Application of composite adaptive grid generation and migration (CAGGM) scheme for phase-change materials processes

Numerical Heat Transfer; Part A: Applications

Volumn 42, Issue 7, 2002, Pages 707-732

  Sahoo, R K ^a   Prasad, V ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b FLORIDA INTERNATIONAL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; CRYSTAL GROWTH FROM MELT; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; HIGH PRESSURE EFFECTS; INTERFACES (MATERIALS); PARTIAL DIFFERENTIAL EQUATIONS; PHASE TRANSITIONS; SOLIDIFICATION;

COMPOSITE ADAPTIVE GRID GENERATION AND MIGRATION; PHASE CHANGE MATERIALS PROCESSES;

COMPUTATIONAL FLUID DYNAMICS;

EID: 0037113324     PISSN: 10407782     EISSN: None     Source Type: Journal    
DOI: 10.1080/10407780290059774     Document Type: Article

References (50)

1. O. Adetutu and V. Prasad, Melting in Rectangular and Cylindrical Cavities: Effects of Curvature, Aspect Ratio and Buoyancy Forces Local Procedures, Advanced Computations in Materials Processing, ASME, vol. HTD-241, pp. 45-56, 1992.
2. H. Akima, A Method of Univariate Interpolation that has the Accuracy of a Third Degree Polynomial, ACM Trans. on Math. Software, vol.17, no. 3, pp. 341-366, 1991.
3. H. Akima, Algorithm 760: Rectangular-Grid-Data Surface Fitting that has the Accuracy of a Bicubic Polynomial, ACM Trans. on Math. Software, vol. 22, no. 3, pp. 357-361, 1996.
4. J. Koziol, A. P. Anselmo, V. Prasad, and K. P. Gupta, Oscillatory Convection in Low Aspect Ratio Czochralski Melts, J. Crystal Growth, vol. 134, pp. 153-165, 1993.
5. W. D. Bennon and F. P. Incropera, A Continuum Method for Momentum, Heat and Species Transport in Binary Solid-Liquid Phase Change Systems-i. Model Formulation. Int. J. Heat Mass Trans., vol. 30, pp. 2161-2170, 1987.
6. R. Bonnert and P. Jamet, Numerical Computation of the Free Boundary for the Two-dimensional Stefan Problem by Space-Time Finite Elements. J. Comp. Phys., vol. 25, pp. 163-181, 1977.
7. A. Chatterjee, R. K. Sahoo, and V. Prasad, Three Dimensional Simulation of Phase Change Processes: Application to Czochralski Crystal Growth, Proc. Adv. Sc. and Tech. Computing Conf. HPC'98, pp. 75-80, 1998.
8. A. Chatterjee, Three Dimensional Adaptive Finite Volume Scheme for Transport Phenomena in Materials Processing: Application to Czochralski Crystal Growth, Ph.D. dissertation, State University of New York Stony Brook, 1998.
9. M. S. Christensen, W. D. Bennon, and F. P. Incropera, Solidification of an Aqueous Ammonium Chloride Solution in a Rectangular Cavity-ii. Comparison of Predicted and Measured Results, Int. J. Heat Mass Trans., vol. 32, pp. 69-79, 1989.
10. I. Demirdzic and M. Peric, Finite Volume Methods for Prediction of Fluid Flow in Arbitrary Shaped Domains with Moving Boundaries, Int. J. Num. Meth. Fluids, vol. 10, pp. 771-790, 1990.
11. J. M. Floryan and H. Rasmussen, Numerical Methods for Viscous Flows with Moving Boundaries, Appl. Mech. Rev., vol. 42, pp. 323-341, 1989.
12. J. N. Reddy and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC Press, Boca Raton, FL, 1994.
13. D. Givoli, J. E. Flaherty, and M. S. Shephard, Analysis of INP Melt Flows Using a Parallel Adaptive Finite Element Scheme, J. Crystal Growth, vol. 180, pp. 510-516, 1997.
14. H. Hirata and K. Hoshikawa, Three Dimensional Numerical Analysis of the Effect of a Cusp Magnetic Field on the Flows, Oxygen Transport and Heat Transfer in a Czochralski Silicon Melt, J. Crystal Growth, vol. 95, pp. 254-302, 1991.
15. J. Holuigue, O. Bertrand, and E. Arquis, Solutal Convection in Crystal Growth: Effect of Interface Curvature on Flow Structuration in a Three Dimensional Cylindrical Configuration, J. Crystal Growth, vol. 180, pp. 597-603, 1997.
16. C. F. Hsu, A Curvilinear-Coordinate Method for Momentum, Heat and Mass Transfer in Domains of Irregular Geometry, Ph.D. thesis, University of Minnesota, Twin Cities, MN, 1981.
17. C. F. Hsu, E. M. Sparrow, and S. V. Patankar, Numerical Solution of Moving Boundary Problems by Boundary Immobilization and a Control Volume Based Finite Difference Scheme, Int. J. Heat Mass Trans., vol. 24, pp. 1335-1343, 1981.
18. M. Lacroix, Computation of Heat Transfer during Melting of a Pure Substance from an Isothermal Wall, Num. Heat Trans., vol. 15, pp. 191-210, 1989.
19. M. Lacroix, Analysis of Mixed Convection Melting of a Pure Metal, Num. Heat. Trans., vol. 17, pp. 401-416, 1990.
20. M. Lacroix and V. R. Voller, Finite Difference Solutions of Solidification Phase Change Problems: Transformed Versus Fixed Grids, Num. Heat Trans., vol. 17, pp. 25-41, 1990.
21. C. R. Maliska and G. D. Raithby, A Method for Computing Three-Dimensional Flows Using Non-orthogonal Body-Fitted Coordinates, Int. J. Num. Meth. Fluids, vol. 4, pp. 518-537, 1984.
