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A hybrid method for higher-order nonlinear diffusion equations

김준석|Jeanman Sur
대한수학회 (The Korean Mathematical Society)|2005.01|대한수학회논문집 (Communications of the KMS)|제20권 제1호|pp. 179-193

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주제분류수학

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Abstract

We present results of fully nonlinear time-dependent simulations of a thin liquid ¯lm °owing up an inclined plane. Equa-tions of the type ht+fy(h) = ¡²3r¢(M(h)r¢h) arise in the context of thin liquid ¯lms driven by a thermal gradient with a counteract-ing gravitational force, where h = h(x; t) is the °uid ¯lm height. A hybrid scheme is constructed for the solution of two-dimensional higher-order nonlinear di??usion equations. Problems in the °uid dynamics of thin ¯lms are solved to demonstrate the accuracy ande??ectiveness of the hybrid scheme.

참고문헌 (8)

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  3. "Undercompressive shocks in thin¯", 134, pp.431~464 (1999)
  4. "Micro-electro-mechanical-systems (MEMS) and °uid °ows", . 30(1998), pp.579~612
  5. "lms with high surface tension", 40, pp.441~462 (1998)
  6. "E±cient implementation of essentially non-oscillatory shock capturing schems II", 83, pp.32~78 (1989)
  7. "Fingering instability of driven spreading ¯", pp.25~30 (1989)
  8. "uller, Multigrid" (2001), Academic press

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