Coupling Water and Smoke to Thin Deformable and Rigid Shells Eran Guendelman 1,2 Andrew Selle 1,3...
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Coupling Water and Smoke to Thin Deformable and Rigid Shells
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
1Stanford University, 2Industrial Light + Magic, 3Intel Corporation
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MotivationMotivation
• Fluid simulation becoming more common
– Engineering, biomedicine, entertainment
• Want interaction with thin solids
– Parachutes
– Cardiovascular simulation
– CG characters w/clothing
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GoalGoal
• Two-way coupling between:
– Smoke or free-surface water
– Thin rigid and deformable open shells
• Prevent leaks across solid
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256x256x192 effective octree; 30k triangles
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Volumetric vs. Thin SolidsVolumetric vs. Thin Solids
Volumetric Thin shell
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Related Work: VolumetricRelated 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]
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Diffuse Interface MethodsDiffuse Interface Methods
• Smear solid onto fluid grid
• e.g. Immersed boundary method [Peskin ‘72]
– Parasitic currents
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Sharp Interface MethodsSharp Interface Methods
• Incorporate jump conditions into stencils
– Ghost fluid method [Fedkiw et al. ’99; Tam et al. ‘05]
– Immersed interface method [LeVeque & Li ’94]
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Our ApproachOur Approach
• Couple using
– Solid velocity & fluid coupling pressure
• Sharp interface treatment
• Prevent leaks using robust ray intersections
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Talk OverviewTalk Overview
• Fluid simulation
• Solid simulation
• Preventing leaks across solid
• Enforcing solid velocity on fluid
• Computing and applying coupling force
• Summary and future work
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Talk OverviewTalk 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
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Fluid SimulationFluid Simulation
• Assume incompressible & inviscid
• Use projection method: [Chorin ’68]
un
Advect un and add gravity ! u*
Project u* ! un+1
un+1
u* violates incompressibility
Compute pressure to enforce incompressibility
(u is fluid velocity)
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Fluid GridFluid Grid
• Uniform & octree grids [Losasso et al. ’04]
• Staggered grid configuration [Harlow & Welch ‘65]
ui+½,j
ui-½,j
vi,j+½
vi,j-½
pi,j
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AdvectionAdvection
• First order semi-Lagrangian [Courant et al. ’52; Stam ‘99]
– Advection on nodes
x-ut
u x
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Particle Level Set MethodParticle Level Set Method
• Level set captures water-air interface
• Particles help correct interface
water
air
[Enright et al. ‘02]
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Water Simulation Step (n!n+1)Water Simulation Step (n!n+1)
un,n
Advance particle level set ! n+1
Advect un and add gravity ! u*
Project u* ! un+1
un+1,n+1
Advect and particles
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Now Add Solids to the Mix…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
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Now Add Solids to the Mix…Now Add Solids to the Mix…
• Black box:
Input: external forces
Output: positions and velocities
[Guendelman et al. ’03] [Bridson et al. ’02,’03]
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Surface QuantitiesSurface Quantities
• Rigid body
– Directly compute
• Deformable body
– Barycentric weights
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Talk OverviewTalk 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
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Key: VisibilityKey: Visibility
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Thin Shell Aware InterpolationThin Shell Aware Interpolation
Check visibility of interpolation nodesUse replacement ghost value when interpolating
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Replacement Ghost ValuesReplacement Ghost Values
Fluid velocity (u)
Level set ()
use solid velocity
average from nearest valid nodes
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Thin Shell Aware AdvectionThin Shell Aware Advection
• Clip semi-Lagrangian rays
u
x-ut
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Crossed Over NodesCrossed Over Nodes
• Represent information from opposite side
• Reassign valid values by averaging
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Thin Shell Aware Fluid StepThin Shell Aware Fluid Step
un,n
Advance particle level set ! n+1
Advect un and add gravity ! u*
Project u* ! un+1
un+1,n+1
Thin shell aware advection( and particles)
Thin shell aware advection (u)
…see paper for more details
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210x140x140 uniform; 30k triangles
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210x140x140 uniform; 30k triangles
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Talk OverviewTalk Overview
• Fluid simulation
• Solid simulation
• Preventing leaks across solid
• Enforcing solid velocity on fluid
• Computing and applying fluid coupling force
• Summary and future work
![Page 30: 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,](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649d645503460f94a46b2f/html5/thumbnails/30.jpg)
Rasterizing SolidRasterizing Solid
• Rasterize onto faces of fluid grid
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Solid Affecting FluidSolid Affecting Fluid
• Solid prescribes velocity on rasterized faces
• Enforce as Neumann boundary conditions in projection step:
Project u* ! un+1
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Which Solid Velocities?Which Solid Velocities?
