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A level set based finite element algorithm for the simulation of dendritic growth

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Computing and Visualization in Science

Abstract

Dendritic growth is a nonlinear process, which falls into the category of self-organizing pattern formation phenomena. It is of great practical importance, since it appears frequently and, in the case of alloys, affects the engineering properties of the resulting solid. We describe a new finite element algorithm for the two–dimensional Stefan problem, where the free boundary is represented as a level set. This allows to handle topological changes of the free boundary. The accuracy of the method is verified and several numerical simulations, including topological changes of the free boundary, are presented.

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  1. Institut für Angewandte Mathematik, Universität Freiburg, 79104, Freiburg, Germany

    Michael Fried

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  1. Michael Fried
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Correspondence to Michael Fried.

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G. Wittum

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Fried, M. A level set based finite element algorithm for the simulation of dendritic growth. Comput. Visual Sci. 7, 97–110 (2004). https://doi.org/10.1007/s00791-004-0141-4

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