Adaptive mesh refinement for thin-film equations

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11 Citations (Scopus)


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) = -ε3∇·(M(h) ∇Δh) 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.

Original languageEnglish
Pages (from-to)1903-1907
Number of pages5
JournalJournal of the Korean Physical Society
Issue number5
Publication statusPublished - 2006 Nov
Externally publishedYes


  • Adaptive mesh refinement
  • Nonlinear diffusion equations
  • Nonlinear multigrid method
  • Thin film

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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