Realistic Simulation of Foam

1. Realistic Simulation of Foam CSE 788.14 Midterm Presentation Oleksiy Busaryev

2. Foam physics • Foams minimize area under volume constraints • Foam equilibrium described by Plateau’s Laws: • three films meet at 120 at edges • four edges meet at 109.47  at angles • films have constant mean curvature • Laplace-Young Law: p = 2H • Optical effects: most of the fluid is in Plateau Borders dry wet

3. Particle-based simulation • “Simulation and Rendering of Liquid Foams”, GI ’02 • Bubbles = interacting spheres • Forces acting on bubbles: • 1st order ODE for bubble positions • For rendering, average intersections

4. Particle foam + level set fluid • “Better with Bubbles”, SCA ’04 • Add bubbles to particle level set fluid • Escaped air particles create bubbles • Additional rendering issues • How to flatten bubbles? • Signed distance should be updated carefully  • Residual air pockets can form 

5. Implicit boundary simulation • “Simulation of Bubbles”, SCA ’06 • Particle bubbles cannot deform  • Level set method loses thin details  • Solution: regional level set • Use regional scalar function: • Unified film thickness change • Semi-implicit surface tension • Efficient method for multi-manifold interface tracking

6. Implicit + no volume loss • “Simulation of Bubbles in Foam With The Volume Control Method”, SIGGRAPH ’07 • Track volume of each fluid region • Apply divergence to compensate for possible volume error • Can be used to change fluid volume (inflate/deflate bubbles) • Bubbles of varying sizes are expensive to maintain 

7. Explicit boundary simulation • “Numerical simulations of two-dimensional foam by the immersed boundary method”, JCP ’10 • Gas = incompressible fluid • Liquid films = network of permeable boundaries • Tension force normal to film

8. Explicit + topology changes • “The immersed boundary method for two-dimensional foam with topological changes”, accepted to CCP. • >3 order junctions are unstable, resolve to 3-junctions • In 2D two atomic changes: T1, T2 • Diffusive coarsening:

9. Our Plan • Explore the particle-based foam simulation method • Can we simulate topology changes/diffusive coarsening? • How to model fluid draining & bubble rupture/merging correctly? • Come up with better model of repulsive/attractive forces • Coupling foams with fluids • Can fluid & foam be simulated on the same grid (e.g. Voronoi)? • If not, should the bubble particles be passive or active? • Coupling foams with solids • How simulate the bubble deformation when touching solids? • Rendering • For large number of bubbles, can we avoid full processing?

10. Tentative timeline • Week 4 (Oct 10-Oct 16) • Implement and experiment with 2D particle foam model • Week 5 (Oct 17-Oct 23) • Come up with physical model for fluid draining • Week 6 (Oct 24-Oct 30) • Experiment with diffusive coarsening/bubble merging • Week 7-8 (Oct 31-Nov 13) • Couple the foam model with a fluid simulator • Week 9-10 (Nov 14-Nov 27) • Convert the simulation to 3D, come up with a rendering model

11. Underlying Fluid Simulation • Use grid-based level set method • Tricubic interpolation for signed distance • Staggered MAC grid • Semi Lagr. advection • NOreinitialization yet • Conjugate gradient • PBRT for rendering

12. Spring-Mass Model for Bubbles • Resting length based on Plateau Laws • d2 = r2 + R2 – rR, so bubbles meet at 120 • Stiff springs => implicit integration • Conjugate gradient to solve the system

13. Voronoi Diagram • How to determine if two bubbles interact? • Simple intersection test is not good  • Interact if share Voronoi edge and intersect

14. Weak attractive force • Attracts bubble on the fluid surface • Caused by liquid surface inclination • Acts if share Voronoi edge but not intersect

15. Coupling with Fluid • Spring force on the surface • Buoyancy in fluid • Gravity in air