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Adaptive Mesh Refinement for Thin-Film Equations  

Kim, Jun-Seok (Department of Mathematics, University of Dongguk)
Publication Information
Journal of the Korean Physical Society / v.49, no.5, 2006 , pp. 1903-1907 More about this Journal
Abstract
An adaptive finite difference method is developed for a class of fully nonlinear time-dependent thin liquid film equations. Equations of the type ht+fy(h) = −3r(M(h)rh) arise in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the fluid film height. Enhanced accuracy for the method is attained by covering the front with a sequence of nested, progressively finer, rectangular grid patches that dynamically follow the front motion. Results of numerical experiments illustrate the accuracy, the efficiency, and the robustness of the method.
Keywords
Adaptive mesh refinement; Nonlinear diffusion equations; Thin film; Nonlinear multigrid method;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
Times Cited By Web Of Science : 5  (Related Records In Web of Science)
Times Cited By SCOPUS : 6
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1 S. M. Troian, E. Herbolzheimer, S. A. Safran and J. F. Joanny, Europhys. Lett. 10, 25 (1989)   DOI
2 M. H. Jung, S. H. Park, K. H. Kim, H. S. Kim, J. H. Chang, D. C. Oh, T. Yao, J. S. Song and H. J. Ko, J. Korean Phys. Soc. 49, 890 (2006)
3 S. M. Wise, J. S. Kim and W. C. Johnson, Thin Solid Films 473, 151 (2005)   DOI   ScienceOn
4 S. M. Wise, J. S. Lowengrub, J. S. Kim, K. Thornton, P. W. Voorhees and W. C. Johnson, Appl. Phys. Lett. 87, 133102-1 (2005)   DOI   ScienceOn
5 A. L. Bertozzi, A. M¨unch, X. Fanton and A. M. Cazabat, Phys. Rev. Lett. 81, 5169 (1998)   DOI   ScienceOn
6 T. G. Myers, SIAM Rev. 40, 441 (1998)   DOI   ScienceOn
7 U. Trottenberg, C. Oosterlee and A. Schuller, MULTIGRID (Academic Press, U.S.A., 2001), p. 372
8 A. L. Bertozzi and M. P. Brenner, Phys. Fluids 9, 530 (1997)   DOI   ScienceOn
9 J. Sur, A. L. Bertozzi and R. P. Behringer, Phys. Rev. Lett. 90, 126105 (2003)   DOI   ScienceOn
10 D. E.Weidner, L.W. Schwartz and M. H. Eres, J. Colloid Interface Sci. 187, 243 (1997)   DOI   ScienceOn
11 C. H. Ho and Y. C. Tai, Annu. Rev. Fluid Mech. 30, 579 (1998)   DOI   ScienceOn
12 S. J. Park, H. T. Lee, J. H. Kim and T. Y. Seong, J. Korean Phys. Soc. 31, 537 (1997)
13 Y. M. Park, Y. J. Park, K. M. Kim, C. H. Roh, C. K. Hyon and E. K. Kim, J. Korean Phys. Soc. 37, 984 (2000)   DOI   ScienceOn
14 J. S. Kim and J. Sur, Commun. Korean Math. Soc. 20, 179 (2005)   DOI
15 A. L. Bertozzi, A. Munch and M. Shearer, Physica D 134, 431 (1999)   DOI   ScienceOn
16 A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell and M. L. Welcome, J. Comp. Phys. 142, 1 (1998)   DOI   ScienceOn
17 J. H. Seok and J. Y. Kim, J. Korean Phys. Soc. 39, S393 (2001)
18 J. S. Kim and J. S. Kim, J. Korean Phys. Soc. 49, 195 (2006)
19 S. M. Wise, J. S. Lowengrub, J. S. Kim and W. C. Johnson, Superlatt. Microstruc. 36, 293 (2004)   DOI   ScienceOn
20 M. J. Berger and I. Rigoustsos, Technical Report NYU- 501, New York University-CIMS, 1991
21 C. W. Shu and S. Osher, J. Comp. Phys. 83, 32 (1989)   DOI