A NOTE ON THE NUMERICAL APPROACH FOR THE REACTION-DIFFUSION PROBLEM WITH A FREE BOUNDARY CONDITION


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Ozugurlu E.

ANZIAM JOURNAL, vol.51, pp.317-330, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51
  • Publication Date: 2010
  • Doi Number: 10.1017/s1446181110000817
  • Title of Journal : ANZIAM JOURNAL
  • Page Numbers: pp.317-330

Abstract

The equation modelling the evolution of a foam (a complex porous medium consisting of a set of gas bubbles surrounded by liquid films) is solved numerically. This model is described by the reaction-diffusion differential equation with a free boundary. Two numerical methods, namely the fixed-point and the averaging in time and forward differences in space (the Crank-Nicolson scheme), both in combination with Newton's method, are proposed for solving the governing equations. The solution of Burgers' equation is considered as a special case. We present the Crank-Nicolson scheme combined with Newton's method for the reaction-diffusion differential equation appearing in a foam breaking phenomenon.