Course 14 Fluid Simulation Monday, Half Day, 8:30 am - 12:15 pm

2. Course 14 Fluid Simulation Monday, Half Day, 8:30 am - 12:15 pm

3. Course Schedule • The Basics of Fluid Flow (Robert, 105 min) • Break (15 min) • The Cutting-Edge in Film (Eran, 45 min) • Real Time Fluids in Games (Matthias, 45 min) • Non-Newtonian Fluids (Robert, 15 min)

4. Talk Outline • Particle level set method • Vorticity confinement & vortex particles • Fire simulation • Solid-fluid coupling

5. Particle Level Set Method [Enright et al. ’02]

6. Level Sets • We like level sets: • Smooth surface for rendering • Geometric information (normals, curvature) • Handle topological changes

7. Problem: Bad Mass Conservation • Even with high order solvers! simple rigid body rotation vortex stretching

8. Lagrangian marker particles Eulerian level set Solution COMBINE

9. Particles • Passively advected with flow • Help correct interface • Especially areas of high curvature • Hybrid surface model [Foster & Fedkiw ’01] • Particles inside water • Particle level set method [Enright et al. ’02] • Particles on both sides

10. Rigid Body Particles Original shape Level set only One-sided particles Particle level set method

11. Particles • Seeded within band of interface • Carry sign and radius • Periodically reseed particles • Add to under-resolved regions • Delete unnecessary particles

12. Error Identification • Escaped particles (on wrong side of interface)

13. Error Quantification • Particles behave like little level set spheres

14. Error Correction • Compute corrections to >0 and <0 regions • Merge into final corrected level set • Take minimum magnitude 

15. Particle Level Set Update • Advect particles & level set • Particle correction • Reinitialize • Particle correction • Adjust radii

16. Reduced Mass Loss simple rigid body rotation vortex stretching

17. Fast and Accurate PLS • Original PLS: • 3rd order RK; 5th order HJ-WENO • [Enright et al. ‘04]: Good results with lower order methods • Semi-Lagrangian (advection) • Fast marching method (redistancing) • 2nd order RK for particles • Easier for adaptive grids

18. Vorticity Confinement & Vortex Particles [Selle et al. ’05]

19. Vorticity • Vorticity: • Local rigid rotation • Want to simulate turbulent phenomena • Problem: numerical dissipation (boring flows)

20. Fixing Boring Flows Boring Flow Vorticity Confinement Vortex Particle Method

21. Vorticity Confinement [Steinhoff & Underhill ’94; Fedkiw et al. ’01] 1. Start with a velocity field 2. Compute vorticity 3. Compute vectors directed toward local maxima in vorticity magnitude 4. Compute a force [Andrew Selle]

22. Confinement Parameter e=0.25 e=0.50

23. Limitations of Vorticity Confinement • Uniformly amplifies vorticity ) grid artifacts • Can only amplify vorticity already on the grid • Unstable with larger  e=2

24. Vortex Equations of Flow Navier-Stokes Equations Vortex Equations of Flow

25. Vortex Particle Method [Selle et al. ’05] • Hybrid method: • Vortex particles & grid-based fluid solver • Evolve both  and u • Easier than trying to computeu from 

26. Vortex Particle Method • Vortex particle update: • Move particles (advection) • Change vorticity (vortex stretching) • Adding vorticity to flow: • Apply analytic confinement force • Ensures vorticity is conserved

27. Results - Smoke Hybrid Method(6000 particles)

28. Results - Smoke

29. Results - Water [320x128x320 effective octree, 600 particles]

30. Fire Simulation [Nguyen et al. ’02]

31. Fire Gaseous fuel Assumed premixed with air Blue core Heating ignition Emission due to chemical reaction Blackbody radiation Yellowish/orange glow Cooling Soot & smoke Visible after cooling

32. Fire Simulation [Nguyen et al. ’01,’02] • 2 phase flow • Gaseous fuel • Hot gaseous product • Level set captures interface (blue core) • Incompressible & inviscid • Model gas expansion

33. Flame Modeling hot gaseous product gaseous fuel thin flame

34. Blue Core • Track using level set (don’t need PLS) Varying flame reaction speed S (smaller on right)

35. Jump Conditions • Using: • e.g. Conservation of mass: Mass flux exitingflame front Mass flux entering flame front Shorthand:

36. Jump Conditions • Conservation of mass and momentum:

37. Jump Conditions • Can rewrite as

38. Varying Density Ratio Larger f / h on right

39. Ghost Values Ghost Fluid Method: [Fedkiw et al. ’99] Ghost Value Hot Gas Fuel

40. Velocity Jump Solve for fuel phase Solve for products phase

41. Pressure Jump • Incorporate into pressure solve (projection step) • e.g. In 1D:

42. When All is Said and Done… • Still symmetric, positive definite!

43. Temperature Used for color map Smoke Density Soot & smoke Temperature & Smoke Density

44. Campfire

45. Flammable Solids • Voxelize solid • Track solid’s temperature (heat conduction) • After ignition • Change solid voxels to negative  (fuel) • Set injection velocity on faces of solid voxels

46. Flammable Ball

47. Multiple Interacting Liquids [2nd talk – “Fluids” papers session – Wed. 8:30-10:15]

48. Solid-Fluid Coupling [Guendelman et al. ’05]

49. Lagrangian (moving) mesh Good for solids Bad for fluids Significant deformation and topology change Eulerian (static) mesh Good for fluids Bad for solids Harder to track moving material quantities Lagrangian vs. Eulerian Meshes

50. Strong coupling (simultaneous solution) Monolothic system More stable Weak coupling (staggered solution) Use existing simulators Less stable Strong vs. Weak Coupling e.g. [Chentanez et al. ’06] SOLIDS SIM SOLIDS + FLUIDS SIM FLUIDS SIM