Chapter 9: Discrete, vorticity-preserving, and stable simplicial fluids

ACM SIGGRAPH 2005 Courses, SIGGRAPH 2005

Volumn , Issue , 2005, Pages

  Elcott, Sharif ^b   Tong, Yiying ^b   Kanso, Eva ^a   Schröder, Peter ^b   Desbrun, Mathieu ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b NONE

Author keywords

Circulation preservation; Computational algorithms; Fluid dynamics discrete exterior calculus

Indexed keywords

ANIMATION; CALCULATIONS; COMPUTER GRAPHICS; DIFFUSION IN LIQUIDS; INTERACTIVE COMPUTER GRAPHICS; NUMERICAL METHODS; VORTICITY;

COMPLEX SIMULATION; COMPUTATIONAL ALGORITHM; COMPUTATIONAL COSTS; COMPUTER ANIMATION; DIFFERENTIAL PROPERTIES; DISCRETE EXTERIOR CALCULUS; DISCRETE OPERATORS; NUMERICAL DIFFUSION;

FLOW OF FLUIDS;

EID: 84921982526     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1198555.1198668     Document Type: Conference Paper

References (33)

1. ABRAHAM, R., MARSDEN, J., AND RATIU, T., Eds. 1988. Manifolds, Tensor Analysis, and Applications. Applied Mathematical Sciences Vol. 75, Springer.
2. BOSSAVIT, A., AND KETTUNEN, L. 1999. Yee-like schemes on a tetrahedral mesh. Int. J. Num. Modelling: Electr. Networks, Dev. and Fields 12(July), 129-142.
3. BOSSAVIT, A. 1998. Computational Electromagnetism. Academic Press, Boston.
4. CHORIN, A., AND MARSDEN, J. 1979. A Mathematical Introduction to Fluid Mechanics, 3rd edition ed. Springer-Verlag.
5. FEDKIW, R., STAM, J., AND JENSEN, H. W. 2001. Visual Simulation of Smoke. In Proceedings of ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 15-22.
6. FELDMAN, B. E., O'BRIEN, J. F., AND KLINGNER, B. M. 2005. A method for animating viscoelastic fluids. ACM Transactions on Graphics (SIGGRAPH) (Aug.).
7. FETECAU, R. C., MARSDEN, J. E., ORTIZ, M., AND WEST, M. 2003. Nonsmooth Lagrangian Mechanics and Variational Collision Integrators. SIAM J. Applied Dynamical Systems 2, 381-416.
8. FOSTER, N., AND FEDKIW, R. 2001. Practical Animation of Liquids. In Proceedings of ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 23-30.
9. FOSTER, N., AND METAXAS, D. 1997. Modeling the Motion of a Hot, Turbulent Gas. In Proceedings of SIGGRAPH 97, Computer Graphics Proceedings, Annual Conference Series, 181-188.
10. GOKTEKIN, T. G., BARGTEIL, A. W., AND O'BRIEN, J. F. 2004. A method for animating viscoelastic fluids. ACM Transactions on Graphics 23, 3(Aug.), 463-468.
11. HIRANI, A. 2003. Discrete Exterior Calculus. PhD thesis, California Institute of Technology.
12. KANE, C., MARSDEN, J. E., ORTIZ, M., AND WEST, M. 2000. Variational integrators and the Newmark algorithm for conservative and dissipative mechanical systems. Internat. J. Numer. Methods Engrg. 49, 1295-1325.
13. LANGTANGEN, H.-P., MARDAL, K.-A., AND WINTER, R. 2002. Numerical Methods for Incompressible Viscous Flow. Advances in Water Resources 25, 8-12(Aug-Dec), 1125-1146.
14. LEW, A., MARSDEN, J. E., ORTIZ, M., AND WEST, M. 2003. Asynchronous Variational Integrators. Arch. Rational Mech. Anal. 167, 85-146.
15. LOSASSO, F., GIBOU, F., AND FEDKIW, R. 2004. Simulating water and smoke with an octree data structure. ACM Transactions on Graphics 23, 3(Aug.), 457-462.
16. MARSDEN, J. E., AND WENSTEIN, A. 1983. Coadjoint orbits, vortices and Clebsch variables for incompressible fluids. Physica D 7, 305-323.
17. MARSDEN, J. E., AND WEST, M. 2001. Discrete Mechanics and Variational Integrators. Acta Numerica, 357-515.
18. MCNAMARA, A., TREUILLE, A., POPOVIC, Z., AND STAM, J. 2004. Fluid Control Using the Adjoint Method. ACM Transactions on Graphics 23, 3(Aug.), 449-456.
19. MORTON, K. W., AND ROE, P. 2001. Vorticity-Preserving Lax-Wendroff-Type Schemes for the System Wave Equation. SIAM Journal on Scientific Computing 23, 1(July), 170-192.
20. MUNKRES, J. R. 1984. Elements of Algebraic Topology. Addison-Wesley.
21. PIGHIN, F., COHEN, J. M., AND SHAH, M. 2004. Modeling and Editing Flows Using Advected Radial Basis Functions. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 223-232.
22. SHAH, M., COHEN, J. M., PATEL, S., LEE, P., AND PIGHIN, F. 2004. Extended Galilean Invariance for Adaptive Fluid Simulation. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 213-221.
23. SHI, L., AND YU, Y. 2004. Inviscid and Incompressible Fluid Simulation on Triangle Meshes. Journal of Computer Animation and Virtual Worlds 15, 3-4(June), 173-181.
24. STAM, J. 1999. Stable Fluids. In Proceedings of ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 121-128.
25. STAM, J. 2001. A Simple Fluid Solver Based on the FFT. Journal of Graphics Tools 6, 2, 43-52.
26. STAM, J. 2003. Flows on Surfaces of Arbitrary Topology. ACM Transactions on Graphics 22, 3(July), 724-731.
27. STEINHOFF, J., AND UNDERHILL, D. 1994. Modification of the Euler Equations for Vorticity Confinement: Applications to the Computation of Interacting Vortex Rings. Physics of Fluids 6, 8(Aug.), 2738-2744.
28. TONG, Y., LOMBEYDA, S., HIRANI, A. N., AND DESBRUN, M. 2003. Discrete Multiscale Vector Field Decomposition. ACM Trans. Graph. 22, 3, 445-452.
29. TONG, Y. 2004. Towards Applied Geometry in Graphics. PhD thesis, University of Southern California.
30. TREUILLE, A., MCNAMARA, A., POPOVIĆ, Z., AND STAM, J. 2003. Keyframe Control of Smoke Simulations. ACM Transactions on Graphics 22, 3(July), 716-723.
31. WARREN, J., SCHAEFER, S., HIRANI, A., AND DESBRUN, M., 2004. Barycentric Coordinates for Convex Sets. Preprint.
32. YAEGER, L., UPSON, C., AND MYERS, R. 1986. Combining Physical and Visual Simulation - Creation of the Planet Jupiter for the Film 2010. Computer Graphics (Proceedings of SIGGRAPH 86) 20, 4, 85-93.
33. ZHONG, G., AND MARSDEN, J. E. 1988. Lie-Poisson Hamilton-Jacobi Theory and Lie-Poisson Integrators. Physics Letters A 133, 3 (Nov.).