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Hans Groot
| Speaker: |
Hans Groot
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| Date: |
Tuesday January 9, 2007
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| Title: |
Analysis of the
Solver Performance for Stokes Flow Problems in Glass
Forming Process Simulation Models (Master's Thesis Presentation)
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Abstract
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During
a glass forming process in industrial glass manufacturing, a glass gob
that comes directly from the furnace is forced into a desired shape. In
general, practical experiments with glass forming are considerably
expensive, whereas the majority has to be performed under complicated
circumstances, e.g. high temperatures. In addition, the glass industry
is fairly secretive about experimental data. Therefore, computer
simulation models are required to gain a better understanding and
improvement of glass forming processes. The glass forming process
simulation models considered revolve around three coupled, principal
physical problems. These are successively a flow problem for the motion
of glass and air, an energy problem for the energy exchange in glass,
air and equipment, and a level set problem for the location of the
interfaces between glass and air. The boundary value problems are
discretised by means of finite element methods and a suitable time
discretisation scheme. Subsequently, an iterative solver with
preconditioning is applied to solve the resulting systems of equations
for each successive time step. Unfortunately, problems regarding the
solver performance occur for flow problems in TNO Glass Group's glass
forming process simulation models, as application of mesh refinement
produces an excessive increase in the number of iterations required by
the iterative solvers for convergence, which finally results in
termination of the solvers. This solver problem does not occur, or at
least to a lesser degree, for the energy problem and the level set
problem. The solver performance is examined for TNO Glass Group's glass
pressing process simulation model. Since the solver is relatively slow
and instable for general three dimensional simulations, the solver
performance is only tested for axi-symmetric problems. The
discretisation methods used for flow problems in the simulation model
can be proven to be stable and produce well-defined systems of
equations. In TNO Glass Group's pressing process simulation model, ILU
preconditioning with Sloan reordering of the unknowns is used to
improve convergence of iterative solvers. ILU preconditioning can be
improved by allowing additional fill-in and using Cuthill Mc Kee
ordering instead of Sloan ordering. The resulting improvement of the
solver performance in TNO Glass Group's axi-symmetric pressing process
simulation model is encouraging. In addition it is shown that ILU
preconditioning is superior in this case to several other
preconditioners, such as Gauss-Seidel and Eisenstat. Other
preconditioners such as multigrid methods are suggested, but not tested
due to implementation issues.
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