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Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Eric Burman

    (Ecole Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique)

  • Marco Picasso

    (Ecole Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique)

  • Jacques Rappaz

    (Ecole Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique)

Abstract

Summary A solutal, anisotropic phase-field model for dendritic growth of an isothermal binary alloy is considered. Existence of a weak solution is established provided the physical anisotropy is small enough. A semi-implicit finite element method is proposed to solve the problem. A priori and a posteriori error estimates are derived when the physical anisotropy is small. An adaptive algorithm which aims at producing meshes with large aspect ratio is proposed. Numerical results show that accurate solutions can be obtained, even when the physical anisotropy is large.

Suggested Citation

  • Eric Burman & Marco Picasso & Jacques Rappaz, 2004. "Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 204-220, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_18
    DOI: 10.1007/978-3-642-18775-9_18
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