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