particle-based fluid-fluid interaction
DESCRIPTION
Particle-Based Fluid-Fluid Interaction. Matthias Müller, Barbara Solenthaler, Richard Keiser, Markus Gross. Eurographics /ACM SIGGRAPH Symposium on Computer Animation (2005),. Abstract. Propose a new technique to model fluid-fluid interaction based on Smoothed Particle Hydrodynamics(SPH) - PowerPoint PPT PresentationTRANSCRIPT
PARTICLE-BASED FLUID-FLUID INTERACTION
Matthias Müller, Barbara Solenthaler, Richard Keiser, Markus Gross
Eurographics/ACM SIGGRAPH Sympo-sium on Computer Animation (2005),
2
ABSTRACT Propose a new technique to model fluid-
fluid interaction based on Smoothed Parti-cle Hydrodynamics(SPH)
Air-water interaction Air particles are generated only where needed
The simulation of various phenomena Boiling water Trapped air The dynamics of lava lamp
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INTRODUCTION Fluid-solid interaction
Fluids with solid boundaries plays a major role In order to keep fluids in place (ex. tank)Has been addressed in many papers
Mutual interaction of different kinds of fluids Interesting phenomena
In boiling water, A liquid interacts with a gas When water flows into a glass, air pockets get
trapped in the fluid and form bubbles In a lava lamp, two types of fluids interact
But has not received as much attention in CG
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INTRODUCTION (CON’D) With Eulerian, grid-based methods
The simulation of multiple fluids or multiple phases is a difficult problem
With a particle methodEach particle have own attributesProperties can be mixed arbitrarilyEasily generated and deleted dynamically
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CONTRIBUTIONS Multiple fluids
Simulate fluids with different particle typesParameters are stored on each particleExtend the equations
Trapped airSimulate trapped air by generating air par-
ticle dynamically Isolated air particles are deleted
Phase transitionBoiling water is modeled by changing the
types and densities of particles dynamically
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RELATED WORK (1/9) Introduce fluid simulation to CG
Realistic animation of liquids [FOSTER et al. 99]
Stable semi-Lagrangian advectionStable fluid [STAM 99]
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RELATED WORK (2/9) Level set methods to track the liquid
surfacePractical animation of liquids[FOSTER et al.
01]Animation and rendering of complex water
surfaces [ENRIGHT et al. 02]
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RELATED WORK (3/9) Fluid solid interaction in the Eulerian
settingRigid fluid: animating the interplay between
rigid bodies and fluid [CARLSON et al. 04]
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RELATED WORK (4/9) Multiphase fluid and bubbles
Eulerian approach is a difficult problemDirect numerical simulations of three-di-
mensional bubbly flows [BUNNER et al. 99]Simulation of a cusped bubble rising in a
viscoelastic fluid with a new numerical method [WAGNER et al. 00]
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RELATED WORK (5/9) Simpler method to simulate bubbles
Better with bubbles: enhancing the visual realism of simulated fluid [GREENWOOD et al. 04] Generate passive air-particle and advect them
using the Eulerian velocity field One-way coupling method
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RELATED WORK (6/9) Volume of fluid method(VOF)
Animation of bubbles in liquid [HONG et al. 03] Smaller bubbles are simulated using a passive
particle system
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RELATED WORK (7/9) Lagrangian, particle-based fluid models
Allow the seamless modeling of fine to large scale fluid-fluid interaction phenomena
Most models are based on the SPH formula-tion
Animate highly deformable solid objectsSmoothed particles: A new paradigm for an-
imating highly deformable bodies [DESBRUN et al. 96]
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RELATED WORK (8/9) Lava
Animating lava flows [STORA et al. 99]
Fluid simulation Particle-based fluid
simulation for interac-tive application [MÜLLER et al. 03]
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RELATED WORK (9/9) Method for fluid-solid interaction
Interaction of fluids with deformable solids [MÜLLER et al. 04]
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SPH MODEL (1/4) A fluid is represented by a set of parti-
clesEach Particle have position xi, mass mi, ad-
ditional attribute Ai
Define how to compute smooth continu-ous field A(x)
ρi is the density of particle iW(r,h) is a smoothing kernel
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SPH MODEL (2/4) Compute density ρi
W(r,h) is typically a smooth, radially sym-metric, normalized function
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SPH MODEL (3/4) Gradient and Laplacian of A(x)
Compute particle body forces
rij is the distance vector xi-xj
pi = k(ρi – ρ0)
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SPH MODEL (4/4) Navier-Stokes equation
Conservation of massConservation of momentum
Navier-Stokes equation for particle sys-tem
PressureExternal forces
Viscosity
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MULTIPLE FLUIDS Standard approach for a single fluid,
many attributes are stored globally (e.g. m, ρ0)
New approach for multiple fluids, Each particle carries all attributes individually
Modify viscosity force Eq.
