1. 19 May 2000 MIGAL for Phoenics 3.3 The New Coupled Algebraic Multi-grid Solver

2. 19 May 2000 8 HOURS !!!!

3. 19 May 2000 Which computer could run PHOENICS 5, 10 or 30 times faster ?

4. 19 May 2000 yours Yours

5. 19 May 2000 Yours with MIGAL 12 mn

6. 19 May 2000 Instead of SIMPLEST

7. 19 May 2000 The Problem Simple, Simpler, Simplec, Simplest, Piso are segregating algorithms Then they need under-relaxation to ensure stability of the velocity-pressure coupling (FALSDT) They are at least N 2 algorithm

8. 19 May 2000 SIMPLEST CPU

9. 19 May 2000 The Idea A better perfomance of the solver for each equation separatly IS NOT the solution We must solve implicitly the velocity-pressure coupling before accelerating with multi-grid

10. 19 May 2000 How ? Linearize the momentum equations but do not solve Build the continuity equation Solve the algebraic system composed of 3x3 or 4x4 blocs : A nb nb = S A nb = S = nb =

11. 19 May 2000 But... The CPU time cost per sweep increase (x10) Additional storage is needed (70 Mb for 100,000 3D cells) Mb/cellStaggeredCo-locative 2D4.E-43.E-4 3D7.E-45.E-4

12. 19 May 2000 3D RAM

13. 19 May 2000 2D RAM

14. 19 May 2000 RAM vs CPU : the Winning Bet

15. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000

16. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10

17. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank

18. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step

19. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step

20. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step 3D Flow Around a Group of Building

21. 19 May 2000 Library Cases 2D Lid-Driven Cavity Re=10,000 2D Flow Past a Flat Plate Re=10 2D Flow in Unit of Staggered Tube Bank 2D Laminar Backward Facing Step 2D Turbulent Backward Facing Step 3D Flow Around a Group of Building 3D Lid-Driven Cavity Re=1,000

22. 19 May 2000 2D Lid-Driven Cavity Re=10,000 87 2 - 133 2 - 166 2 - 194 2 - 218 2 - 240 2 - 260 2

23. 19 May 2000 2D Cavity CPU

24. 19 May 2000 2D Cavity Speed-up

25. 19 May 2000 2D Flow Past a Flat Plate Re=10 20x70 - 40x140 - 52x190

26. 19 May 2000 2D Plate CPU

27. 19 May 2000 2D Plate Speed-up

28. 19 May 2000 Flow in Symmetry Unit of Staggered Tub Bank Re=140 10x21 - 50x105 - 100x210

29. 19 May 2000 Tube bank CPU

30. 19 May 2000 Tube Bank Speed-up

31. 19 May 2000 Backward Facing Step Laminar Re=150

32. 19 May 2000 Bstep_L CPU

33. 19 May 2000 Bstep_L Speed_up

34. 19 May 2000 Backward Facing Step Turbulent Quick-Koren (65x30) Re = 50,000

35. 19 May 2000 Backward Facing Step (turbulent 65x30)

36. 19 May 2000 3D Flow Around Buildings

37. 19 May 2000 Buildings CPU

38. 19 May 2000 Buildings Speed-up

39. 19 May 2000 3D Lid-Driven Cavity Re=1,000 10 3 - 27 3 - 34 3 - 39 3 - 43 3 - 47 3

40. 19 May 2000 3D Cavity CPU

41. 19 May 2000 3D Cavity Speed-up

42. 19 May 2000 How to use MIGAL for Phoenics ?

43. 19 May 2000 Activating MIGAL (1/2) Set large false time steps –relax(U1, falsdt, 1.E+10) –relax(V1, falsdt, 1.E+10) –relax(W1, falsdt, 1.E+10) Activate MIGAL for pressure-velocity –spedat(MIGAL, SOLVED1, c, HYDRO)

44. 19 May 2000 Activating MIGAL (2/2) Activate MIGAL for scalar variables –spedat(MIGAL, SOLVED3, c, SMOKE) Change default parameters –spedat(MIGAL, RELAX1, r, 0.9) –spedat(MIGAL, LITER3, i, 3)

45. 19 May 2000 Conclusion Coupled Multi-grid Method are already of great interest for 2D and 3D flows. and will be unbeatable in the future. MIGAL is boosting Phoenics with large speed- ups increasing with the number of cells.

46. 19 May 2000 Roadmap for MIGAL With an affordable PC under 2500$

47. 19 May 2000 WWW.mfrdc.com michel.ferry@mfrdc.com