Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations

Dongsun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations.

Original languageEnglish
Pages (from-to)35-56
Number of pages22
JournalMathematics and Computers in Simulation
Publication statusPublished - 2016 Jan 1


  • Cahn-Hilliard equation
  • Conservation of mass
  • Conservative Allen-Cahn equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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