An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

J. A. Mackenzie, M. L. Robertson, Mark George Beckett

Research output: Contribution to journalArticlepeer-review

Abstract

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.

Original languageEnglish
Pages (from-to)805-826
Number of pages22
JournalCommunications in computational physics
Volume1
Issue number5
Publication statusPublished - Oct 2006

Keywords

  • phase change
  • phase-field
  • equidistribution
  • moving meshes
  • adaptive method
  • MOVING MESH METHOD
  • NUMERICAL-SOLUTION
  • CRYSTAL-GROWTH
  • COMPUTATION
  • MODELS
  • SOLIDIFICATION
  • GENERATION
  • REFINEMENT
  • STEFAN
  • PDES

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