A Level Set Approach for the Numerical Simulation of Dendritic Growth

  • Authors:

  • Frédéric Gibou;Ronald Fedkiw;Russel Caflisch;Stanley Osher

  • Affiliations:

  • Mathematics Department & Computer Science Department, Stanford University, Stanford, California 94305. fgibou@math.Stanford.edu;Computer Science Department, Stanford University, Stanford, California 94305;Mathematics Department, University of California, Los Angeles, California 90095-1555;Mathematics Department, University of California, Los Angeles, California 90095-1555

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2003

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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 interfacial 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.