1. Coupling Water and Smoke to Thin Deformable and Rigid Shells Eran Guendelman 1,2 Andrew Selle 1,3 Frank Losasso 1,2 Ronald Fedkiw 1,2 1 Stanford University, 2 Industrial Light + Magic, 3 Intel Corporation

2. Motivation Fluid simulation becoming more common – Engineering, biomedicine, entertainment Want interaction with thin solids – Parachutes – Cardiovascular simulation – CG characters w/clothing

3. Goal Two-way coupling between: – Smoke or free-surface water – Thin rigid and deformable open shells Prevent leaks across solid

4. 256x256x192 effective octree; 30k triangles

5. Volumetric vs. Thin Solids VolumetricThin shell

6. Related Work: Volumetric DLM / “Rigid Fluid” [Glowinski et al. ’94;Carlson et al. ’04] Inter-particle forces [Génevaux et al. ’03; Müller et al. ’04] Coupling solid velocity & fluid pressure – Incompressible: [Takahashi et al. ’02] – Compressible: [Yngve et al. ’00; Fedkiw ’02]

7. Diffuse Interface Methods Smear solid onto fluid grid e.g. Immersed boundary method [Peskin ‘72] – Parasitic currents

8. Sharp Interface Methods Incorporate jump conditions into stencils – Ghost fluid method [Fedkiw et al. ’99; Tam et al. ‘05] – Immersed interface method [LeVeque & Li ’94]

9. Our Approach Couple using – Solid velocity & fluid coupling pressure Sharp interface treatment Prevent leaks using robust ray intersections

10. Talk Overview Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying coupling force Summary and future work

11. Talk Overview Fluid simulation (focus on water) Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Summary and future work

12. Fluid Simulation Assume incompressible & inviscid Use projection method: [Chorin ’68] unun Advect u n and add gravity ! u* Project u* ! u n+1 u n+1 u* violates incompressibility Compute pressure to enforce incompressibility (u is fluid velocity)

13. Fluid Grid Uniform & octree grids [Losasso et al. ’04] Staggered grid configuration [Harlow & Welch ‘65]

14. Advection First order semi-Lagrangian [Courant et al. ’52; Stam ‘99] – Advection on nodes

15. Particle Level Set Method Level set  captures water-air interface Particles help correct interface water air [Enright et al. ‘02]

16. Water Simulation Step (n ! n+1) un,nun,n Advance particle level set !  n+1 Advect u n and add gravity ! u* Project u* ! u n+1 u n+1,  n+1 Advect  and particles

17. Now Add Solids to the Mix… Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Summary and future work

18. Now Add Solids to the Mix… Black box: Input: external forces Output: positions and velocities [Guendelman et al. ’03][Bridson et al. ’02,’03]

19. Surface Quantities Rigid body – Directly compute Deformable body – Barycentric weights

20. Talk Overview Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Examples, summary, and future work

21. Key: Visibility

22. Thin Shell Aware Interpolation Check visibility of interpolation nodes Use replacement ghost value when interpolating

23. Replacement Ghost Values Fluid velocity (u) Level set (  ) use solid velocity average from nearest valid nodes

24. Thin Shell Aware Advection Clip semi-Lagrangian rays

25. Crossed Over Nodes Represent information from opposite side Reassign valid values by averaging

26. Thin Shell Aware Fluid Step un,nun,n Advance particle level set !  n+1 Advect u n and add gravity ! u* Project u* ! u n+1 u n+1,  n+1 Thin shell aware advection (  and particles) Thin shell aware advection (u) …see paper for more details

27. 210x140x140 uniform; 30k triangles

29. Talk Overview Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Summary and future work

30. Rasterizing Solid Rasterize onto faces of fluid grid

31. Solid Affecting Fluid Solid prescribes velocity on rasterized faces Enforce as Neumann boundary conditions in projection step: Project u* ! u n+1

32. Which Solid Velocities? At time n+1 ! n+2, at solid-fluid interface – Fluid moves with velocity enforced during u n+1 projection – Solid moves from to X n+1 to X n+2 Want these motions to match (reduce mass loss) Solution: – Enforce effective solid velocity: V eff =(X n+2 -X n+1 )/  t

33. One-Way Coupling Step u n,  n,S n,S n+1 Advance particle level set !  n+1 Advect u n and add gravity ! u* Project u* ! u n+1 u n+1,  n+1,S n+1,S n+2 Advance solid ! S n+2 Enforce effective solid velocities (n+1 ! n+2) at solid-fluid interface (S is the solid’s state)

34. 160x192x160 effective octree

35. 192x192x192 effective octree; 60k triangles

36. Talk Overview Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Summary and future work

37. Fluid Coupling Force Want to use fluid pressure Incompressible pressure can be noisy – Incompressibility = hard constraint – Enforcing solid velocity = hard constraint – Better for compressible fluids [Yngve et al. ‘00; Fedkiw ‘02]

38. Smoother Coupling Pressure Treat solid as fluid Solve variable density fluid for p c Similar to projection step, but: – Solid velocities not enforced – Fluid velocities not modified!

39. Two Pressure Solves! Incompressible pressure (projection): – Enforce incompressibility & solid velocity – Essential for reducing mass loss Coupling pressure: – Does not modify fluid velocity – Essential for smoother coupling force on solid

40. Must Enforce Solid Velocity Enforced! Enforcing solid velocity Rigid Fluid [Carlson et al. ’04] Mass loss

41. Computing Force on Solid Fluid pressure pushes on both sides

42. Computing Force on Solid Net force is proportional to pressure jump [p c ]

43. Computing Force on Solid Rasterize solidCompute coupling pressurePressure jumps on facesAverage to nodes ExtrapolateInterpolate at centroid Compute force

44. Two-Way Coupling Step u n,  n,S n,S n+1 Advance particle level set !  n+1 Advect u n and add gravity ! u* Advance solid ! S n+2 Project u* ! u n+1 u n+1,  n+1,S n+1,S n+2 Compute coupling pressure and apply force to solid

45. 148x148x111 uniform; 2.5k triangles

46. 200x200x200 effective octree; 30k triangles

47. 256x256x192 effective octree; 30k triangles

49. Talk Overview Fluid simulation Solid simulation Preventing leaks across solid Enforcing solid velocity on fluid Computing and applying fluid coupling force Summary and future work

50. Summary Sharp interface treatment – Prevent leaks using ray intersections (visibility) Solid prescribes velocity boundary conditions – Use effective velocity to reduce mass loss Smooth coupling force applied to solid – Treat solid as fluid to compute smoother pressure

51. Future Work Absorption, adhesion, permeability Compare against experiments

52. Acknowledgements Mike Houston, Christos Kozyrakis, Mark Horowitz, Bill Dally, Vijay Pande Stanford Graphics Lab ONR, ARO, NSF, PECASE, Sloan Foundation, Packard Foundation

53. The End