Open Access

ARTICLE

Adaptive 3D finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage

by Jacek Narski¹, Marco Picasso¹

1 Institut d’Analyse et Calcul Scientifique, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
2 Supported by the Swiss National Science Foundation

Fluid Dynamics & Materials Processing 2007, 3(1), 49-64. https://doi.org/10.3970/fdmp.2007.003.049

Abstract

An adaptive phase field model for the solidification of binary alloys in three 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 tetrahedrons having high aspect ratio whenever needed. Numerical results show that our method is effective and allows to perform complicated simulations with relatively few computer resources needed. The simultaneous evolution of several solutal dendrites can be efficiently simulated on a single workstation.

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