Removing the stiffness from interfacial flows with surface tension

Journal of Computational Physics

Volumn 114, Issue 2, 1994, Pages 312-338

  Hou, Thomas Y ^a   Lowengrub, John S ^b   Shelley, Michael J ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008283862     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1006/jcph.1994.1170     Document Type: Article

References (53)

1. R. Almgren, W.-S. Dai, and V. Hakim, Phys. Rev. Lett. 71, 3461 (1993).
2. W. F. Ames, Numerical Methods for Partial Differential Equations (Academic press, New York, 1977).
3. C. Anderson, J. Comput. Phys. 62, 111 (1986).
4. G. Baker, “Generalized Vortex Methods for Free-Surface Flows, ” in Waves on Fluid Interfaces, edited by R. E. Meyer (Academic Press, New York/London, 1983).
5. G. Baker, R. Caflisch, and M. Siegel, J. Fluid Mech. 252, 51 (1993).
6. G. Baker, D. Meiron, and S. Orszag, J. Fluid Mech. 123, 477 (1982)
7. G. Baker and A. Nachbin, preprint.
8. G. R. Baker and M. J. Shelley, J. Comput. Phys. 64, 112 (1986).
9. G. R. Baker and M. J. Shelley, J. Fluid Mech. 215, 161 (1990).
10. J. T. Beale, T. Y. Hou, and J. S. Lowengrub, “On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension, ” in Singularities in Fluids, Plasmas and Optics, edited by R. C. Caflisch and G. C. Papanicolaou (Kluwer Academic, London, 1993).
11. J. T. Beale, T. Y. Hou, and J. S. Lowengrub, Commun. Pure Appl. Math., to appear.
12. J. T. Beale, T. Y. Hou, and J. S. Lowengrub, in preparation.
13. G. Birkhoff, Proc. Symp. Appl. Math. 13, 55 (1962).
14. G. Carrier, M. Krook, and C. Pearson, Functions of a Complex Variable (McGraw-Hill, New York, 1966).
15. W. Dai, L. Kadanoff, and S. Zhou, Phys. Rev. A 43, 6672 (1991).
16. W.-S. Dai and M. J. Shelley, Phys. Fluids A 5, 2131 (1993).
17. A. J. DeGregoria and L. W. Schwartz, J. Fluid Mech. 164, 383 (1986).
18. R. Goldstein, A. Pesci, and M. Shelley, Phys. Rev. Lett. 70, 3043 (1993).
19. R. Goldstein, A. Pesci, and M. Shelley, in preparation.
20. R. Goldstein and D. M. Petrich, Phys. Rev. Lett. 67, 3203 (1991).
21. J. Goodman, T. Y. Hou, and E. Tadmor, Numer. Math., to appear.
22. A. Greenbaum, L. Greengard, and G. B. McFadden, J. Comput. Phys. 105, 267 (1993).
23. L. Greengard and V. Rokhlin, J. Comput. Phys. 73, 325 (1987).
24. M. Gurtin, Thermomechanics of Evolving Phase Boundaries in the Plane (Clarendon Press, Oxford, 1993).
25. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Aplications, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 26 (SIAM, Philadelphia, 1977).
26. T. Halsey and M. Leibig, Phys. Rev. A 46, 7793 (1992).
27. E. Meiburg and G. Homsy, Phys. Fluids 31, 429 (1988).
28. T. Hou, J. Lowengrub, and M. Shelley, in preparation.
29. J. M. Hyman and M. J. Naughton, in Proc. SIAM-AMS Conf. on Large Computation in Fluid Mechanics (SIAM, Philadelphia, 1984).
30. D. Kellogg, Foundations of Potential Theory (Dover, New York, 1929).
31. R. Krasny, J. Fluid Mech. 167, 65 (1986).
32. H.-O. Kreiss and J. Oliger, SIAM J. Numer. Anal. 16, 421 (1979).
33. D. Moore, Proc. R. Soc. London A 365, 105 (1979).
34. W. Mullins, J. Appl. Phys. 27, 900 (1956).
35. W. Mullins and R. Sekerka, J. Appl. Phys. 34, 323 (1963)
36. A. Prosperetti, L. A. Crum, and H. C. Pumphrey, J. Geophys. Res. 94, 3255 (1989).
37. D. A. Pugh, Ph.D. thesis, Imperial College, London, 1989.
38. D. I. Pullin, J. Fluid Mech. 119, 507 (1982).
39. R. Rangel and W. Sirignano, Phys. Fluids 31, 1845 (1988).
40. D. Reinelt, J. Fluid Mech. 183, 219 (1987).
41. R. Rogallo, NASA TM-73203 (unpublished).
42. Y. Saad and M. Schultz, SIAM J. Sci. Stat. Comput. 7, 856 (1986).
43. P. G. SafTman and G. R. Baker, Annu. Rev. Fluid Mech. 11, 95 (1979).
44. M. Shelley, J. Fluid Mech. 244, 493 (1992).
45. M. J. Shelley and M. Vinson, Nonlinearity 5, 323 (1992).
46. A. Sidi and M. Israeli, J. Sci. Comput. 3, 201 (1988).
47. H. E. Stanley and N. Ostrowsky (Eds), Random Fluctuations and Pattern Growth: Experiments and Models (Kluwer Academic, London, 1988).
48. J. Strain, J. Comput. Phys. 85, 342 (1989).
49. E. Tadmor, SIAM Rev. 29, 525 (1987).
50. S. Thorpe, J. Fluid Mech. 39, 25 (1969).
51. G. Tryggvason and H. Aref, J. Fluid Mech. 136, 1 (1983).
52. P. W. Voorhees, G. B. McFadden, R. F. Boisvert, and D. I. Meiron, Acta Metall. 36, 207 (1988).
53. T. A. Witten and L. M. Sander, Phys. Rev. B 27, 5686 (1983).