“Simulation of bubbles in foam with the volume control method” by Kim, Liu, Llamas, Jiao and Rossignac

Liquid and gas interactions often produce bubbles that stay for a long time without bursting on the surface, making a dry foam structure. Such long lasting bubbles simulated by the level set method can suffer from a small but steady volume error that accumulates to a visible amount of volume change. We propose to address this problem by using the volume control method. We track the volume change of each connected region, and apply a carefully computed divergence that compensates undesired volume changes. To compute the divergence, we construct a mathematical model of the volume change, choose control strategies that regulate the modeled volume error, and establish methods to compute the control gains that provide robust and fast reduction of the volume error, and (if desired) the control of how the volume changes over time.

1. Bazhlekov, I. B., van De Vosse, F. N., and Meijer, H. E. 2001. Boundary integral method for 3D simulation of foam dynamics. In Lecture Notes in Computer Science, vol. 2179, 401–408. Google ScholarDigital Library
2. Bridson, R., Muller-Fischer, M., Guendelman, E., and Fedkiw, R. 2006. Fluid simulation. In SIGGRAPH 2006 course notes, http://www.cs.ubc.ca/rbridson/fluidsimulation/. Google ScholarDigital Library
3. Carlson, M., Mucha, P. J., and Turk, G. 2004. Rigid fluid: Animating the interplay between rigid bodies and fluid. In ACM SIGGRAPH, 377–384. Google ScholarDigital Library
4. Courant, R., Isaacson, E., and Rees, M. 1952. On the solution of nonlinear hyperbolic differential equations by finite differences. Comm. Pure Appl. Math. 5, 243–255.Google ScholarCross Ref
5. Dupont, T. F., and Liu, Y. 2003. Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function. Journal of Computational Physics 190, 1, 311–324. Google ScholarDigital Library
6. Dupont, T. F., and Liu, Y. 2007. Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations. Math. Comp. 76, 647–668.Google ScholarCross Ref
7. Durian, D. 1997. Bubble-scale model of foam mechanics: Melting, nonlinear behavior, and avalanches. Physical Review E55, 2, 1739–1751.Google Scholar
8. Enright, D., Marschner, S., and Fedkiw, R. 2002. Animation and rendering of complex water surfaces. In ACM SIGGRAPH. Google ScholarDigital Library
9. Enright, D., Losasso, F., and Fedkiw, R. 2005. A fast and accurate semi-lagrangian particle level set method. Computers and Structures 83, 479–490. Google ScholarDigital Library
10. Exerowa, D., and Kruglyakov, P. M. 1998. Foams and Foam Films. Elsevier, ISBN 0-444-81922-3.Google Scholar
11. Fedkiw, R., Stam, J., and Jensen, H. 2001. Visual simulation of smoke. In ACM SIGGRAPH, 23–30. Google ScholarDigital Library
12. Feldman, B. E., O’Brien, J. F., and Arikan, O. 2003. Animating suspended particle explosions. In ACM SIGGRAPH, 708–715. Google ScholarDigital Library
13. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In ACM SIGGRAPH, 15–22. Google ScholarDigital Library
14. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graphical Models and Image Processing 58, 5, 471–483. Google ScholarDigital Library
15. Goktekin, T. G., Bargteil, A. W., and O’Brien, J. F. 2004. A method for animating viscoelastic fluids. In ACM SIGGRAPH, 463–468. Google ScholarDigital Library
16. Greenwood, S., and House, D. 2004. Better with bubbles: Enhancing the visual realism of simulated fluid. In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 287–296. Google ScholarDigital Library
17. Guendelman, E., Selle, A., Losasso, F., and Fedkiw, R. 2005. Coupling water and smoke to thin deformable and rigid shells. In ACM SIGGRAPH. Google ScholarDigital Library
18. Haario, H., Korotkaya, Z., Luukka, P., and Smolianski, A. 2004. Computational modelling of complex phenomena in bubble dynamics: Vortex shedding and bubble swarms. In Proceedings of ECCOMAS 2004.Google Scholar
19. Hong, J.-M., and Kim, C.-H. 2005. Discontinuous fluids. In ACM SIGGRAPH. Google ScholarDigital Library
20. Kang, M., Fedkiw, R. P., and Liu, X.-D. 2000. A boundary condition capturing method for multiphase incompressible flow. Journal of Scientific Computing 15, 3 (Sep). Google ScholarDigital Library
21. Kass, M., and Miller, G. 1990. Rapis stable fluid dynamics for computer graphics. In ACM SIGGRAPH, 49–57. Google ScholarDigital Library
22. Kim, B., Liu, Y., Llamas, I., and Rossignac, J. 2005. FlowFixer: Using BFECC for fluid simulation. In Eurographics Workshop on Natural Phenomena. Google ScholarCross Ref
23. Kück, H. Vogelgsang, C., and Greiner, G. 2002. Simulation and rendering of liquid foams. In Proceedings of Graphics Interface, 81–88.Google Scholar
24. Kumar, A. V., and Lee, J. 2006. Step function representation of solid models and application to mesh free engineering analysis. Journal of Mechanical Design 128, 46–56.Google ScholarCross Ref
