Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A HYBRID METHOD FOR HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS

  • KIM JUNSEOK (Department of Mathematics University of California) ;
  • SUR JEANMAN (Department of Physics Center for Nonlinear and Complex Systems Duke University)
  • Published : 2005.01.01
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Abstract

We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing up an inclined plane. Equations of the type $h_t+f_y(h) = -{\in}^3{\nabla}{\cdot}(M(h){\nabla}{\triangle}h)$ arise in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, t) is the fluid film height. A hybrid scheme is constructed for the solution of two-dimensional higher-order nonlinear diffusion equations. Problems in the fluid dynamics of thin films are solved to demonstrate the accuracy and effectiveness of the hybrid scheme.

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References

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