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Interfaces and Free Boundaries

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Volume 2, Issue 1, 2000, pp. 95–115
DOI: 10.4171/IFB/14

Published online: 2000-03-31

Simulation of dendritic crystal growth with thermal convection

Eberhard Bänsch and Alfred Schmidt[1]

(1) Universität Freiburg, Germany

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 a 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.

Keywords: Dendritic solidification; crystal growth; natural convection; Gibbs-Thomson; Navier-Stokes equations; finite elements

Bänsch Eberhard, Schmidt Alfred: Simulation of dendritic crystal growth with thermal convection. Interfaces Free Bound. 2 (2000), 95-115. doi: 10.4171/IFB/14