexandrou, Int. J. Numer. Methods. Eng. 28, 2383 (1989).
12. 12. K. O'Neill and D. R. Lynch, Numerical Methods in Heat Transfer, edited by R. W. Lewis, K. Morgan, and O. C. Zinkiewicz (Wiley, New York, 1981), Chap. 11.
13. 13. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 35, 444 (1964).
14. 14. V. V. Voronkov, Sov. Phys. Solid State 6, 2378 (1965).
15. 15. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 34, 323 (1963).
16. 16. J. W. Cahn, in Crystal Growth, edited by H. S. Peiser (Pergamon, Oxford, 1967), p. 681.
17. 17. S. R. Coriell and R. L. Parker, in Crystal Growth, edited by H. S. Peiser (Pergamon, Oxford, 1967), p. 703.
18. 18. G. P. Ivantsov, Dokl. Akad. Nauk. SSSR 58, 567 (1947).
19. 19. D. E. Temkin, Dokl. Akad. Nauk. SSSR 132, 1307 (1960).
20. 20. G. F. Bolling and W. A. Tiller, J. Appl. Phys. 32, 2587 (1961).
21. 21. R. Trivedi, Acta Metall. 18, 287 (1970).
22. 22. M. E. Glicksman and R. J. Schaefer, J. Crystal Growth 1, 297 (1967).
23. 23. M. E. Glicksman and R. J. Schaefer, J. Crystal Growth 2, 239 (1968).
24. 24. M. E. Glicksman and S. P. Marsh, in Handbook of Crystal Growth, Vol. 1B, edited by D. T. J. Hurle (North-Holland, Amsterdam, 1993), p. 1075.
25. 25. G. E. Nash and M. E. Glicksman, Acta Metall. 22, 1283 (1974).
26. 26. G. E. Nash and M. E. Glicksman, Acta Metall. 22, 1291 (1974).
27. 27. J. S. Langer and H. Müller-Krumbhaar, J. Crystal Growth 42, 11 (1977).
28. 28. J. S. Langer and H. Müller-Krumbhaar, Acta Metall. 26, 1681 (1978).
29. 29. J. S. Langer and H. Müller-Krumbhaar, Acta Metall. 26, 1689 (1978).
30. 30. J. S. Langer and H. Müller-Krumbhaar, Acta Metall. 26, 1697 (1978).
31. 31. M. E. Glicksman, M. B. Koss, and E. A. Winsa, Phys. Rev. Lett. 73, 573 (1994).
32. 32. M. E. Glicksman, M. B. Koss, L. T. Bushnell, J. C. LaCombe, R. N. Smith, and E. A. Winsa, in Heat Transfer in Microgravity Systems, HTD, Vol. 290, edited by S. S. Sadhal and A. Gopinath (ASME, New York, 1994), p. 1.
33. 33. D. Kessler, J. Koplik, and H. Levine, Phys. Rev. A 34, 4980 (1986).
34. 34. D. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37(3), 255 (1988).
35. 35. J.S. Langer, in Chance and Matter, edited by J. Souletie, J. Vannimenus, and R. Stora (North-Holland, Amsterdam, 1987), p. 629.
36. 36. J. S. Langer, Science 243, 1150 (1989).
37. 37. P. Pelcé, Dynamics of Curved Fronts (Academic Press, New York, 1988).
38. 38. J. P. Gollub, in Nonlinear Phenomena Related to Growth and Form, edited by M. Ben Amar, P. Pelcé, and P. Tabeling (Plenum, New York, 1991).
39. 39. W. Kurz and R. Trivedi, Acta Metall. Mater. 38, 1 (1990).
40. 40. Y. Miyata, M. E. Glicksman, and S. H. Tirmizi, J. Crystal Growth 110, 683 (1991).
41. 41. E. R. Rubinstein and M. E. Glicksman, J. Crystal Growth 112, 84 (1991).
42. 42. E. R. Rubinstein and M. E. Glicksman, J. Crystal Growth 112, 97 (1991).
43. 43. J. M. Sullivan Jr., D. R. Lynch, and K. O'Neill, J. Comput. Phys. 69, 81 (1987).
44. 44. J. M. Sullivan Jr. and D. R. Lynch, Int. J. Numer. Methods Eng. 25, 415 (1988).
45. 45. J. M. Sullivan Jr. and H. Hao, in Heat Transfer in Melting, Solidification and Crystal Growth, HTD, Vol. 234, edited by I. S. Habib and S. Thynell (ASME, New York, 1993), p. 14.
46. 46. K. H. Tacke, in Free Boundary Problems: Theory and Applications, Vol. II, edited by K. H. Hoffmann and J. Sprekels (Longman Sci. Tech., Essex, UK, 1990), p. 636.
47. 47. J. A. Sethian and J. Strain, J. Comput. Phys. 98(2), 231 (1992).
48. 48. R. Almgren, J. Comput. Phys. 106, 337 (1993).
49. 49. A. R. Roosen and J. E. Taylor, J. Comput. Phys. 114, 113 (1994).
