A Finite Element Method for Dendritic Growth

E. Bänsch and A. Schmidt
Institut für Angewandte Mathematik,
Hermann-Herder-Str. 10, 79104 Freiburg, Germany

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Abstract:
A numerical method for the motion of solid/liquid boundaries in undercooled media is presented. This algorithm is based on the combination of an adaptive heat equation solver in 2 or 3 dimensions and a (prescribed) mean curvature flow procedure for curves or surfaces. Both parts use finite elements.
The triangulation of the solid/liquid region is (more or less) independent of the free boundary; local refinement is monitored by an error estimator for the temperature, not directly by the position of the liquid/solid interface.
At the moment, we present results for the 2d case only, but the method is easily extendable to 3d, and the application is under work.


in Jean E. Taylor (Ed.): Computational Crystal Growers Workshop, AMS Selected Lectures in Mathematics, 1992 (5 pages)

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