相场方法已被发掘出用于直接求解含时的自由边界问题-著名的斯特藩方程.该方法作为晶体生长过程中模拟复杂图形成因的计算工具,已呈现出强有力的生命力.目前的研究在于努力发展精巧的计算技术,以便对于晶体生长和金属凝固过程进行理论模拟,而这些技术将有可能广泛地应用于工业流程.相场方法之所以具有吸引力,基于如下事实:在计算机模拟过程中,既可避免对于边界的实时追踪,又不需要反复判别是否满足显式边界条件.在过去的10年中,它已逐步被用于研究晶体生长的基础课题.诸如:热质输运、晶体生长动力学、二维和三维枝晶生长、图形选择、生长形态和显微结构等.本文对相场方法进行评述,同时给出其最新应用结果.
The phase-field method has been explored to solve directly the full timedependent free boundary problem described as well known Stefan equations and it has recently emerged as a viable computational tool for simulating formation of complex interfacial patterns in crystal growth. Recent research efforts have led to development of sophisticated computational techniques for modeling important dynamical processes in crystal growth and solidification. These techniques are applicable to the wide range of industrial processes. Its attractiveness is from the fact that explicit tracking of the interface and explicitly satisfying interfacial boundary conditions is completely avoided. In the past decade,the phasefield method has been used to study the fundamental subjects on crystal growth, such as the transport of heat and /or solute,the kinetics of crystal growth, the two and three dimensional dendritic growth,the pattern selection,the crystal morphology and microscopic structure etc.An overview of the phasefield method and somes new results for its application are given in this paper.
参考文献
| [1] | Barbieri A;Langer J S .Predictions of Dendritic Growth Rates in the Linearized Solvability Theory[J].Physical Review A,1999,39(10):5314. |
| [2] | David Kessler A;Joel Koplik;Herbert Levine .Pattern Selection in Fingered Growth Phenomena[J].Advances in Physics,1988,37(03):255-339. |
| [3] | Karma A.;Plapp M.;Lee YH. .Three-dimensional dendrite-tip morphology at low undercooling[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(4 Pt.b):3996-4006. |
| [4] | Alain Karma;Wouter-Jan Rappel .Phase-field for Efficient Modeling of Solidification with Arbitrary Interface Kinetics[J].Physical Review E,1996,53(04):R3017. |
| [5] | Halperin B I;Hohenberg P C .Renormalization-group Methods for Critical Dynamics:Recursion Relations and Effects of Energy Conservation[J].Physical Review B,1974,10(01):139. |
| [6] | Wang S L;Sekerka R F;Wheeler A A et al.Thermodynamically-consistent Phase-field Models for Solidification[J].Physica D-Nonlinear Phenomena,1993,69:189-200. |
| [7] | Alain Karma;Wouter-Jan Rappel .Quantitative Phase-flied Modeling of Dendritic Growth in Two and Three Dimensions[J].Physical Review E,1998,57(04):4323. |
| [8] | Caginalp G .Stefan Hele-Shaw Type Models as Asymptotic Limits of the Phase-field Equations[J].Physical Review A,1989,39(11):5887. |
| [9] | Caginalp P C;Xie W .Phase-field and Shapr-interface Alloy models[J].Physical Review E,1993,48(03):1897. |
| [10] | Wheeler A A;Murray B T;Schaefer R J .Computation of Dendrites using a Phase Field Model[J].Physica D-Nonlinear Phenomena,1993,66:243-262. |
| [11] | Murray BT.;Glicksman ME.;Wheeler AA. .SIMULATIONS OF EXPERIMENTALLY OBSERVED DENDRITIC GROWTH BEHAVIOR USING A PHASE-FIELD MODEL[J].Journal of Crystal Growth,1995(3/4):386-400. |
| [12] | Ryo Kobayashi .Modeling and Numerical Simulations of Dendritic Crystal Growth[J].Physica D-Nonlinear Phenomena,1993,63:410-423. |
| [13] | William;Boettinger J;James Warren A .The phase-field Method:Simulation of Dendritic Solidification during Recoalescence[J].Metallurgical and Materials Transactions A:Physical Metallurgy and Materials Science,1996,27:657. |
| [14] | BRAUN R J;Murray B T .Adaptive Phase-field Computations of Dendritic Crystal Growth[J].Journal of Crystal Growth,1997,174:41-53. |
| [15] | Beckermann C;Diepers H J;Sterinbach I et al.Modeling Melt Convection in Phase-Field Simulation of Solidification[J].Journal of Computational Physics,1999,154:468-496. |
| [16] | Popov DI.;Wilcox WR.;Regel LL. .One-dimensional phase-field model for binary alloys[J].Journal of Crystal Growth,2000(3/4):574-583. |
| [17] | Caginalp G;Jones J .A Derivation and Analysis of Phase Field Models of Thermal Alloys[J].Annals of Physics,1995,237:66-107. |
| [18] | Alain Karma;Wouter-Jan Rapplel .Phase-field Simulation of Three-dimensional Dendrites:Is Microscopic Solvability Theory Correct?[J].Journal of Crystal Growth,1997,174:54-64. |
| [19] | Alain Karma;Wouter-Jan Rappel .Numerical Simulation of Three-dimensional Dendritic Growth[J].Physical Review Letters,1996,77(19):4050. |
| [20] | Tonhardt R.;Amberg G. .Phase-field simulation of dendritic growth in a shear flow[J].Journal of Crystal Growth,1998(3/4):406-425. |
| [21] | Tong X.;Karma A.;Beckermann C. .Velocity and shape selection of dendritic crystals in a forced flow[J].Physical review.E.Statistical physics, plasmas, fluids, and related interdisciplinary topics,2000(1):R49-R52. |
| [22] | Nikolas Provatas;Nigel Goldenfeld;Jonathan Dantzig .Efficient Computation Microstructure Adaptive Mesh Refinement[J].Physical Review Letters,1998,80(15):3308. |
| [23] | Joseph Collins B .Diffuse Interface of Diffusion-limited Crystal Growth[J].Physical Review B,1985,31(09):6119. |
| [24] | McCarthy J F .One-dimensional Phase Field Models with Adaptive Grids[J].Journal of Heat Transfer,1998,120:956. |
- 下载量()
- 访问量()
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%