Three-dimensional, time-dependent features of melt flows which occur during the Czochralski growth of oxide crystals are analyzed using a theoretical bulk-flow model. The transition from a steady, axisymmetric flow to a time-dependent, three-dimensional state characterized by an annular wave structure is found to strongly affect the temperature distribution and heat transfer through the melt. The results are obtained using a novel, massively parallel implementation of the Galerkin finite element method which affords high spatial resolution of the computed flows.
Bibliographical noteFunding Information:
This work was supported in part by the National Science Foundation under grant number DMR-9058386, the University of Minnesota Army High Performance Computing Research Center (under the auspices of the US Army, Army Research Office), and the Minnesota Supercomputer Institute.