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Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage

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Free Boundary Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 154))

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Abstract

An adaptive phase field model for the solidification of binary alloys in two space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid.

Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh triangles having high aspect ratio whenever needed.

Numerical results are presented for dendritic growth of four dendrites.

Jacek Narski is supported by the Swiss National Science Foundation.

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Author information

Authors and Affiliations

  1. Institut d’Analyse et Calcul Scientifique, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland

    Jacek Narski & Marco Picasso

Authors
  1. Jacek Narski
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  2. Marco Picasso
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Editor information

Editors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal

    Isabel Narra Figueiredo

  2. Universidade de Lisboa / CMAF, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Lisa Santos

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Narski, J., Picasso, M. (2006). Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_32

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