Slide 1

Matthias Mller, Barbara Solenthaler, Richard Keiser, Markus Gross Eurographics/ACM SIGGRAPH Symposium on Computer Animation (2005), Slide 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 Slide 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 Slide 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 Slide 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 Slide 6 Introduce fluid simulation to CG Realistic animation of liquids [FOSTER et al. 99] Stable semi-Lagrangian advection Stable fluid [STAM 99] 6 Slide 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 Slide 8 Fluid solid interaction in the Eulerian setting Rigid fluid: animating the interplay between rigid bodies and fluid [CARLSON et al. 04] 8 Slide 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 Slide 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 Slide 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 Slide 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 Slide 13 Lava Animating lava flows [STORA et al. 99] Fluid simulation Particle-based fluid simulation for interactive application [MLLER et al. 03] 13 Slide 14 Method for fluid-solid interaction Interaction of fluids with deformable solids [MLLER et al. 04] 14 Slide 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) i is the density of particle i W(r,h) is a smoothing kernel 15 Slide 16 Compute density i W(r,h) is typically a smooth, radially symmetric, normalized function 16 Slide 17 Gradient and Laplacian of A(x) Compute particle body forces r ij is the distance vector x i -x j p i = k( i 0 ) 17 Slide 18 Navier-Stokes equation Conservation of mass Conservation of momentum Navier-Stokes equation for particle system 18 Pressure External forces Viscosity Slide 19 Standard approach for a single fluid, many attributes are stored globally (e.g. m, 0 ) New approach for multiple fluids, Each particle carries all attributes individually Modify viscosity force Eq. 19 Slide 20 The parameter 0 is defined per particle p i = k( i 0 ) 20 Two fluids mixed Density gradient Pressure gradient Less dense fluid to rise inside the denser fluid Slide 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 Proportional to and the interface tension coefficient i 21 Slide 22 Color attribute setting Normal on the interface n = c i Curvature = - 2 c i /|n| 22 liquid 2 liquid 1 Surface Interface Slide 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 ( : user defined constant) Slide 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 dont contribute to the simulation anymore 24 Slide 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 Slide 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 Slide 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 Slide 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 Slide 29 Diffusion effect Lava lamp 29 Simulation time 11fps, rendering 3min per frame4800 blue, 1200 red particles Slide 30 Pouring water into a glass 30 3000 water particle 400 air particle Simulation : 18~40 fps Rendering : 8min per frame Slide 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 Slide 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