Particle-Based Fluid-Fluid Interaction

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

2. Abstract • 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

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 method • Each particle have own attributes • Properties can be mixed arbitrarily • Easily generated and deleted dynamically

5. Contributions • 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

6. Related work (1/9) • Introduce fluid simulation to CG • Realistic animation of liquids [FOSTER et al. 99] • Stable semi-Lagrangian advection • Stable fluid [STAM 99]

7. Related Work (2/9) • 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]

8. Related Work (3/9) • Fluid solid interaction in the Eulerian setting • Rigid 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 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]

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 formulation • Animate highly deformable solid objects • Smoothed particles: A new paradigm for animating 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 interactive 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 particles • Each Particle have position xi, mass mi, additional attribute Ai • Define how to compute smooth continuous field A(x) • ρi is the density of particle i • W(r,h) is a smoothing kernel

16. SPH MODEL (2/4) • Compute density ρi • W(r,h) is typically a smooth, radially symmetric, 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 mass • Conservation of momentum • Navier-Stokes equation for particle system Pressure Viscosity Externalforces

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)

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 force • Liquids trying to minimize the curvature κ • Proportional to κ and the interface tension coefficient σi

22. Interaction Method-Immiscible Liquids (con’d) • Color attribute setting • Normal on the interface • n = ∇ci • Curvature κ • κ = -∇2ci/|n| liquid 1 Surface liquid 2 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 formalism (α : user defined constant)

24. Interaction Method-Trapped air • 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

25. Air Particle Generation • Air particle need to be generated near the surface of liquid • The gradient of the csfield 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 Generation (con’d) • Location of air particle • Shifted by the vector -d∇cp • 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 Air particle

27. Air Particle Deletion • Delete air particles whose ∇csis sufficiently 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 thousand times the density of air • Large ratio can cause stability problems • Rest density in demo • Water 1000kg/m3, Air : 100 kg/m3 • 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 water air

29. Result (1/3) • Diffusion effect • Lava lamp 4800 blue, 1200 red particles Simulation time 11fps , rendering 3min per frame

30. Result (2/3) • Pouring water into a glass 3000 water particle 400 air particle Simulation : 18~40 fps Rendering : 8min per frame

31. Result (3/3) • 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

32. Conclusions and Future 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 approach • Single particles or badly sampled droplets • Proposed a technique to circumvent the problem • Different ways such as bilateral filtering