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.

BS2_10.gif, 41 kB
Dirichlet (no-slip) boundary conditions

BS2_2.gif, 47 kB
Neumann (transparent) boundary conditions, additional advection

Interfaces and Free Boundaries 2 (2000), 95-115. Send me an email if you would like to get a copy.