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

3

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

4

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

5

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

6

RELATED WORK (1/9) Introduce fluid simulation to CG

Realistic animation of liquids [FOSTER et al. 99]

Stable semi-Lagrangian advectionStable fluid [STAM 99]

7

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]

8

RELATED WORK (3/9) Fluid solid interaction in the Eulerian

settingRigid fluid: animating the interplay between

rigid bodies and fluid [CARLSON et al. 04]

9

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]

10

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

11

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

12

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]

13

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]

14

RELATED WORK (9/9) Method for fluid-solid interaction

Interaction of fluids with deformable solids [MÜLLER et al. 04]

15

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

16

SPH MODEL (2/4) Compute density ρi

W(r,h) is typically a smooth, radially sym-metric, normalized function

17

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)

18

SPH MODEL (4/4) Navier-Stokes equation

Conservation of massConservation of momentum

Navier-Stokes equation for particle sys-tem

PressureExternal forces

Viscosity

19

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.

20

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

21

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

22

INTERACTION METHOD-IMMISCIBLE LIQUIDS (CON’D) Color attribute setting

Normal on the interfacen = ∇ci

Curvature κκ = -∇2ci/|n|

liquid 2

liquid 1Surface

Interface

23

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)

24

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

25

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

26

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

27

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

28

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

29

RESULT (1/3) Diffusion effect

Lava lamp

Simulation time 11fps , rendering 3min per frame4800 blue, 1200 red particles

30

RESULT (2/3) Pouring water into a glass

3000 water particle400 air particle

Simulation : 18~40 fpsRendering : 8min per frame

31

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

32

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