Fast and accurate numerical approaches for stefan problems and crystal growth

Numerical Heat Transfer, Part B: Fundamentals

Volumn 35, Issue 4, 1999, Pages 461-484

  Li, Zhilin ^a   Soni, Bharat ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CRYSTAL GROWTH; FLUIDS; MATHEMATICAL MODELS; SOLIDIFICATION; TEMPERATURE;

ACCURACY; ALTERNATING DIRECTIONAL IMPLICIT METHOD; CRANK-NICHOLSON METHOD; LEVEL SET METHOD; SPEED UP; STEFAN PROBLEMS;

NUMERICAL METHODS;

EID: 0032635767     PISSN: 10407790     EISSN: 15210626     Source Type: Journal    
DOI: 10.1080/104077999275848     Document Type: Article

References (27)

1. J. S. Langer, Instabilities and Pattern Formation in Crystal Growth, Rev. Mod. Phys., vol. 52, pp. 1-28, 1980.
2. R. Kobayashi, Modeling and Numerical Simulations of Dendritic Crystal-Growth, Phys-icaD, vol. 63, pp. 410-423, 1993.
3. R. J. Braun, Adaptive Phase-field Computation of Dendritic Crystal Growth, J. Crystal Growth, vol. 174, pp. 41-43, 1997.
4. J. Crank, Free and Moving Boundary Problems, Oxford University Press, Oxford, 1984.
5. J. M. Sullivan, D. R. Lynch, and K. Oneil, Finite-Element Simulation of Planar Instabilities during Solidification of an Undercooled Melt, J Comput. Phys., vol. 69, pp. 81-111, 1987.
6. P. Sackinger, P. Schunk, and R. Rao, A Newton-Raphson Pseudo-solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation, J Comput. Phys., vol. 125, pp. 83-103, 1996.
7. A. Schmidt, Computation of Three Dimensional Dendrites with Finite Elements, J Comput. Phys., vol. 125, pp. 293-312, 1996.
8. K. H. Tacke, in K. H. Hoffmann and J. Parckcle (eds.), Free Boundary Problems: Theory and Applications, vol. 2, p. 636, Longman, UK, 1990.
9. R. Almgren, Variational Algorithms and Pattern Formulation in Dendritic Solidification, J Comput. Phys., vol. 106, pp. 337-354, 1993.
10. K. Brattkus and D. Meiron, Numerical Simulations of Unsteady Crystal Growth, SIAMJ Appl. Math., vol. 528, pp. 1303-1320, 1992.
11. A. R. Roosen and J. E. Taylor, Modeling Crystal-Growth in a Diffusion Field Using Fully Faceted Interfaces, J Comput. Phys., vol. 114, pp. 113-128, 1994.
12. D. Juric and G. Tryggvason, A Front-Tracking Method for Dentritic Solidification, J Comput. Phys., vol. 123, pp. 127-1487, 1996.
13. J. Sethian, Crystal Growth and Dendritic Solidification, J. Comput. Phys., vol. 98, pp. 231-2539, 1992.
14. S. Chen, B. Merriman, P. Smereka, and S. Osher, A Fast Level Set Based Algorithm for Stefan Problems, J. Comput. Phys., vol. 135, pp. 8-29, 1997.
15. S. Osher and J. A. Sethian, Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, J Comput. Phys., vol. 79, pp. 12-49, 1988.
16. Z. Li and A. Mayo, ADI Methods for Heat Equations with Discontinuities along an Arbitrary Interface, in W. Gautschi (ed.), Proc. Symp. Appl. Math., vol. 48, pp. 311-315, 1993.
17. R. J. LeVeque and Z. Li, The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources, SIAM J. Numer. Anal., vol. 31, pp. 1019-1044, 1994.
18. Z. Li, A Note on Immersed Interface Methods for Three Dimensional Elliptic Equations, Computers Math. Appl., vol. 31, pp. 9-17, 1996.
19. T. Hou, Z. Li, S. Osher, and H. Zhao, A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow, J Comput. Phys., vol. 134, pp. 236-252, 1997
20. R. J. LeVeque and Z. Li, Simulation of Bubbles in Creeping Flow Using the Immersed Interface Method, in Proc. Sixth Int. Symp. on Computational Fluid Dynamics, pp. 688-693, Lake Tahoe, Nevada, 1995.
21. Z. Li, A Fast Iterative Algorithm for Elliptic Interface Problems, SIAM J. Numer. Anal., vol. 35, pp. 230-254, 1998.
22. Z. Li, The Immersed Interface Method-A Numerical Approach for Partial Differential Equations with Interfaces, Ph.D. thesis, University of Washington, Seattle, 1994.
23. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, 1989.
24. R. P. Beyer and R. J. LeVeque, Analysis of a One-Dimensional Model for the Immersed Boundary Method, SIAM J. Numer. Anal., vol. 29, pp. 332-364, 1992.
25. Z. Li, Immersed Interface Method for Moving Interface Problems, Numer. Algorithms, vol. 14, pp. 269-293, 1997.
26. K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1995.
27. J. C. Strikwerda, Finite Difference Scheme and Partial Differential Equations, Wadsworth & Brooks, Chapman & Hall, New York, 1989.