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INTERACTION METHOD- BOUYANCY The parameter ρ0 is defined per particle pi = k(ρi – ρ0)
Two fluids mixed
Density gradient
Pressure gradient
Less dense fluid to rise inside the
denser fluid
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INTERACTION METHOD-IMMISCIBLE LIQUIDS Water and oil are immiscible
Water molecules are polar, oil molecules are not
The energy of bonded water molecules in cluster is lower than the energy of single water molecules dispersed
Interface body forceLiquids trying to minimize the curvature κProportional to κ and the interface tension
coefficient σi
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INTERACTION METHOD-IMMISCIBLE LIQUIDS (CON’D) Color attribute setting
Normal on the interfacen = ∇ci
Curvature κκ = -∇2ci/|n|
liquid 2
liquid 1Surface
Interface
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INTERACTION METHOD-DIFFUSION Diffusion equation
Describes how heat gets distributed in a fluid
Integrate the attribute using Euler scheme
Temperature influence the rest density
SPH for-malism
(α : user defined constant)
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INTERACTION METHOD-TRAPPED AIR Standard SPH approach
Air is not explicitly modeled Trapped air will immediately disappear
TrialExplicitly simulate air as a separate fluidBut large number of air particles is needed
SolutionGenerate air particles whenever bubbles
are about to be formed and to delete the particles when they don’t contribute to the simulation anymore
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AIR PARTICLE GENERA-TION Air particle need to be generated near
the surface of liquidThe gradient of the cs field is large
The generation stops when there are enough air particles Implicit color attribute cp Because only liquid particles generate air
particles, It is enough to test ∇cp
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AIR PARTICLE GENERA-TION (CON’D)
Location of air particle Shifted by the vector -
d∇cp
The velocity of air parti-cle Initialized with the veloc-
ity of the liquid particle Air particle is only a
good candidate for be-ing trapped if it is lo-cated below the liquid front
Air particle
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AIR PARTICLE DELETION Delete air particles whose ∇cs is suffi-
ciently small Problem 1
Air particles inside large trapped bubbles get deleted
Testing whether ∇cp is larger than threshold Problem 2
Isolated strayed air particles Checking whether actual density get below
threshold
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ARTIFICIAL BUOYANCY The density of water is about a thou-
sand times the density of airLarge ratio can cause stability problems
Rest density in demoWater 1000kg/m3, Air : 100 kg/m3
Ratio 10,bubbles to rise more slowly in wa-ter
The SPH is not suited for small air bub-bles
Introduce an artificial buoyancy force
g is gravity and b a user parameter air
water
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RESULT (1/3) Diffusion effect
Lava lamp
Simulation time 11fps , rendering 3min per frame4800 blue, 1200 red particles
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RESULT (2/3) Pouring water into a glass
3000 water particle400 air particle
Simulation : 18~40 fpsRendering : 8min per frame
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RESULT (3/3) Boiling water
Bubbles form first on solid surface in con-tact with the liquid at cavitation sites
5500 water particles & 3000 flame particlesSimulation 8 fps, rendering 5min per frame
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CONCLUSIONS AND FU-TURE WORK Enhance particle based fluid simulation Particles are particularly well suited for
modeling the interaction of different types of fluids and phase transitions
Particles can be generated and deleted dynamically
Limitation of the SPH approachSingle particles or badly sampled dropletsProposed a technique to circumvent the
problemDifferent ways such as bilateral filtering