A. Schmidt
Institut für Angewandte Mathematik,
Hermann-Herder-Str. 10, 79104 Freiburg, Germany
Simulation of a dendrite growing in an undercooled melt - Interface and
temperature mesh
A. Schmidt
Institut für Angewandte Mathematik,
Hermann-Herder-Str. 10, 79104 Freiburg, Germany
Simulation of a dendrite growing in an undercooled melt - Interface and
temperature mesh
Abstract:
Starting from an initial seed crystal inside of an undercooled liquid,
the solid phase begins to grow rapidly and develops instable growth
patterns. Some growth directions are preferred because of anisotropic
parameters in the physical model. This results in the development of
dendrites. The physical model includes the heat equation for both the
liquid and solid phases; the Gibbs--Thomson law couples velocity and
curvature of the interface and the temperature.
We describe a numerical method that enables us to compute dendritic
growth of crystals in two and three space dimensions.
The method consists of two coupled finite element algorithms. The
first one solves the heat equation; the other one operates on a
discretization of the free boundary and computes the evolution of this
moving interface. The two methods work with totally independent
grids. By using timedependent, locally refined and coarsened adaptive
meshes in both methods, we are able to reach a spatial resolution
necessary to compute dendritic growth in two and three space
dimensions.
AMS-Classification: 65C20, 65M50, 65M60, 65N30
Keywords:
crystal growth, dendritic growth, finite element method,
adaptive mesh refinement, moving grid