Simulation of Czochralski melt flows using parallel adaptive finite element procedures

摘要

Simulation of steady-state and transient melt flows in a Czochralski (CZ) crystal growth process is performed. To this end, a new three-dimensional finite element scheme is developed, that is based on a Galerkin least-squares (GLS) space - time variational formulation, with capabilities which include general unstructured mesh generation, automatic adaptive mesh refinement and coarsening, and parallel implementation with automatic load-balancing. Numerical results are obtained for flows in silicon and indium phosphide (InP) melts, with or without a viscous encapsulant, in crucibles with a flat or curved bottom. The effects of natural convection due to buoyancy, forced convection due to crystal and crucible rotations, and their combination, are considered.