Fluid simulation: SIGGRAPH 2006 course notes (Fedkiw and Muller-Fischer presenation videos are available from the citation page)

ABSTRACT

These course notes are designed to give you a practical introduction to fluid simulation for graphics. The field of fluid dynamics, even just in animation, is vast and so not every topic will be covered. The focus of these notes is animating fully three-dimensional incompressible flow, from understanding the math and the algorithms to actual implementation. However, we will include a small amount of material on heightfield simplifications which are important for real-time animation.In general the approach is to make things as simple as possible, but no simpler. Constructing a fluid solver for computer animation is not the easiest thing in the world--there end up being a lot of little details that need attention-- but is perhaps easier than it may appear from surveying the literature. We will also provide pointers to some more advanced topics here and there.

References

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2. {Bat67} G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press, 1967.
3. {BB06} Christopher Batty and Robert Bridson. Accurate irregular boundaries in fluid simulation. In preparation, 2006.
4. {BR86} J. U. Brackbill and H. M. Ruppel. FLIP: a method for adaptively zoned, particle-in-cell calculuations of fluid flows in two dimensions. J. Comp. Phys., 65:314--343, 1986.
5. {Cor05} Richard Corbett. Point-based level sets and progress towards unorganised particle based fluids. Master's thesis, UBC Dept. Computer Science, 2005.
6. {EFFM02} D. Enright, R. Fedkiw, J. Ferziger, and I. Mitchell. A hybrid particle level set method for improved interface capturing. J. Comp. Phys., 183:83--116, 2002.
7. {EMF02} Douglas Enright, Stephen Marschner, and Ronald Fedkiw. Animation and rendering of complex water surfaces. ACM Trans. Graph. (Proc. SIGGRAPH), 21(3):736--744, 2002.
8. {FF01} Nick Foster and Ronald Fedkiw. Practical animation of liquids. In Proc. SIGGRAPH, pages 23--30, 2001.
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10. {FSJ01} R. Fedkiw, J. Stam, and H. Jensen. Visual simulation of smoke. In Proc. SIGGRAPH, pages 15--22, 2001.
11. {GBO04} Tolga G. Goktekin, Adam W. Bargteil, and James F. O'Brien. A method for animating viscoelastic fluids. ACM Trans. Graph. (Proc. SIGGRAPH), 23:463--468, 2004.
12. {GFCK02} F. Gibou, R. Fedkiw, L.-T. Cheng, and M. Kang. A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. J. Comp. Phys., 176:205--227, 2002.
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14. {HBW03} Ben Houston, Chris Bond, and Mark Wiebe. A unified approach for modeling complex occlusions in fluid simulations. In ACM SIGGRAPH Technical Sketches, 2003
15. {HK05} Jeong-Mo Hong and Chang-Hun Kim. Discontinuous fluids. ACM Trans. Graph. (Proc. SIGGRAPH), 24:915--920, 2005.
16. {HNB+06} Ben Houston, Michael B. Nielsen, Christopher Batty, Ola Nilsson, and Ken Museth. Hierarchical rle level set: A compact and versatile deformable surface representation. ACM Trans. Graph., 2006.
17. {HNC02} D. Hinsinger, F. Neyret, and M.P. Cani. Interactive animation of ocean waves. In Proc. ACM SIGGRAPH/Eurographics Symp. Comp. Anim., pages 161--166, 2002.
18. {HW65} F. Harlow and J. Welch. Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface. Phys. Fluids, 8:2182--2189, 1965.
19. {JBS06} M. Jones, A. Baerentzen, and M. Sramek. 3D distance fields: A survey of techniques and applications. IEEE Trans. Vis. Comp. Graphics, 2006.
20. {Jef03} A. Jeffrey. Applied Partial Differential Equations. Academic Press, 2003.
21. {LGF04} F. Losasso, F. Gibou, and R. Fedkiw. Simulating water and smoke with an octree data structure. ACM Trans. Graph. (Proc. SIGGRAPH), 23:457--462, 2004.
22. {MCG03} Matthias Muller, David Charypar, and Markus Gross. Particle-based fluid simulation for interactive applications. In Proc. ACM SIGGRAPH/Eurographics Symp. Comp. Anim., pages 154--159, 2003.
23. {Mon92} J. J. Monaghan. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys., 30:543--574, 1992.
24. {NFJ02} Duc Quang Nguyen, Ronald Fedkiw, and Henrik Wann Jensen. Physically based modeling and animation of fire. ACM Trans. Graph. (Proc. SIGGRAPH), pages 721--728, 2002.
25. {OF02} S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, 2002. New York, NY.
26. {OH95} J. O'Brien and J. Hodgins. Dynamic simulation of splashing fluids. In Computer Animation, pages 198--205, 1995.
27. {PTB+03} Simon Premoze, Tolga Tasdizen, James Bigler, Aaron Lefohn, and Ross Whitaker. Particle--based simulation of fluids. In Comp. Graph. Forum (Eurographics Proc.), volume 22, pages 401--410, 2003.
28. {REN+04} N. Rasmussen, D. Enright, D. Nguyen, S. Marino, N. Sumner, W. Geiger, S. Hoon, and R. Fedkiw. Directible photorealistic liquids. In Proc. ACM SIGGRAPH/Eurographics Symp. Comp. Anim., pages 193--202, 2004.
29. {Set96} J. Sethian. A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci., 93:1591--1595, 1996.
30. {SRF05} Andrew Selle, Nick Rasmussen, and Ronald Fedkiw. A vortex particle method for smoke, water and explosions. ACM Trans. Graph. (Proc. SIGGRAPH), pages 910--914, 2005.
31. {Sta99} Jos Stam. Stable fluids. In Proc. SIGGRAPH, pages 121--128, 1999.
32. {Tsa02} Yen-Hsi Richard Tsai. Rapid and accurate computation of the distance function using grids. J. Comput. Phys., 178(1):175--195, 2002.
33. {Tsi95} J. Tsitsiklis. Efficient algorithms for globally optimal trajectories. IEEE Trans. on Automatic Control, 40:1528--1538, 1995.
34. {WMT05} Huamin Wang, Peter J. Mucha, and Greg Turk. Water drops on surfaces. ACM Trans. Graph. (Proc. SIGGRAPH), pages 921--929, 2005.
35. {ZB05} Yongning Zhu and Robert Bridson. Animating sand as a fluid. ACM Trans. Graph. (Proc. SIGGRAPH), pages 965--972, 2005.
36. {Zha05} Hongkai Zhao. A fast sweeping method for Eikonal equations. Math. Comp., 74:603--627, 2005.

Index Terms

• Applied computing

  • Document management and text processing

    • Document capture

      • Graphics recognition and interpretation

• Computing methodologies

  • Artificial intelligence

    • Computer vision

      • Image and video acquisition

        • 3D imaging

  • Computer graphics

    • Animation

  • Modeling and simulation

    • Simulation types and techniques

      • Simulation by animation