A numerical method for the Cahn-Hilliard equation with a variable mobility

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Abstract

We consider a conservative nonlinear multigrid method for the Cahn-Hilliard equation with a variable mobility of a model for phase separation in a binary mixture. The method uses the standard finite difference approximation in spatial discretization and the Crank-Nicholson semi-implicit scheme in temporal discretization. And the resulting discretized equations are solved by an efficient nonlinear multigrid method. The continuous problem has the conservation of mass and the decrease of the total energy. It is proved that these properties hold for the discrete problem. Also, we show the proposed scheme has a second-order convergence in space and time numerically. For numerical experiments, we investigate the effects of a variable mobility.

Original languageEnglish
Pages (from-to)1560-1571
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume12
Issue number8
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes

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Keywords

  • Cahn-Hilliard equation
  • Nonlinear multigrid method
  • Phase separation
  • Variable mobility

ASJC Scopus subject areas

  • Mechanical Engineering
  • Statistical and Nonlinear Physics

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