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Parallel Finite Element Simulations of Czochralski Melt Flows

Summary: Parallel Finite Element Simulations
of Czochralski Melt Flows
S. Adjerid, J.E. Flaherty, K. Jansen, M.S. Shephard
Scienti c Computation Research Center
Rensselaer Polytechnic Institute
Troy, NY 12180-3590, USA
We use a nite element software based on the stabilized Galerkin Least-Squares method to solve
the Navier Stokes equations with the Boussinesq approximation coupled to an energy equation through
the temperature. We study melt ows associated with a Czochralski crystal growth process with the
goal of understanding the transition from a steady laminar regime to an unsteady one as the Grashof
number increases.
Single crystals having speci c electrical, mechanical, and optical properties are needed for high-
performance electronic and opto-electronic applications involving, e.g., semiconductors and laser mod-
ulators. Mathematical modeling and numerical simulation have improved the ability to understand the
bulk crystal-growth processes 1 . With powerful parallel computers, this can be advanced further to
enhance and control these complex systems. The more limited goal of this investigation is an under-
standing of the transition from steady laminar, to transient, to turbulent ow of a molten liquid crystal
with increasing Grashof number. The popular Czochralski CZ process 2 of bulk crystal growth fea-


Source: Adjerid, Slimane - Department of Mathematics, Virginia Tech


Collections: Mathematics