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

Dongsun Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

46 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

Bibliographical note

Funding Information:
The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The author (D. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2012-003115 ). The authors are grateful to the anonymous referees whose valuable suggestions and comments significantly improved the quality of this paper.

Publisher Copyright:
© 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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