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Hans Groot
| Speaker: |
Hans Groot
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| Date: |
Tuesday January 9, 2006 |
| 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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