REFERENCES
- M. Asta , C. Beckermann , A. Karman , W. Kurz , R. Napolitano , M. Plapp , G. Purdy , M. Rappaz , and R. Trivedi , Solidification Microstructures, and Solid-State Parallels: Recent Development, Future Directions , Acta Mater. , vol. 57 , pp. 941 – 971 , 2009 .
- J. S. Langer , Models of Pattern Formation in First-Order Phase Transitions , in G. Grinstein and G. Mazenko (eds.), Directions in Condensed Matter Physics , p. 165 , World Scientific , New York , 1986 .
- W. Wheeler , G. McFadden , and W. Boettinger , Phase-Field Model for Solidification of a Eutectic Alloy , Proc. Roy. Soc. Lond., Ser. A , vol. 452 , pp. 495 – 525 , 1996 .
- D. U. Furrer , Application of Phase-Field Modeling to Industrial Materials and Manufacturing Processes , Curr. Opin. Solid State Mater. Sci. , vol. 15 , pp. 134 – 140 , 2011 .
- W. J. Boettinger , J. A. Warren , C. Beckermann , and A. Karma , Phase-Field Simulation of Solidification , Annu. Rev. Mater. Res. , vol. 32 , pp. 163 – 194 , 2002 .
- A. Karma and W.-J. Rappel , Phase-Field Method for Computationally Efficient Modeling of Solidification with Arbitrary Interface Kinetics, Phys. Rev. E , vol. 53, pp. R3017–R3020, 1996.
- A. Karma and W.-J. Rappel , Quantitative Phase-Field Modeling of Dendritic Growth in Two and Three Dimensions , Phys. Rev. E , vol. 57 , pp. 4323 – 4349 , 1998 .
- N. Provatas , N. Goldenfeld , and J. Dantzig , Efficient Computation of Dendritic Microstructures Using Adaptive Mesh Refinement , Phys. Rev. Lett. , vol. 80 , pp. 3308 – 3311 , 1998 .
- C. W. Lan , C. C. Liu , and C. M. Hsu , An Adaptive Finite Volume Method for Incompressible Heat Flow Problems in Solidification , J. Comput. Phys. , vol. 178 , pp. 464 – 497 , 2002 .
- A. Karma , Phase-Field Formulation for Quantitative Modeling of Alloy Solidification , Phys. Rev. Lett. , vol. 87 , pp. 115701 – 1–4 , 2001 .
- B. Echebarria , R. Folch , A. Karma , and M. Plapp , Quantitative Phase-Field Model of Alloy Solidification , Phys. Rev. E , vol. 70 , pp. 061604 – 1–22 , 2004 .
- Y. L. Tsai , C. C. Chen , and C. W. Lan , Three-Dimensional Adaptive Phase Field Modeling of Directional Solidification of a Binary Alloy: 2D-3D Transition , Int. J. Heat Mass Transfer , vol. 53 , pp. 2272 – 2283 , 2010 .
- G. J. Fix , Phase Field Methods for Free Boundary Problems , in A. Fasano and M. Primicerio (eds.), Free Boundary Problems: Theory and Applications , pp. 580 – 589 , Pitman Advanced Publishing Program , Boston , 1983 .
- C. Beckermann , H.-J. Diepers , I. Steinbach , A. Karma , and X. Tong , Modeling Melt Convection in Phase-Field Simulations of Solidification , J. Comput. Phys. , vol. 154 , pp. 468 – 496 , 1999 .
- R. Tonhardt and G. Amberg , Phase-Field Simulation of Dendritic Growth in a Shear Flow , J. Crystal Growth , vol. 194 , pp. 406 – 425 , 1998 .
- R. Tonhardt and G. Amberg , Dendritic Growth of Randomly Oriented Nuclei in a Shear Flow , J. Crystal Growth , vol. 213 , pp. 161 – 187 , 2000 .
