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Numerical Simulation of Dendritic Crystal Growth
Author(s) -
Müller Rüdiger,
Warnecke Gerald
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610356
Subject(s) - supercooling , curvature , interface (matter) , stefan problem , finite element method , level set method , representation (politics) , level set (data structures) , set (abstract data type) , crystal (programming language) , mechanics , physics , computer science , mathematical analysis , boundary (topology) , thermodynamics , mathematics , geometry , surface tension , image (mathematics) , artificial intelligence , politics , law , political science , image segmentation , programming language , gibbs isotherm
We consider the modified Stefan‐Problem with Gibbs‐Thomson correction, but vanishing kinetic undercooling. In this case the interface velocity is not given by mean curvature flow, but has to be computed explicitly from the temperature gradients at the interface. A finite element method on adaptive refined multigrids is presented here. Dirichlet conditions have to be satisfied along the solid‐liquid interface that in general may intersect the elements. We use an implicit level‐set representation of the interface that preserves it as a sharp surface, in contrast to the phase‐field method. In numerical simulations we observe dendritic patterns that show good agreement with different features of physical experiments. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)