1. Analysis of the Solver Performance for Stokes Flow Problems in Glass Forming Process Simulation Models
Speaker: Hans Groot
Supervisors: Dr. Hegen (TNO Science and Technology)
Dr. Giannopapa (TU/e)
Prof. dr. Mattheij (TU/e)
Dr. Rienstra (TU/e)

2. Overview Introduction Simulation Models Problem Description Results
Conclusions

3. Glass Manufacturing Glass Melting Glass Conditioning
Automatic Inspection
Glass Forming
Surface Treatment
Pressing
Press-blowing
Blow-blowing
Introduction
Simulation Models
Problem Description
Results
Conclusions

4. Pressing Process plunger ring glass mould Introduction
Simulation Models
Problem Description
Results
Conclusions

5. Press-Blowing Process
glass
mould
Pressing stage
Blowing stage
ring
plunger
ring
preform
mould
Introduction
Simulation Models
Problem Description
Results
Conclusions

6. Process Simulation Packages
At TNO Glass Group (and some of its customers):
glass forming process simulation tools
Sepran based
Sepran
finite element library
Fortran 77 based
originally developed at TU Delft
Introduction
Simulation Models
Problem Description
Results
Conclusions

7. Purpose of Process Simulation
Analysis
current/existing process
comparison between results and measurements
Optimisation
Innovation
current/existing/new process
Introduction
Simulation Models
Problem Description
Results
Conclusions

8. Characteristics of Glass Forming Models
Flow of glass and air
Stokes flow problem:
Energy exchange in glass, air and equipment
Convection diffusion problem:
Evolution of glass-air interfaces
Convection problem for level sets:
Introduction
Simulation Models
Problem Description
Results
Conclusions

9. Finite Element Discretisation
Partition domain into triangular Mini-elements
Numerical computation solution in nodes . . .
Introduction
Simulation Models
Problem Description
Results
Conclusions

10. Glass Pressing Model Temperature Introduction Simulation Models
Problem Description
Results
Conclusions

11. Increase Solver Iterations (BiCGstab with ILU preconditioning)
Iterations energy problem & level set problem
Iterations flow problem
Accumulative iterations
2 by 2 mesh refinements
Introduction
Simulation Model
Problem Description
Results
Conclusions

12. Test Model Pressing time step in rectangle Uniform mesh: V = constant
left: symmetry
right: free flow
top: constant inflow
top/bottom: no slip
Uniform mesh:
half square triangular Mini-elements
V = constant y x
Introduction
Simulation Model
Problem Description
Results
Conclusions

13. Solver Performance Test Model
34.6
3.61
5.80E-1
1.37E-1
CPU time direct method
1.39E3
8.27
7.73E-1
1.68E-1
CPU time BiCGstab/ILU
7985
153 36 20
iterations
180224
45056
11264
2816
elements
Introduction
Simulation Model
Problem Description
Results
Conclusions

14. Possible Causes Solver problem not caused by:
discretisation methods
choice iterative solver
large condition number
Suggestions for improvement:
reordering unknowns
additional fill-in for ILU
implement other preconditioner
Introduction
Simulation Model
Problem Description
Results
Conclusions

15. CMK, pressure-last/level
Reordering Unknowns
None
Sloan
CMK (Cuthill Mc Kee)
CMK, pressure-last/level

16. Additional Fill-In for ILU
Zero Fill-In:
ILU for non-zero elements only
Additional Fill-In:
ILU for non-zero and some zero elements
Better approximation of LU factorisation
Introduction
Simulation Model
Problem Description
Results
Conclusions

17. Performance for Additional Fill-In
CMK, p-last/level,
extra fill-in
CMK, p-last/level
Sloan
6.1
8.45E-1
1.50E-1
17.3
8.65E-1
1.40E-1
50.9
1.77
2.04E-1
CPU time
32768
8192
2048
elements
Introduction
Simulation Model
Problem Description
Results
Conclusions

18. Improved Pressing Model
180 time steps
900 time steps
Introduction
Simulation Model
Problem Description
Results
Conclusions

19. Conclusions and Recommendations
Improvement solver performance/reduction CPU time for ILU preconditioning:
CMK instead of Sloan
pressure-last/level
additional fill-in
Other preconditioners suggested:
multigrid methods
domain decomposition methods
stabilised/modified ILU
Introduction
Simulation Models
Problem Description
Results
Conclusions

20. Questions?

21. Finite Element Mesh Introduction Simulation Models Problem Description
Results
Conclusions

22. Other Preconditioners besides ILU
Some other preconditioners tested, e.g. Eisenstat, Gauss-Seidel:
solver performance worse than for ILU
Multigrid and domain decomposition methods:
suitable for Stokes flow problems
multigrid computations increase linearly with unknowns
not tested due to implementation issues
Introduction
Simulation Model
Problem Description
Results
Conclusions

23. Performance for Different Orderings
Introduction
Simulation Model
Problem Description
Results
Conclusions

24. Accuracy of Results Introduction Simulation Model Problem Description
Conclusions