Speaker: Hans Groot

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

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

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

6. Conclusions Introduction Simulation Models Results Problem Description 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

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

8. Conclusions Introduction Simulation Models Results Problem Description 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:

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

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

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

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

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

14. Conclusions Introduction Problem Description Results Simulation Model 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

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

16. Conclusions Introduction Problem Description Results Simulation Model 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

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

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

19. Problem Description Introduction Simulation Models Conclusions Results 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

20. Questions?

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

22. Conclusions Introduction Problem Description Results Simulation Model 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

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

24. Conclusions Introduction Problem Description Results Simulation Model Accuracy of Results