1. Evolving Sub-Grid Turbulence for Smoke Animation Hagit Schechter Robert Bridson SCA 08

2. The Challenge licensed under Creative Commons

3. The Goal  Scalability  Speed  Realism

4. Related Work  Kolmogorov spectrum  Stam and Fiume 1993  Neyret 2003  Kim, Thürey, James, and Gross 2008  Vorticity confinement, Vortex particles  Fedkiw, Stam, and Jensen 2001  Selle, Rasmussen, and Fedkiw 2005  Park and Kim 2005

5. Contributions  Multi-scale evolution of turbulent energy (K-Epsilon, Kolmogorov)  Turbulence procedure suitable to run on a GPU (parallelized trivially)  Reduced numerical dissipation of angular momentum

6. Talk Overview  Turbulence model  Method overview  Large-scale simulation  Small-scale simulation  Results

7. Turbulence model Method overview Large-scale simulation Small-scale simulation Results

8. Related Work (Physics)  Kolmogorov model  Richardson, 1922  Kolmogorov, 1941, 1942  K-Epsilon model  Davidov, 1961  Harlow and Nakayama, 1968  Hanjalic, 1970  Jones and Launder, 1972  Launder and Sharma, 1974

9. Decomposition of Turbulent Flow Large-scale flowSub-grid turbulence flow

10. Kolmogorov model: Kinetic energy is transported from largest scale to smaller and smaller scales and is dissipated to heat in the smallest scales Energy Cascade

11. The K-Epsilon Model Viscous forces Gained from large-scale Dissipation at smallest scale We use simplified viscosity term Apply K-Epsilon to all turbulent scales Our turbulence model:

12. In space Across scales 2D Energy Transport Model

13. Turbulence model Method overview Large-scale simulation Small-scale simulation Results

14. Method Overview Large-scale flow  Add forces  Advect  Project  Output velocities Turbulence properties  Evaluate  Transport  Output properties Large-scale simulationSmall-scale simulation Small-scale flow  Read turbulence properties  Apply them to generate small-scale velocities Synthesize  Read large-scale velocities  Synthesize velocities  Advance particles

15. Turbulence model Method overview Large-scale simulation Small-scale simulation Results

16. Navier-Stokes Buoyancy forces Large-Scale Simulation temperature gravity FLIP: MAC grid plus particles for advection

17. Turbulence Properties Evaluate, advect, and transport For every turbulence scale On every timestep turbulent energy density

18. Previous step energy Viscous forces Gain from larger scale Loss to smaller scale Transport Turbulence Properties K-Epsilon equation

19. Preserving Angular Momentum AdvectionProjection The problem: numerical dissipation (time-split)

20. Our solution: time-split predictor Advect+predictProjection

21. Turbulence model Method overview Large-scale simulation Small-scale simulation Results

22. Small-Scale Simulation  Perlin 1985, 2002  Bridson et al 2007  Perlin and Neyret 2001 Our model:  Turbulence driven Curl-Noise to generate small-scale flow  Synthesize with large-scale flow

23. 2. Compute small-scale velocity for every particle Initialize: Plant marker particles On Every time-step: The Procedure 1. Rotate basis vectors for every turbulence scale Time coherence: turbulence driven vorticity Turbulence driven Curl-Noise

24. Synthesize Small-scale algorithm can be trivially parallelized to run on a GPU ! Update positions

25. Results

26. To Summarize  Capture the time evolution of turbulence  Combine coarse grid simulation with procedural method that is suitable to run on a GPU  Detail level is tunable and scalable

27. Acknowledgements Natural Sciences and Engineering Research Council of Canada, BC Innovation Council, and Precarn Incorporated

28. The End Questions?