A numerical method for the ternary Cahn-Hilliard system with a degenerate mobility

Junseok Kim, Kyungkeun Kang

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.

Original languageEnglish
Pages (from-to)1029-1042
Number of pages14
JournalApplied Numerical Mathematics
Volume59
Issue number5
DOIs
Publication statusPublished - 2009 May 1

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Keywords

  • Degenerate mobility
  • Nonlinear multigrid
  • Phase separation
  • Ternary Cahn-Hilliard

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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