Lattice Boltzmann phase-field modelling of binary-alloy solidification

Physica A: Statistical Mechanics and its Applications

Volumn 362, Issue 1, 2006, Pages 78-83

  Miller, W ^a   Rasin, I ^a   Succi, S ^b  

^a LEIBNIZ INSTITUTE FOR CRYSTAL GROWTH   (Germany)

^b CNR   (Italy)

Author keywords

Binary alloys; Cellular structure; Convection; Lattice Boltzmann equation; Phase field equation; Solidification

Indexed keywords

MATHEMATICAL MODELS; PHASE TRANSITIONS; SOLIDIFICATION; TWO PHASE FLOW;

CELLULAR STRUCTURE; CONVECTION; LATTICE BOLTZMANN EQUATION; PHASE-FIELD EQUATION;

BINARY ALLOYS;

EID: 31944431613     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2005.09.021     Document Type: Article

References (17)

1. D. Medvedev, K. Kassner, Lattice-Boltzmann scheme for dendritic growth in presence of convection, J. Crystal Growth 275 (2005) e1495-e1500.
2. O. Filippova, and D. Hänel Grid refinement for lattice-BGK models J. Comput. Phys. 147 1998 219 228
3. W. Miller, S. Succi, and D. Mansutti A lattice Boltzmann model for anisotropic liquid/solid phase transition Phys. Rev. Lett. 86 16 2001 3578 3581
4. P.C. Hohenberg, and B.I. Halperin Theory of dynamical critical phenomena Rev. Mod. Phys. 49 1977 435 480
5. W.J. Boettinger, and J.A. Warren Simulation of the cell to plane front transition during directional solidification at high velocity J. Crystal Growth 200 1999 583 591
6. C.W. Lan, and Y.C. Chang Efficient adaptive phase field simulation of directional solidification of a binary alloy J. Crystal Growth 250 1-2 2003 525 537
7. S. Succi The lattice Boltzmann equation, Numerical Mathematics and Scientific Computation 2001 Clarendon Press Oxford
8. D.A. Wolf-Gladrow Lattice-Gas Cellular Automata and Lattice Boltzmann Models Lecture Notes in Mathematics vol. 1725 2000 Springer Berlin, Heidelberg, New York
9. R. Benzi, S. Succi, and M. Vergassola The lattice Boltzmann equation: theory and applications Phys. Rep. 222 1992 145 197
10. F. Higuera, S. Succi, and R. Benzi Lattice gas dynamics with enhanced collisions Europhys. Lett. 9 1989 345 349
11. P. Lallemand, L.-S. Luo, Theory of lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E.
12. Y. Qian, D. D'Humières, and P. Lallemand Lattice BGK models for Navier-Stokes equation Europhys. Lett. 17 1992 479 484
13. J.S. Langer Instabilities and pattern formation in crystal growth Rev. Mod. Phys. 52 1 1980 1 28
14. A.A. Wheeler, W.J. Boettinger, and G.B. McFadden Phase-field model for isotherm phase transitions in binary alloys Phys. Rev. A 45 10 1992 7424 7439
15. S.G. Kim, W.T. Kim, and T. Suzuki Phase-field model for binary alloys Phys. Rev. E 60 6 1999 7186 7197
16. W. Miller, I. Rasin, and F. Pimentel Growth kinetics and melt convection J. Crystal Growth 266 1-3 2004 283 288
17. I. Rasin, W. Miller, Numerical study of the development of cellular structure during the Czochralski growth of GeSi bulk crystals, J. Crystal Growth 275 (2005) e67-e71.