50. 50. W. Shyy, H. S. Udaykumar, and S.-J. Liang, Int. J. Heat Mass Transfer 36(7), 1833 (1993).
51. 51. K. Brattkus and D. I. Meiron, SIAM J. Appl. Math. 52(5), 1303 (1992).
52. 52. J. S. Langer, in Directions in Condensed Matter Physics, edited by G. Grinstein and G. Mazenko (World Scientific, Singapore, 1986), p. 164.
53. 53. G. Fix, in Free Boundary Problems, edited by A. Fasano and M. Primocerio (Pitman, London, 1983), p. 580.
54. 54. G. Caginalp, Arch. Rat. Mech. Anal. 92, 205 (1986).
55. 55. G. Caginalp, Phys. Rev. A 39, 5887 (1989).
56. 56. G. Caginalp, in Free Boundary Problems Involving Solids, edited by J. M. Chadam and H. Rasmussen (Longman Sci. Tech., Essex, UK, 1993), p. 92.
57. 57. G. Caginalp and P. Fife, SIAM J. Appl. Math. 48, 506 (1988).
58. 58. J. B. Collins and H. Levine, Phys. Rev. B 31, 6119 (1985).
59. 59. G. Caginalp and E. A. Socolovsky, J. Comp. Phys. 95, 85 (1991).
60. 60. G. Caginalp and E. A. Socolovsky, in Free Boundary Problems Involving Solids, edited by J. M. Chadam and H. Rasmussen (Longman Sci. Tech., Essex, UK, 1993), p. 100.
61. 61. R. Kobyashi, J. Jpn. Assoc. Cryst. Growth 18(2), 209 (1991). [Japanese]
62. 62. R. Kobyashi, in Pattern Formation in Complex Dissipative Systems, edited by S. Kai (World Scientific, Singapore, 1992), p. 121.
63. 63. R. Kobyashi, Physica D 63, 410 (1993).
64. 64. A. A. Wheeler, in Handbook of Crystal Growth, Vol. 1B, edited by D. T. J. Hurle (North-Holland, Amsterdam, 1993), p. 683.
65. 65. O. Penrose and P. Fife, Physica D 43, 44 (1990).
66. 66. 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, 189 (1993).
67. 67. A. A. Wheeler, B. T. Murray, and R. J. Schaefer, Physica D 66, 243 (1993).
68. 68. B. T. Murray, W. J. Boettinger, G. B. McFadden, and A. A. Wheeler, in Heat Transfer in Melting, Solidification and Crystal Growth, HTD, Vol. 234, edited by I. S. Habib and S. Thynell (ASME, New York, 1993), p. 67.
69. 69. R. J. Braun, G. B. McFadden, and S. R. Coriell, Phys. Rev. E 49(5), 4336 (1994).
70. 70. N. M. H. Lightfoot, Proc. London Math. Soc. 31, 97 (1929).
71. 71. V. Alexiades and A. D. Solomon, Mathematical Modeling of Melting and Freezing Processes (Hemisphere, Washington, DC, 1993, p. 92.
72. 72. V. Alexiades, A. D. Solomon, and D.G. Wilson, J. Non-Equilib. Thermodyn. 13, 281 (1988).
73. 73. D. Turnbull, J. Appl. Phys. 21, 1022 (1950).
74. 74. S. O. Unverdi, Ph.D. thesis, The University of Michigan, 1990.
75. 75. S. O. Unverdi and G. Tryggvason, Physica D 60, 70 (1992).
76. 76. S. O. Unverdi and G. Tryggvason, J. Comput. Phys. 100(1), 25 (1992).
77. 77. Y.-J. Jan and G. Tryggvason, Phys. Fluids, submitted.
78. 78. M. R. Nobari, Y.-J. Jan, and G. Tryggvason, Phys. Fluids A, submitted.
79. 79. S. Nas and G. Tryggvason, in AMD 174/FED 175 Fluid Mechanics Phenomena in Microgravity, 1993 ASME Winter Annual Meeting, edited by D. A. Siginer, R. L. Thompson, and L. M. Trefethen, p. 71.
80. 80. C. S. Peskin, J. Comput. Phys. 25, 220 (1977).
81. 81. C. S. Peskin, personal communication, 1993.
82. 82. R. J. LeVeque and Z. Li, SIAM J. Numer. Anal. 31(4), 1019 (1994).
83. 83. E. A. Brandes and G.B. Brook (Eds.), Smithells Metals Reference Book (Butterworth, Heinemann, Oxford, UK, 1992), p. 14-1.
84. 84. M. E. Glicksman, R. J. Schaefer, and J. D. Ayers, Metall. Trans. A 7A, 1747 (1976).
85. 85. M. E. Glicksman and N. B. Singh, in Rapidly Solidified Powder Aluminum Alloys, edited by M. E. Fine and E. A. Starke Jr. (ASTM, Philadelphia, PA, 1986), p. 44.
86. 86. M. Muschol, D. Liu, and H. Z. Cummins, Phys. Rev. A 46, 1038 (1992).