Particle-based Viscoelastic Fluid Simulation

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Particle-based ViscoelasticFluid Simulation

• Simon Clavet, Philippe Beaudion, and Pierre
  Poulin
• LIGUM, Dept. IRO, Universite de Montreal
• Eurographics/
• ACM SIGGRAPH Symposium on Computer Animation

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? Particle-based Fluid Simulation? ???? ???
???? ???? ??? elastic? plastic? rest length?
????? Spring?? ??? ? ??? ???? ??? ???? ????
Abstract
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OverView
? Previous work ? Integration scheme ? Density
relaxation ? Viscoelasticity ? Interactions with
objects ? Implementation details, results, and
conclusion
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Previous work
? Grid?? ??

• High-quality liquid animationEnright et al.
  2002
• Viscous, elastic, and plastic materials Goktekin
  et al. 2004

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Previous work
? Particle?? ??

• SPH for highly deformable bodiesDesbrun,
  Gascuel 1996
• Interactive water simulation
• Müller et al. 2003
• Elastic and plastic materialsMüller et al.
  2004

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Integration Scheme
Apply gravity
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Integration Scheme
Apply gravity
and viscosity
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Integration Scheme
Apply gravity
and viscosity
Advance to predicted positions
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Integration Scheme
Apply gravity
and viscosity
Advance to predicted positions
Relax (density and springs)
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Integration Scheme
Apply gravity
and viscosity
Advance to predicted positions
Relax (density and springs)
Obtain new velocities
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Integration Scheme
Apply gravity
and viscosity
Advance to predicted positions
Relax (density and springs)
Obtain new velocities
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Integration Scheme
Apply gravity
and viscosity
Advance to predicted positions
Relax (density and springs)
Obtain new velocities
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? ? ???? ??, - ??? Density? ??? - ?
rest-density? ? ???? ??? ???? ???
Density Relaxation
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? Density ?? ??? ???? ?
Density Relaxation
density kernel
h
r
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? Pseudo-Pressure
Density Relaxation
i
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? Pseudo-Pressure
Density Relaxation
i
i
i
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? Displacement? distance kernen? ??
Density Relaxation
r
h
i
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? ??? ??
Density Relaxation
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? ??? ??
Density Relaxation
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? ????? ?? ????? ??????? rest-length? ??? ?
?? ? Clustering
Density Relaxation
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? ??? ????? ???? ?? ? ?? ?? ??? Density? ???
near-Density? ??
Double Density Relaxation
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near-density kernel (1-r/h)
density kernel (1-r/h)
h
r
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? ? ???? ??, - Density? Near Density? ?? -
Density? near-Density? ???? ? ???? ??? ??
???? ??
Double Density Relaxation
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? ? ???? ??, - Density? Near Density? ?? -
Density? near-Density? ???? ? ???? ??? ??
???? ??
Double Density Relaxation
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? Near-density? zero rest value? ?? ?
Displacement? ?? ??? ?? ??
Double Density Relaxation
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OverView
? Previous work ? Integration scheme ? Density
relaxation ? Viscoelasticity ? Interactions with
objects ? Implementation details, results, and
conclusion
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Elasticity
? ?? ???? ??? Spring? ?? ? rest-length L?
interaction length h? ?? ?, Spring ?? ???
force magnitude
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Plasticity
? ??? rest-length? ???? ? Linear plasticity ?
Non-Linear plasticity - Deformation? ??? ? ????
plastic flow
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Plasticity
? Interaction range h ??? ?? ??, ? ???? ???
Spring? ??? ? ? ???? rest-length? interaction
range h?? ?? ?? ?, Spring? ???
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Interactions with objects
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Interactions with objects
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Implementation Details
? ???? hashing? ?? ???? ?? ? Surface? ?????
?? ? OpenGL display
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Result
? 20,000 paticles 2sec/frame ? 1,000
paticles 10 FPS
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Conclusion
? ????? ??? Particle?? Fluid Simulation? ?? ?
Double density relaxation? ?? Incompressiblity?
?? ?? ?? ? Viscoelasticity? ?? ?? rest-length
spring
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Future Work
? ?? ??? ? ??? ??? Spring? ??? ???? ???? ??