Particlebased 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 animationEnright et al.
  2002
• Viscous, elastic, and plastic materials Goktekin
  et al. 2004

5
Previous Work

• Particle-based techniques
• SPH for highly deformable bodiesDesbrun,
  Gascuel 1996
• Interactive water simulation
• Müller et al. 2003
• Elastic and plastic materialsMüller 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 Relaxation

• Density sum of weighted neighbor contributions

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
Density Relaxation

• Particles can reach rest-density by strongly
  attracting a small number of neighbors

Clustering
22
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)
h
r
23
Double Density Relaxation

• For each particle,
• Compute density and near-density
• Modify the particle and its neighbors predicted
  positions to approach constant density and zero
  near-density

24
Double Density Relaxation

• For each particle,
• Compute density and near-density
• Modify the particle and its neighbors predicted
  positions to approach constant density and zero
  near-density

Surface tension effects without curvature
computation!
demo
25
Double Density Relaxation

• Near-density has zero rest value
• Add new term to displacement

26
Viscosity
27
Overview

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

28
Elasticity

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

force magnitude
29
Plasticity

• Change rest-length based on current length
• Linear plasticity

• Non-linear plasticity plastic flow only if
  deformation is large enough

video
30
Plasticity

• Add a spring between two particles when they come
  closer than the interaction range h
• Remove the spring when its rest-length becomes
  larger than h

31
Interactions with objects
demo
32
Implementation Details

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

33
Results

• 20000 particles
• 2 sec / frame
• 1000 particles
• 10 FPS

34
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