A Level Set Approach for the Numerical Simulation of Dendritic Growth

Frédéric Gibou, Ronald Fedkiw, Russel Caflisch, Stanley Osher

Research output: Contribution to journalArticle

Abstract

In this paper, we present a level set approach for the modeling of dendritic solidification. These simulations exploit a recently developed second order accurate symmetric discretization of the Poisson equation, see [12]. Numerical results indicate that this method can be used successfully on complex intsrfacial shapes and can simulate many of the physical features of dendritic solidification. We apply this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results are presented in both two and three spatial dimensions.

Original languageEnglish (US)
Pages (from-to)183-199
Number of pages17
JournalJournal of Scientific Computing
Volume19
Issue number1-3
DOIs
StatePublished - Dec 2003

Keywords

  • Dendritic growth
  • Ghost fluid method
  • Interfaces
  • Level set method
  • Poisson equation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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