22. K. Morgan, A Numerical Analysis of Freezing and Melting with Convection, Comp. Meth. Appl. Engg., vol. 28, pp. 275-284, 1981.
23. G. Muller, Convection and Inhomogeneities in Crystal Growth from Melt, vol. 12, Handbook of Crystal Growth, Springer-Verlag, Berlin, 1988.
24. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.
25. V. Prasad, H. Zhang, and A. P. Anselmo, Transport Phenomena in Crystal Growth, Advances in Heat Transfer, 1997.
26. M. M. Rai, A Conservative Treatment of Zonal Boundaries for Euler Equation Calculations, J. Comp. Phys., vol. 62, pp. 472-503, 1996.
27. N. Ramachandran, J. P. Gupta, and Y. Jaluria, Two-Dimensional Solidification with Natural Convection in the Melt with Convection and Radiation Boundary Conditions, Num. Heat Trans., vol. 4, pp. 469-484, 1981.
28. N. Ramachandran, J. P. Gupta, and Y. Jaluria, Thermal and Fluid Flow Effects during Solidification in a Rectangular Enclosures, Int. J. Heat Mass Trans., vol. 25, pp. 187-194, 1982.
29. W. Y. Raw and S. L. Lee, Application of Weighting Function Scheme on Convection-Conduction Phase Change Problems, Int. J. Heat Mass Trans., vol. 34, pp. 1503-1513, 1991.
30. J. L. Lumley and J. R. Ristorcelli, Instabilities, Transition, and Turbulence in the Czochralski Crystal Melt, J. Crystal Growth, vol. 116, pp. 447-460, 1992.
31. W. D. Rolph and K. J. Bathe, An Efficient Algorithm for Analysis of Nonlinear Heat Transfer with Phase Change, Int. J. Num. Meth. Eng., vol. 18, pp. 119-134, 1982.
32. R. K. Sahoo, Composite Adaptive Grid Generation, Migration and Parallel Algorithms for Computational Materials Processing, Ph.D. dissertation, State University of New York, Stony Brook, 1998.
33. R. K. Sahoo and V. Prasad, A Composite Adaptive Grid Generation and Migration Technique for Materials Processing Problems, SIAM J. Scientific Computing, in press.
34. M. Salcudean and Z. Abdullah, On the Numerical Modeling of Heat Transfer during Solidification Problems, Int. J. Num. Meth. Engg, vol. 28, pp. 445-473, 1988.
35. N. Shamsunder and E. M. Sparrow, Analysis of Multidimensional Conduction Phase Change via the Enthalpy Model, J. Heat Trans., vol. 97, pp. 333-340, 1975.
36. W. Shyy, Computational Modeling for Fluid Flow and Interfacial Transport, Elsevier Science, 1994.
37. W. Shyy, H. S. Udaykumar, M. M. Rao, and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries, Taylor & Francis, Washington, DC, 1996.
38. M. Tanaka, M. Hasebe, and N. Saito, Pattern Transition of Temperature Distribution at Czochralski Silicon Melt Surface, J. Crystal Growth, vol. 180, pp. 487-496, 1997.
39. P. D. Thomas and C. K. Lombard, The Geometric Conservation Law: A Link between Finite Difference and Finite Volume Methods of Flow Computation on Moving Grids, AIAA J., vol. 17, pp. 1030-1037, 1979.
40. V. R. Voller, N. C. Markatos, and M. Cross, Techniques for Accounting for the Moving Interface in Convection/Diffusion Phase Change, Numerical Methods in Thermal Problems, vol. 4, 1985.
41. V. R. Voller, N. C. Markatos, and M. Cross, Solidification in Convection and Diffusion, Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes, 1986.
42. V. R. Voller, M. Cross, and N. C. Markatos, An Enthalpy Method for Convection/Diffusion Phase Change, Int. J. Num. Meth. Engg., vol. 24, pp. 271-284, 1987.
43. V. R. Voller, An Overview of Numerical Methods for Solving Phase Change Problems, Advances in Num. Heat Trans., vol. 1, 1996.
44. F. Wolf and R. Viskanta, Solidification of a Pure Metal at a Vertical Wall in the Presence of Liquid Superheat, Int. J. Heat Mass Trans., vol. 31, pp. 1735-1744, 1988.
45. Q. Xiao and J. J. Derby, Three Dimensional Melt Flows in Czochralski Oxide Growth: High-Resolution, Massively Parallel, Finite Element Computations, J. Crystal Growth, vol. 152, pp. 169-181, 1995.
46. H. Zhang, A Multizone Adaptive Grid Generation Technique for Simulations of Moving and Free Boundary Problems, Ph.D. dissertation, Polytechnique University, 1993.
47. H. Zhang and M K. Moallemi, A Multizone Adaptive Grid Generation Technique for Simulation of Moving and Free Boundary Problems, Num. Heat Trans., Part B, vol. 27, pp. 255-276, 1995.
48. H. Zhang and V. Prasad, A Multizone Adaptive Process Model for Czochralski Crystal Growth at Low and High Pressures, J. Crystal Growth, vol. 155, pp. 47-65, 1995.
49. H. Zhang, V. Prasad, and M. K. Moallemi, Numerical Algorithm Using Multizone Adaptive Grid Generation for Multiphase Transport Processes with Moving Boundaries, Num. Heat Trans., part B, vol. 29, pp. 399-421, 1996.
50. Y. Zhou and J. J. Derby, Three Dimensional Computations of Solution Hydrodynamics during the Growth of Potassium Dihidrogen Phosphate i. Spin Up and Steady Rotation, J. Crystal Growth, vol. 180, pp. 497-509, 1997.