Particle-based Viscoelastic Fluid Simulation

Simon ClavetPhilippe Beaudoin

Pierre Poulin

LIGUM, Université de Montréal

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

Overview

• Previous work

• Integration scheme

• Density relaxation

• Viscoelasticity

• Interactions with objects

• Implementation details, results, and conclusion

Previous Work

• Grid-based techniques

– High-quality liquid animation[Enright et al. 2002]

– Viscous, elastic, and plastic materials [Goktekin et al. 2004]

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]

Integration Scheme

• Advance particles to predicted positions• Relax according to positional constraints

Apply gravity

Integration Scheme

Apply gravity and viscosity

Integration Scheme

Apply gravity and viscosity

Advance to predicted positions

Integration Scheme

Apply gravity and viscosity

Advance to predicted positions

Relax (density and springs)

Integration Scheme

Apply gravity and viscosity

Advance to predicted positions

Relax (density and springs)

Obtain new velocities

Integration Scheme

Apply gravity and viscosity

Advance to predicted positions

Relax (density and springs)

Obtain new velocities

Integration Scheme

Apply gravity and viscosity

Advance to predicted positions

Relax (density and springs)

Obtain new velocities

Integration Scheme

Density Relaxation

• For each particle, – Compute its density– Modify the particle and its neighbors predicted

positions to approach rest-density

• Density: sum of weighted neighbor contributions

)(

2

1iNj

iji h

r

density kernel

h r

Density Relaxation

Density Relaxation

• Pseudo-Pressure:

P

0i

i

0~ iiP

Density Relaxation

• Pseudo-Pressure:

0~ iiP

P

0 i

iii

Density Relaxation

• Displacement also depends on a distance kernel

h

rPD iji 1~

h r

i

Density Relaxation

• Linear and angular momentum conservation: apply radial, equal, and opposite displacements

Density Relaxation

• Linear and angular momentum conservation: apply radial, equal, and opposite displacements

demo

Double Density Relaxation

• Use another SPH-like force to push near-particles• Define near-density similarly to density, but with a

sharper kernel

density kernel (1-r/h)2 near-density kernel (1-r/h)

h r

3

• 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

Double Density Relaxation

2

11~

h

rP

h

rPD ijNEAR

iij

i

0~ iiP

NEARi

NEARiP ~

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

Overview

• Previous work

• Integration scheme

• Density relaxation

• Viscoelasticity

• Interactions with objects

• Implementation details, results, and conclusion

Elasticity

• Add linear springs between neighboring particles• Scale spring stiffness so that force vanishes

when rest-length L equals interaction range h

)(1~ rLh

L

force magnitude

r

L

)(~ rLF

Plasticity• Change rest-length based on current length

• Linear plasticity: )(~ LrL • Non-linear plasticity:

plastic flow only if deformation is large enough

L

L r

LL

L r

video

Interactions with objects

demo

Implementation Details

• Neighbor finding through spatial hashing

• Marching Cube for surface generation

• OpenGL display or offline raytracing

Results

• 20000 particles≈ 2 sec / frame

• 1000 particles≈ 10 FPS

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