A Numerical procedure for solving 2D phase-field model problems

Ying Xu, J. M. McDonough, K. A. Tagavi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We present a general 2D phase-field model, but without anisotropy, applied to freezing into a supercooled melt of pure nickel. The complete numerical procedure and details of assigning the numerical parameters are provided; convergence of the numerical method is demonstrated by conducting grid function convergence tests. The physics of solidification problems such as conditions for nucleation and crystal growth rate are discussed theoretically and shown to display at least qualitative agreement numerically. In particular, comparison of the computed critical radius with the theoretical one and the consistency of the computational dendrite structure for different Stefan numbers, the relationship between the growth rate and the Stefan number, etc., with the theoretical and experimental evidence indicate that phase-field models are able to capture the physics of supercooled solidification.

Original languageEnglish
Pages (from-to)770-793
Number of pages24
JournalJournal of Computational Physics
Issue number2
StatePublished - Nov 1 2006

Bibliographical note

Funding Information:
This work was supported by grants from NASA-EPSCoR WKU 522762-98-03 and WKURF 596183-03-09. It was also supported by University of Kentucky Center for Computational Sciences. We are grateful to University of Kentucky Computing Center for providing the HP SuperDome for all computations.


  • Numerical procedure
  • Phase-field model
  • Solidification
  • Supercooling

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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