1. Matthias Müller, Barbara Solenthaler, Richard Keiser, Markus Gross Eurographics/ACM SIGGRAPH Symposium on Computer Animation (2005),

2.  Propose a new technique to model fluid-fluid interaction based on Smoothed Particle 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 2

3.  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 3

4.  With Eulerian, grid-based methods  The simulation of multiple fluids or multiple phases is a difficult problem  With a particle method  Each particle have own attributes  Properties can be mixed arbitrarily  Easily generated and deleted dynamically 4

5.  Multiple fluids  Simulate fluids with different particle types  Parameters are stored on each particle  Extend the equations  Trapped air  Simulate trapped air by generating air particle dynamically  Isolated air particles are deleted  Phase transition  Boiling water is modeled by changing the types and densities of particles dynamically 5

6.  Introduce fluid simulation to CG  Realistic animation of liquids [FOSTER et al. 99]  Stable semi-Lagrangian advection  Stable fluid [STAM 99] 6

7.  Level set methods to track the liquid surface  Practical animation of liquids[FOSTER et al. 01]  Animation and rendering of complex water surfaces [ENRIGHT et al. 02] 7

8.  Fluid solid interaction in the Eulerian setting  Rigid fluid: animating the interplay between rigid bodies and fluid [CARLSON et al. 04] 8

9.  Multiphase fluid and bubbles  Eulerian approach is a difficult problem  Direct numerical simulations of three- dimensional 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] 9

10.  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 10

11.  Volume of fluid method(VOF)  Animation of bubbles in liquid [HONG et al. 03] Smaller bubbles are simulated using a passive particle system 11

12.  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 formulation  Animate highly deformable solid objects  Smoothed particles: A new paradigm for animating highly deformable bodies [DESBRUN et al. 96] 12

13.  Lava  Animating lava flows [STORA et al. 99]  Fluid simulation  Particle-based fluid simulation for interactive application [MÜLLER et al. 03] 13

14.  Method for fluid-solid interaction  Interaction of fluids with deformable solids [MÜLLER et al. 04] 14

15.  A fluid is represented by a set of particles  Each Particle have position x i, mass m i, additional attribute A i  Define how to compute smooth continuous field A(x)  ρ i is the density of particle i  W(r,h) is a smoothing kernel 15

16.  Compute density ρ i  W(r,h) is typically a smooth, radially symmetric, normalized function 16

17.  Gradient and Laplacian of A(x)  Compute particle body forces  r ij is the distance vector x i -x j  p i = k(ρ i – ρ 0 ) 17

18.  Navier-Stokes equation  Conservation of mass  Conservation of momentum  Navier-Stokes equation for particle system 18 Pressure External forces Viscosity

19.  Standard approach for a single fluid, many attributes are stored globally (e.g. m, ρ 0 )  New approach for multiple fluids, Each particle carries all attributes individually  Modify viscosity force Eq. 19

20.  The parameter ρ 0 is defined per particle  p i = k(ρ i – ρ 0 ) 20 Two fluids mixed Density gradient Pressure gradient Less dense fluid to rise inside the denser fluid

21.  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 force  Liquids trying to minimize the curvature κ  Proportional to κ and the interface tension coefficient σ i 21

22.  Color attribute setting  Normal on the interface  n = ∇ c i  Curvature κ  κ = - ∇ 2 c i /|n| 22 liquid 2 liquid 1 Surface Interface

23.  Diffusion equation  Describes how heat gets distributed in a fluid  Integrate the attribute using Euler scheme  Temperature influence the rest density 23 SPH formalism (α : user defined constant)

24.  Standard SPH approach  Air is not explicitly modeled  Trapped air will immediately disappear  Trial  Explicitly simulate air as a separate fluid  But large number of air particles is needed  Solution  Generate air particles whenever bubbles are about to be formed and to delete the particles when they don’t contribute to the simulation anymore 24

25.  Air particle need to be generated near the surface of liquid  The gradient of the c s field is large  The generation stops when there are enough air particles  Implicit color attribute c p  Because only liquid particles generate air particles, It is enough to test ∇ c p 25

26.  Location of air particle  Shifted by the vector -d ∇ c p  The velocity of air particle  Initialized with the velocity of the liquid particle  Air particle is only a good candidate for being trapped if it is located below the liquid front 26 Air particle

27.  Delete air particles whose ∇ c s is sufficiently small  Problem 1  Air particles inside large trapped bubbles get deleted  Testing whether ∇ c p is larger than threshold  Problem 2  Isolated strayed air particles  Checking whether actual density get below threshold 27

28.  The density of water is about a thousand times the density of air  Large ratio can cause stability problems  Rest density in demo  Water 1000kg/m 3, Air : 100 kg/m 3  Ratio 10,bubbles to rise more slowly in water  The SPH is not suited for small air bubbles  Introduce an artificial buoyancy force  g is gravity and b a user parameter 28 air water

29.  Diffusion effect  Lava lamp 29 Simulation time 11fps, rendering 3min per frame4800 blue, 1200 red particles

30.  Pouring water into a glass 30 3000 water particle 400 air particle Simulation : 18~40 fps Rendering : 8min per frame

31.  Boiling water  Bubbles form first on solid surface in contact with the liquid at cavitation sites  5500 water particles & 3000 flame particles  Simulation 8 fps, rendering 5min per frame 31

32.  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 approach  Single particles or badly sampled droplets  Proposed a technique to circumvent the problem  Different ways such as bilateral filtering 32