25. Lorensen, W. E., and Cline, H. E. 1987. Marching cubes: A high resolution 3D surface construction algorithm. In ACM SIGGRAPH, 163–169. Google ScholarDigital Library
26. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. In ACM SIGGRAPH, 457–462. Google ScholarDigital Library
27. Losasso, F., Irving, G., Guendelman, E., and Fedkiw, R. 2006. Melting and burning solids into liquids and gases. IEEE Transactions on Visualization and Computer Graphics 12, 343–353. Google ScholarDigital Library
28. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. In ACM SIGGRAPH, 812–819. Google ScholarDigital Library
29. Mihalef, V., Unlusu, B., Sussman, M., and Metaxas, D. 2006. Physically based boiling simulation. In ACM Siggraph/Eurographics Symposium in Computer Animation. Google ScholarDigital Library
30. Muller, M., Solenthaler, B., Keiser, R., and Gross, M. 2005. Particle-based fluid-fluid interaction. In Proceedings of SIGGRAPH’05 Symposium on Computer Animation, 237–244. Google ScholarDigital Library
31. Nils Thurey, U. R. 2004. Free surface lattice-boltzmann fluid simulations with and without level sets. In Workshop on Vision, Modeling, and Visualization.Google Scholar
32. O’Brien, J., and Hodgins, J. 1995. Dynamic simulation of splashing fluids. In IEEE Computer Animation, 198–205. Google ScholarDigital Library
33. Osher, S. J., and Fedkiw, R. P. 2002. Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, ISBN 0-387-95482-1.Google Scholar
34. Osher, S., and Sethian, J. A. 1988. Fronts propagating with curvature-dependent speed: Algorithms based on hamilton-jacobi formulations. Journal of Computational Physics 79, 12–49. Google ScholarDigital Library
35. Park, S. I., and Kim, M. J. 2005. Vortex fluid for gaseous phenomena. In Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
36. Pohl, T., Deserno, F., Thurey, N., Rude, U., Lammers, P., Wellein, G., and Zeiser, T. 2004. Performance evaluation of parallel large-scale lattice boltzmann applications on three supercomputing architectures. In Supercomputing, 2004. Proceedings of the ACM/IEEE SC2004 Conference. Google ScholarDigital Library
37. Prud’home, R. K., and Khan, S. A. 1996. Foams: Theory, Measurements, and Applications. Marcel Dekker, Inc, ISBN 0-8247-9395-1.Google Scholar
38. Schreiner, J., Scheidegger, C., and Silva, C. 2006. High-quality extraction of isosurfaces from regular and irregular grids. IEEE Transactions on Visualization and Computer Graphics 12, 5, 1205–1212. Google ScholarDigital Library
39. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In ACM SIGGRAPH. Google ScholarDigital Library
40. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. 2007. An unconditionally stable MacCormack method. J. Sci. Comput. (in review). Google ScholarDigital Library
41. Sethian, J. A. 1999. Level Set Methods and Fast Marching Methods. Cambridge University Press, ISBN 0-521-64557-3.Google Scholar
42. Shi, L., and Yu, Y. 2004. Visual smoke simulation with adaptive octree refinement. In Computer Graphics and Imaging.Google Scholar
43. Shinners, S. M. 1978. Modern Control System Theory and Application. Addison Wesley. Google ScholarDigital Library
44. Song, O., Shin, H., and Ko, H. 2005. Stable but nondissipative water. ACM Transactions on Graphics 24, 1, 81–97. Google ScholarDigital Library
45. Stam, J. 1999. Stable fluids. In ACM SIGGRAPH, 121–128. Google ScholarDigital Library
46. Stubenrauch, C., and von Klitzing, R. 2003. Disjoining pressure in thin liquid foam and emulsion films – new concepts and perspective. Journal of Physics Condensed Matter 15, 3–4, 173–181.Google ScholarCross Ref
47. Sussman, M., Smereka, P., and Osher, S. 1994. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 114, 1, 146–159. Google ScholarDigital Library
48. Sussman, M. 2003. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles. Journal of Computational Physics 187, 110–136. Google ScholarDigital Library
49. Takahashi, T., Fujii, H., Kunimatsu, A., Hiwada, K., Saito, T., Tanaka, K., and Ueki, H. 2003. Realistic animation of fluid with splash and foam. In EUROGRAPHICS, vol. 22.Google Scholar
50. Tsai, Y.-H. R., Cheng, L.-T., Osher, S., and Zhao, H.-K. 2001. Fast sweeping algorithms for a class of hamilton-jacobi equations. Tech. Rep. 01–27, University of California, Los Angeles, http://www.math.ucla.edu/applied/cam/index.html.Google Scholar
51. Wang, H., Mucha, P. J., and Turk, G. 2005. Water drops on surfaces. In ACM SIGGRAPH. Google ScholarDigital Library
52. Weaire, D., and Hutzler, S. 1999. The Physics of Foams. Oxford, ISBN 0-19-851097-7.Google Scholar
53. Zheng, W., Yong, Y.-H., and Paul, J.-C. 2006. Simulation of bubbles. In ACM Siggraph/Eurographics Symposium in Computer Animation. Google ScholarDigital Library