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The Level Set Method for Solid-Solid Phase Transformations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • E. Javierre

    (Delft University of Technology, Delft Institute of Applied Mathematics)

  • C. Vuik

    (Delft University of Technology, Delft Institute of Applied Mathematics)

  • F. Vermolen

    (Delft University of Technology, Delft Institute of Applied Mathematics)

  • A. Segal

    (Delft University of Technology, Delft Institute of Applied Mathematics)

  • S. van der Zwaag

    (Delft University of Technology, Laboratory of Materials Science
    Netherlands Institute for Metals Research (N.I.M.R.))

Abstract

In this work we consider the homogenization process in Aluminum alloys, in which inhomogeneities dissolve. This process is governed by diffusion, and mass conservation leads to the Stefan condition on the moving interface. The Level Set Method is used to model this problem, due to its convenience to handle merging/ breaking interfaces, compared with other available methods. In binary alloys, the interface concentration is the solid solubility predicted from thermodynamics. However, in multicomponent alloys, the interface concentrations must satisfy a hyperbolic coupling, and therefore, have to be found as part of the solution. In this work we present a computational method to solve three-dimensional dissolution of binary alloys, and we study its extension to multicomponent alloys. In this respect, we restrict ourselves to one-dimensional problems and we focus our attention in the solution of the nonlinear coupled system of diffusion equations.

Suggested Citation

  • E. Javierre & C. Vuik & F. Vermolen & A. Segal & S. van der Zwaag, 2006. "The Level Set Method for Solid-Solid Phase Transformations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 712-719, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_69
    DOI: 10.1007/978-3-540-34288-5_69
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