Computation of Solid-Liquid Phase Fronts in the Sharp Interface Limit on Fixed Grids

Journal of Computational Physics

Volumn 153, Issue 2, 1999, Pages 535-574

  Udaykumar, H S ^a   Mittel, R ^a   Shyy, Wei ^a  

^a UNIVERSITY OF FLORIDA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PHASE INTERFACES;

CARTESIAN GRID; FINITE THICKNESS; FIXED GRIDS; PHASE FRONT; SECOND ORDERS; SHARP INTERFACE; SHARP INTERFACE LIMITS; SIMPLE++; SOLID-LIQUID PHASE; SOLID/LIQUID BOUNDARY;

SOLIDIFICATION;

EID: 0347611279     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6294     Document Type: Article

References (59)

1. R. Almgren, Variational algorithms and pattern formation in dendritic solidification, J. Comput. Phys. 106, 337 (1993).
2. R. P. Beyer and R. J. LeVeque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29, No. 2, 332 (1992).
3. J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100, 335 (1992).
4. G. Caginalp, in Applications of Field Theory to Statistical Mechanics, edited by L. Garrido, Lecture Notes in Physics, No. 216 (Springer-Verlag, Berlin, 1984), p. 216.
5. H. Carslaw and J. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959).
6. S. Chen, B. Merriman, S. Osher, and P. Smereka, A simple level set method for solving Stefan problems, J. Comput. Phys. 134 (1997).
7. A. J. Chorin, Hairpin removal in vortex interactions, J. Comput. Phys. 91, 1 (1990).
8. J. Crank, Free and Moving Boundary Problems (Clarendon Press, Oxford, UK, 1984).
9. A. J. DeGregoria and L. W. Schwartz, A boundary integral method for two-phase displacement in Hele-Shaw cells, J. Fluid Mech. 164, 383 (1986).
10. M. D. Dembo, D. C. Torney, K. Saxman, and D. A. Hammer, The reaction-limited kinetics of membrane-to-surface adhesion and detachment, Proc. R. Soc. London B 234, 55 (1988).
11. C. Dong, R. Skalak, K.-L. P. Sung, G. W. Schmid-Schonbein, and S. Chien, Passive deformation analysis of human leukocytes, J. Biomech. Eng. 110, 27 (1988).
12. L. J. Fauci and C. S. Peskin, A computational model of aquatic animal locomotion, J. Comput. Phys. 77, 85 (1988).
13. J. Glimm, J. Grove, B. Lindquist, O. A. McBryan, and G. Tryggvason, The bifurcation of tracked scalar waves, SIAM J. Sci. Statist. Comput. 1, 61 (1988).
14. R. Glowinski, T.-S. Pan, and J. Periaux, A fictitious domain method for Dirichlet problem and applications, Comput. Methods Appl. Mech. Eng. 111, 283 (1994).
15. D. Goldstein, R. Handler, and L. Sirovich, Modeling a no-slip surface with an external force field, J. Comput. Phys. 105, 354 (1993).
16. D. Goldstein, R. Handler, and L. Sirovich, Direct numerical simulation of turbulent flow over a modeled riblet covered surface, J. Fluid Mech. 302, 333 (1995).
17. C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39, 201 (1981).
18. T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys. 114, 312 (1994).
19. T. Y. 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. 134, No. 2, 236 (1997).
20. V. Jayaraman, H. S. Udaykumar, and W. Shyy, Adaptive unstructured grid for three-dimensional interface representation, Numer. Heat Transfer Part B 32, 247 (1997).
21. R. A. Johnson and D. M. Belk, Multigrid approach to overset grid comunication, AIAA J. 33, 2305 (1995).
22. D. A. Jones, C. W. Smith, and L. V. McIntire, Effects of fluid shear stress on leukocyte adhesion to endothelial cells, in Physiology and Pathophysiology of Leukocyte Adhesion, Vol. 148 (Oxford Univ. Press, New York, 1995).
23. D. Juric and G. Tryggvason, A front tracking method for dendritic solidification, J. Comput. Phys. 123, 127 (1996).
24. H.-C. Kan, H. S. Udaykumar, W. Shyy, and R. Tran-Son-Tay, Hydrodynamics of a compound drop with application to leukocyte modeling, Phys. Fluids 10, No. 4, 760 (1998).
25. A. Karma and W.-J. Rappel, Numerical simulation of three-dimensional dendrite growth, Phys. Rev. Lett. 77, No. 19, 4050 (1996).
26. D. A. Kessler, J. Koplik, and H. Levine, Pattern selection in fingered growth phenomena, Adv. Phys. 37, 255 (1988).
27. R. Kobayashi, Modeling and numerical simulation of dendritic crystal growth, Physica D 63, 410 (1993).
28. D. B. Kothe and R. C. Mjolsness, Ripple: A new model for incompressible flows with free surfaces, AIAA J. 30, 2694 (1992).
29. J. S. Langer, Instabilities and pattern formation in crystal growth, Rev. Mod. Phys. 52, No. 1, 1 (1980).
