Phase-field simulations of crystal growth with adaptive mesh refinement

Yibao Li, Junseok Kim

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


In this paper, we propose the phase-field simulation of dendritic crystal growth in both two- and three-dimensional spaces with adaptive mesh refinement, which was designed to solve nonlinear parabolic partial differential equations. The proposed numerical method, based on operator splitting techniques, can use large time step sizes and exhibits excellent stability. In addition, the resulting discrete system of equations is solved by a fast numerical method such as an adaptive multigrid method. Comparisons to uniform mesh method, explicit adaptive method, and previous numerical experiments for crystal growth simulations are presented to demonstrate the accuracy and robustness of the proposed method.

Original languageEnglish
Pages (from-to)7926-7932
Number of pages7
JournalInternational Journal of Heat and Mass Transfer
Issue number25-26
Publication statusPublished - 2012 Dec

Bibliographical note

Funding Information:
This research 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. 2011-0023794 ). The authors also wish to thank the anonymous referee for the constructive and helpful comments on the revision of this article.


  • Adaptive mesh refinement
  • Crystal growth
  • Multigrid method
  • Operator splitting
  • Phase-field simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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