• At time n+1!n+2, at solid-fluid interface
– Fluid moves with velocity enforced during un+1 projection
– Solid moves from to Xn+1 to Xn+2
• Want these motions to match (reduce mass loss)
• Solution:
– Enforce effective solid velocity: Veff=(Xn+2-Xn+1)/t
![Page 33: 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,](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649d645503460f94a46b2f/html5/thumbnails/33.jpg)
One-Way Coupling StepOne-Way Coupling Step
un,n,Sn,Sn+1
Advance particle level set ! n+1
Advect un and add gravity ! u*
Project u* ! un+1
un+1,n+1,Sn+1,Sn+2
Advance solid ! Sn+2
Enforce effective solid velocities (n+1! n+2) at
solid-fluid interface
(S is the solid’s state)
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160x192x160 effective octree
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192x192x192 effective octree; 60k triangles
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Talk OverviewTalk Overview
• Fluid simulation
• Solid simulation
• Preventing leaks across solid
• Enforcing solid velocity on fluid
• Computing and applying fluid coupling force
• Summary and future work
![Page 37: 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,](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649d645503460f94a46b2f/html5/thumbnails/37.jpg)
Fluid Coupling ForceFluid 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]
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Smoother Coupling PressureSmoother Coupling Pressure
• Treat solid as fluid
• Solve variable density fluid for pc
• Similar to projection step, but:
– Solid velocities not enforced
– Fluid velocities not modified!
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Two Pressure Solves!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
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Must Enforce Solid VelocityMust Enforce Solid Velocity
Enforced!
Enforcing solid velocity
Rigid Fluid [Carlson et al. ’04]
Mass loss
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Computing Force on SolidComputing Force on Solid
• Fluid pressure pushes on both sides
p1
p2
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Computing Force on SolidComputing Force on Solid
• Net force is proportional to pressure jump [pc]
p1 - p2
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Computing Force on SolidComputing Force on Solid
Rasterize solid
Compute coupling pressure
Pressure jumps on faces
Average to nodes
Extrapolate
Interpolate at centroid
Compute force
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Two-Way Coupling StepTwo-Way Coupling Step
un,n,Sn,Sn+1
Advance particle level set ! n+1
Advect un and add gravity ! u*
Advance solid ! Sn+2
Project u* ! un+1
un+1,n+1,Sn+1,Sn+2
Compute coupling pressure and apply force to solid
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148x148x111 uniform; 2.5k triangles
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200x200x200 effective octree; 30k triangles
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256x256x192 effective octree; 30k triangles
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256x256x192 effective octree; 30k triangles
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Talk OverviewTalk Overview
• Fluid simulation
• Solid simulation
• Preventing leaks across solid
• Enforcing solid velocity on fluid
• Computing and applying fluid coupling force
• Summary and future work
![Page 50: 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,](https://reader036.fdocuments.in/reader036/viewer/2022062423/56649d645503460f94a46b2f/html5/thumbnails/50.jpg)
SummarySummary
• 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
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Future WorkFuture Work
• Absorption, adhesion, permeability
• Compare against experiments
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AcknowledgementsAcknowledgements
• Mike Houston, Christos Kozyrakis, Mark Horowitz, Bill Dally, Vijay Pande
• Stanford Graphics Lab
• ONR, ARO, NSF, PECASE, Sloan Foundation, Packard Foundation
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The EndThe End