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

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Ozugurlu E.

ANZIAM JOURNAL, cilt.51, ss.317-330, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1017/s1446181110000817
  • Dergi Adı: ANZIAM JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.317-330
  • Anahtar Kelimeler: foam drainage, nonlinear partial differential equation, Crank-Nicolson method, breaking front, Plateau border, reaction-diffusion problem, free boundary problem, FOAM DRAINAGE, DYNAMICS
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.