Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification

Journal of Computational Physics

Volumn 165, Issue 2, 2000, Pages 592-619

  Plapp, Mathis ^a   Karma, Alain ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Adaptive meshing; Dendritic growth; Monte Carlo method; Moving boundary problem; Multiscale algorithm; Phase transformations; Solidification; Stefan problem

Indexed keywords

DIFFUSION; PHASE INTERFACES; RANDOM PROCESSES; UNDERCOOLING;

ADAPTIVE MESHING; DENDRITIC GROWTH; DENDRITIC SOLIDIFICATION; DIFFUSION FIELDS; MONTECARLO METHODS; MOVING BOUNDARY PROBLEMS; MULTISCALE ALGORITHMS; PHASES TRANSFORMATION; STEFAN PROBLEM; UNDERCOOLINGS;

MONTE CARLO METHODS;

EID: 0001073230     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6634     Document Type: Article

References (36)

1. Kurz W., Fisher D. J. Fundamentals of solidification. 1992.
2. Matsushita M., Sano M., Hayakawa Y., Honjo H., Sawada Y. Fractal structures of zinc metal leaves grown by electrodeposition. Phys. Rev. Lett. 53:1984;286.
3. Ben-Jacob E., Shmueli H., Shochet O., Tenenbaum A. Adaptive self-organization during growth of bacterial colonies. Physica A. 187:1992;378.
4. Braun R. J., Murray M. T. Adaptive phase-field computations of dendritic crystal growth. J. Cryst. Growth. 174:1997;41.
5. Schmidt A. Computations of three-dimensional dendrites with finite elements. J. Comput. Phys. 125:1996;293.
6. Provatas N., Goldenfeld N., Dantzig J. Efficient computation of dendritic microstructures using adaptive mesh refinement. Phys. Rev. Lett. 80:1998;3308.
7. Provatas N., Goldenfeld N., Dantzig J. Adaptive mesh refinement computation of solidification microstructures using dynamic data structures. J. Comput. Phys. 148:1999;265.
8. Koonin S. E., Meredith D. C. Computational Physics. 1992.
9. Kadanoff L. P. Simulating hydrodynamics: A pedestrian model. J. Stat. Phys. 39:1985;267.
10. Liang S. Random-walk simulations of flow in Hele Shaw cells. Phys. Rev. A. 33:1986;2663.
11. Vicsek T. Pattern formation in diffusion-limited aggregation. Phys. Rev. Lett. 53:1984;2281.
12. Nittmann J., Stanley H. E. Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy. Nature. 321:1986;663.
13. Karma A. Beyond steady-state lamellar eutectic growth. Phys. Rev. Lett. 59:1987;71.
14. Saito Y., Ueta T. Monte Carlo studies of equilibrium and growth shapes of a crystal. Phys. Rev. A. 40:1989;3408.
15. Meakin P. Diffusion-controlled cluster formation in 2-6-dimensional space. Phys. Rev. A. 27:1983;1495.
16. Brener E., Müller-Krumbhaar H., Temkin D. Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth. Phys. Rev. E. 54:1996;2714.
17. Langer J. S. Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise. Phys. Rev. A. 36:1987;3350.
18. Plapp M., Karma A. Multiscale random-walk algorithm for simulating interfacial pattern formation. Phys. Rev. Lett. 84:2000;1740.
19. Karma A., Lee Y., Plapp M. Three-dimensional dendrite tip morphology at low undercooling. Phys. Rev. E. 61:2000;3996.
20. Langer J. S. Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52:1980;1.
21. Kessler D. A., Koplik J., Levine H. Pattern selection in fingered growth phenomena. Adv. Phys. 37:1988;255.
22. Brener E. A., Mel'nikov V. I. Pattern selection in two-dimensional dendritic growth. Adv. Phys. 40:1991;53.
23. Huang S.-C., Glicksman M. E. Fundamentals of dendritic solidification I. Steady-state tip growth. Acta Metall. 29:1981;701.
24. Rubinstein E. R., Glicksman M. E. Dendritic growth kinetics and structure I. Pivalic acid. J. Cryst. Growth. 112:1991;84.
25. Muschol M., Liu D., Cummins H. Z. Surface-tension-anisotropy measurements of succinonitrile and pivalic acid: Comparison with microscopic solvability theory. Phys. Rev. A. 46:1992;1038.
26. Glicksman M. E., Koss M. B., Winsa E. A. Dendritic growth velocities in microgravity. Phys. Rev. Lett. 73:1994;573.
27. Bisang U., Bilgram J. Shape of the tip and the formation of sidebranches of xenon dendrites. Phys. Rev. E. 54:1996;5309.
28. Sethian J. A., Strain J. Crystal growth and dendritic solidification. J. Comput. Phys. 98:1992;231.
29. Ihle T., Müller-Krumbhaar H. Fractal and compact growth morphologies in phase transitions with diffusion transport. Phys. Rev. E. 49:1994;2972.
30. Karma A., Rappel W.-J. Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E. 57:1998;4323.
31. Karma A., Rappel W.-J. Phase-field model of dendritic sidebranching with thermal noise. Phys. Rev. E. 60:1999;3614.
32. Barbieri A., Langer J. S. Prediction of dendritic growth rates in the linearized solvability theory. Phys. Rev. A. 39:1989;5314.
33. Brener E., Temkin D. Noise-induced sidebranching in the three-dimensional nonaxisymmetric dendritic growth. Phys. Rev. E. 51:1995;351.
34. Dougherty A., Kaplan P. D., Gollub J. P. Development of side branching in dendrite crystal growth. Phys. Rev. Lett. 58:1987;1652.
35. Li Q., Beckermann C. Scaling behavior of three-dimensional dendrites. Phys. Rev. E. 57:1998;3176.
36. Beckermann C., Diepers H.-J., Steinbach I., Karma A., Tong X. Modeling melt convection in phase-field simulations of solidification. J. Comput. Phys. 154:1999;468.