Simulation of dendritic crystal growth with thermal convection
Eberhard Bänsch
Zentrum fürTechnomathematik, Universität Bremen
and
Alfred Schmidt
Institut für Angewandte Mathematik,
Hermann-Herder-Str. 10, 79104 Freiburg, Germany
Abstract:
The dendritic growth of crystals under gravity influence shows a
strong dependence on convection in the liquid. The situation is
modelled by the Stefan problem with Gibbs-Thomson condition coupled
with the Navier-Stokes equations in the liquid phase. A finite
element method for the numerical simulation of dendritic crystal
growth including convection effects is presented. It consists of a
parametric finite element method for the evolution of the interface,
coupled with finite element solvers for the heat equation and
Navier-Stokes equations in a time dependent domain. Results from
numerical simulations in two space dimensions
with Dirichlet and transparent boundary conditions
are included.
Dirichlet (no-slip) boundary conditions
Neumann (transparent) boundary conditions, additional advection
Interfaces and Free Boundaries 2 (2000), 95-115.