Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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NUMERICAL COMPARISON OF WENO TYPE SCHEMES TO THE SIMULATIONS OF THIN FILMS

  • Kang, Myungjoo (DEPARTMENT OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY) ;
  • Kim, Chang Ho (DEPARTMENT OF COMPUTER ENGINEERING, GLOCAL CAMPUS, KONKUK UNIVERSITY) ;
  • Ha, Youngsoo (NATIONAL INSTITUTE FOR MATHEMATICAL SCIENCES)
  • Received : 2012.04.20
  • Accepted : 2012.08.13
  • Published : 2012.09.25
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Abstract

This paper is comparing numerical schemes for a differential equation with convection and fourth-order diffusion. Our model equation is $h_t+(h^2-h^3)_x=-(h^3h_{xxx})_x$, which arises in the context of thin film flow driven the competing effects of an induced surface tension gradient and gravity. These films arise in thin coating flows and are of great technical and scientific interest. Here we focus on the several numerical methods to apply the model equation and the comparison and analysis of the numerical results. The convection terms are treated with well known WENO methods and the diffusion term is treated implicitly. The diffusion and convection schemes are combined using a fractional step-splitting method.

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References

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