- R. Tonhardt and G. Amberg , Simulation of Natural Convection Effects on Succinonitrile Crystals , Phys. Rev. E , vol. 62 , pp. 828 – 836 , 2000 .
- Y. Lu , C. Beckermann , and J. C. Ramirez , Three-Dimensional Phase-Field Simulation of the Effect of Convection on Free Dendritic Growth , J. Crystal Growth , vol. 280 , pp. 320 – 334 , 2005 .
- X. Tong , C. Beckermann , and A. Karma , Velocity, and Shape Selection of Dendritic Crystals in a Forced Flow , Phys. Rev. E , vol. 61 , pp. R49 – R52 , 2000 .
- X. Tong , C. Beckermann , A. Karma , and Q. Li , Phase-Field Simulations of Dendritic Crystal Growth in a Forced Flow , Phys. Rev. E , vol. 63 , pp. 061601 – 1–15 , 2001 .
- J.-H. Jeong , N. Goldenfeld , and J. A. Dantzig , Phase Field Model for Three-Dimensional Dendritic Growth with Fluid Flow , Phys. Rev. E , vol. 64 , pp. 041602 – 1–14 , 2001 .
- C. C. Chen , Y. L. Tsai , and C. W. Lan , Adaptive Phase Field Simulation of Dendritic Crystal Growth in Forced Flow: 2D vs 3D Morphologies , Int. J. Heat Mass Transfer , vol. 52 , pp. 1158 – 1166 , 2009 .
- P. Zhao , J. C. Heinrich , and D. R. Poirier , Dendritic Solidification Binary Alloys with Free and Forced Convection , Int. J. Numer. Meth. Fluids , vol. 49 , pp. 233 – 266 , 2005 .
- D. M. Anderson , G. B. McFadden , and A. A. Wheeler , A Phase-Field Model of Solidification with Convection , Physica D , vol. 135 , pp. 175 – 194 , 2000 .
- H. S. Udaykumar and W. Shyy , Development of a Grid-Supported Marked Particle Scheme for Interface Tracking, AIAA-93–3384, 11th AIAA Computational Fluid Dynamics Conference, Orlando, FL, 1993.
- D. Juric and G. Tryggvason , A Front-Tracking Method for Dendritic Solidification , J. Comput. Phys. , vol. 123 , pp. 127 – 148 , 1996 .
- J.-H. Jeong , J. A. Dantzig , and N. Goldenfeld , Dendritic Growth with Fluid Flow in Pure Materials , Metall. Mater. Trans. A , vol. 34A , pp. 459 – 466 , 2003 .
- V. E. Badalassi , H. D. Ceniceros , and S. Banerjee , Computation of Multiphase System with Phase Field Models, J. Comput. Phys. , vol. 190, pp. 371–397, 2003.
- R. Kobayashi , Modeling and Numerical Simulations of Dendritic Crystal Growth , Physica D , vol. 63 , pp. 410 – 423 , 1993 .
- B. P. Leonard , A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 .
- S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , Washington , DC , 1980 .
- C. M. Rhie and W. L. Chow , Numerical Study of the Turbulent Flow past an Airfoil with Trailing Edge Separation , AIAA J. , vol. 21 , pp. 1525 – 1532 , 1983 .
- T. W. H. Sheu , H. F. Ting , and R. K. Lin , An Immersed Boundary Method for the Incompressible Navier-Stokes Equations in Complex Geometry , Int. J. Numer. Meth. Fluids , vol. 56 , pp. 877 – 898 , 2008 .
- C. C. Chen and C. W. Lan , Efficient Adaptive Three-Dimensional Phase-Field Simulation of Dendritic Crystal Growth from Various Supercoolings Using Rescaling , J. Crystal Growth , vol. 311 , pp. 702 – 706 , 2009 .
- R. Mittal and G. Iaccarino , Immersed Boundary Methods , Annu. Rev. Fluid Mech. , vol. 37 , pp. 239 – 261 , 2005 .
- Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/unhb.