Particle-based Viscoelastic Fluid Simulation

1. Particle-based Viscoelastic Fluid Simulation Simon Clavet Philippe Beaudoin Pierre Poulin LIGUM, Université de Montréal

2. Goals • Intuitive and versatile framework for particle-based fluid simulation • Stable integration scheme • Small scale surface tension effects • Simple scheme for viscoelasticity • Two-way coupling with rigid bodies

3. Overview • Previous work • Integration scheme • Density relaxation • Viscoelasticity • Interactions with objects • Implementation details, results, and conclusion

4. Previous Work • Grid-based techniques • High-quality liquid animation[Enright et al. 2002] • Viscous, elastic, and plastic materials [Goktekin et al. 2004]

5. Previous Work Particle-based techniques SPH for highly deformable bodies[Desbrun, Gascuel 1996] Interactive water simulation [Müller et al. 2003] Elastic and plastic materials[Müller et al. 2004]

6. Integration Scheme Advance particles to predicted positions Relax according to positional constraints

7. Integration Scheme Apply gravity

8. Integration Scheme Apply gravity and viscosity

9. Integration Scheme Apply gravity and viscosity Advance to predicted positions

10. Integration Scheme Apply gravity and viscosity Advance to predicted positions Relax (density and springs)

11. Integration Scheme Apply gravity and viscosity Advance to predicted positions Relax (density and springs) Obtain new velocities

12. Integration Scheme Apply gravity and viscosity Advance to predicted positions Relax (density and springs) Obtain new velocities

13. Integration Scheme Apply gravity and viscosity Advance to predicted positions Relax (density and springs) Obtain new velocities

14. Density Relaxation • For each particle, • Compute its density • Modify the particle and its neighbors predicted positions to approach rest-density

15. Density: sum of weighted neighbor contributions Density Relaxation density kernel r h

16. Density Relaxation Pseudo-Pressure: i

17. Density Relaxation Pseudo-Pressure: i i i

18. Density Relaxation Displacement also depends on a distance kernel r h i

19. Density Relaxation • Linear and angular momentum conservation: apply radial, equal, and opposite displacements

20. Density Relaxation • Linear and angular momentum conservation: apply radial, equal, and opposite displacements demo

21. Double Density Relaxation Use another SPH-like force to push near-particles Define near-density similarly to density, but with a sharper kernel 3 2 near-density kernel (1-r/h) density kernel (1-r/h) r h

22. For each particle, Compute density and near-density Modify the particle and its neighbors predicted positions to approach constant density and zero near-density Double Density Relaxation

23. Double Density Relaxation • Near-density has zero rest value • Add new term to displacement:

24. Overview • Previous work • Integration scheme • Density relaxation • Viscoelasticity • Interactions with objects • Implementation details, results, and conclusion

25. Elasticity • Add linear springs between neighboring particles • Scale spring stiffness so that force vanishes when rest-length L equals interaction range h force magnitude

26. Plasticity Change rest-length based on current length Linear plasticity: • Non-linear plasticity: plastic flow only if deformation is large enough video

27. Interactions with objects demo

28. Implementation Details • Neighbor finding through spatial hashing • Marching Cube for surface generation • OpenGL display or offline raytracing

29. Results • 20000 particles ≈ 2 sec / frame • 1000 particles ≈ 10 FPS

30. Conclusion • Particle-based fluid simulation with simple and stable integration scheme • Incompressiblity, anticlustering and surface tension effects through double density relaxation • Dynamic rest-length springs for viscoelasticity • Two-way coupling with rigid bodies Future Work • Multiple particle types • Rotating particles with directional springs • Multiresolution