A HYBRID METHOD FOR HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS

Title & Authors
A HYBRID METHOD FOR HIGHER-ORDER NONLINEAR DIFFUSION EQUATIONS
KIM JUNSEOK; SUR JEANMAN;

Abstract
We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing up an inclined plane. Equations of the type $\small{h_t+f_y(h) = -{\in}^3{\nabla}{\cdot}(M(h){\nabla}{\triangle}h)}$ 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.
Keywords
nonlinear diffusion equations;thin film;nonlinear multigrid method;
Language
English
Cited by
1.
THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF A PHASE-FIELD MODEL FOR ANISOTROPIC INTERFACIAL ENERGY,;

대한수학회논문집, 2007. vol.22. 3, pp.453-464
1.
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2.
Adaptive mesh refinement for simulation of thin film flows, Meccanica, 2014, 49, 1, 239
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