The Level Set Method for Solid-Solid Phase Transformations

E. Javierre (), C. Vuik (), F. Vermolen (), A. Segal () and S. van der Zwaag ()
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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

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 712-719 from Springer

Abstract: 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.

Keywords: Binary Alloy; Stefan Problem; Nonlinear Coupling; Multicomponent Alloy; Interface Position (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_69

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DOI: 10.1007/978-3-540-34288-5_69

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