30. J. S. Langer, in Directions in Condensed Matter Physics, edited by G. Grinstein and G. Mazenko (World Scientific, Philadelphia, 1986), p. 164.
31. R. J. LeVeque and Z. Li, The immersed boundary method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31, No. 4, 1019 (1994).
32. J. E. Melton, F. Y. Enomoto, and M. J. Berger, 3D automatic grid generation for Euler flows, AIAA Paper 93-3386-CP (1993).
33. S. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based in Hamilton-Jacobi formulations, J. Comput. Phys. 79, 12 (1988).
34. P. Pelce, Dynamics of Curved Fronts (Academic Press, New York, 1988).
35. R. B. Pember, J. B. Bell, and P. Colella, An adaptive Cartesian grid method for unsteady compressible flow in irregular regions, J. Comput. Phys. 120, 278 (1995).
36. C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25, 220 (1977).
37. J. J. Quirk, An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies, ICASE Report No. 92-7 (NASA Langley Research Center, Hampton, VA, 1992).
38. Y. Saito, G. Goldbeck-Wood, and H. Muller-Krumbhaar, Numerical simulation of dendrite growth, Phys. Rev. A 38, No. 4, 2148 (1988).
39. R. Scardovelli and S. Zaleski, Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech. 31, 567-584 (1999).
40. A. Schmidt, Computation of three dimensional dendrites with finite elements, J. Comput. Phys. 125, 293 (1996).
41. J. A. Sethian, Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science (Cambridge Univ. Press, Cambridge, UK, 1996).
42. J. A. Sethian and J. Strain, Crystal growth and dendritic solidification, J. Comput. Phys. 98, 231 (1992).
43. W. Shyy, Computational Modelling for Fluid Flow and Interfacial Transport (Elsevier, Amsterdam, The Netherlands, 1994).
44. W. Shyy, H. S. Udaykumar, M. M. Rao, and R. W. Smith, Computational Fluid Dynamics with Moving Boundaries (Hemisphere, Washington, DC, 1996).
45. R. W. Smith and W. Shyy, Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: A comparison with classical theory, Phys. Fluids 8, 3346 (1996).
46. J. Snyder and A. R. Woodbury, Interval methods for multi-point collisions between time-dependent curved surfaces, in Comput. Graphics Proceedings, Annual Conference Series, SIGGRAPH 93 (1993), p. 321.
47. J. L. Steger, Thoughts on the Chimera grid method of simulation of three-dimensional viscous flow, in Proceedings, Computational Fluid Dynamics Symposium on Aeropropulsion, NASA CP-3078 (Natl. Aeronautics & Space Admin., Washington, DC, 1991), p. 1.
48. C. Tu and C. S. Peskin, Stability and instability in the computation of flows with moving immersed boundaries: A comparison of three methods, SIAM J. Sci. Statist. Comput. 13, 1361 (1992).
49. H. S. Udaykumar and W. Shyy, A grid-supported marker particle scheme for interface tracking, Numer. Heat Transfer B 27, 127 (1995a).
50. H. S. Udaykumar and W. Shyy, Simulation of morphological instabilities during solidification; Part I: Conduction and capillarity effects, Int. J. Heat Mass Transfer 38, 2057 (1995b).
51. H. S. Udaykumar, W. Shyy, and M. M. Rao, ELAFINT - A mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries, Int. J. Numer. Methods Fluids 22, 691 (1996).
52. H. S. Udaykumar, H.-C. Kan, W. Shyy, and R. Tran-Son-Tay, Multiphase dynamics in arbitrary geometries on fixed Cartesian grids, J. Comput. Phys. 137, 366 (1997).
53. S. O. Unverdi and G. Tryggvason, A front tracking method for viscous, incompressible, multifluid flows, J. Comput. Phys. 100, 25 (1992).
54. V. Venkatakrishnan, Perspectives on unstructured grid flow solvers, AIAA J. 34, 533 (1996).
55. V. R. Voller and C. Prakash, A fixed grid numerical modeling methodology for convection-diffusion mushy region phase-change problems, Int. J. Heat Mass Transfer 30, 1709 (1987).
56. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phase field model for isothermal phase transitions in binary alloys, Phys. Rev. A 45, 7424 (1992).
57. D. P. Young, R. G. Melvin, M. B. Bieterman, F. T. Johnson, S. S. Samant, and J. E. Bussoletti, A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics, J. Comput. Phys. 92, 1 (1992).
58. W. J. Goirier and K. G. Powell, "Solution-adaptive Cartesian cell approach for viscous and inviscid flows," AIAA J. 34, 938-945 (1996).
59. H. Zhang, L. L. Zheng, V. Prasad, and T. Y. Hou, A curvilinear level set formulation for highly deformable free surface problems with application to solidification, Numer. Heat Transfer Part B 34, 1 (1998).