skip to main content
10.1145/1185657.1185667acmconferencesArticle/Chapter ViewAbstractPublication PagessiggraphConference Proceedingsconference-collections
Article

Stable, circulation-preserving, simplicial fluids

Published: 30 July 2006 Publication History

Abstract

Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid and deformable body simulation benefits greatly from conservation of linear and angular momenta. In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently, they often introduce a visually disturbing numerical diffusion of vorticity. Visually just as important is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally delicate. In this chapter, we propose a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, i.e., the conservation of circulation along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: (1) arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; (2) the computations are efficient due to discrete operators with small support; (3) the method is stable for arbitrarily large time steps; (4) it preserves discrete circulation avoiding numerical diffusion of vorticity; and (5) its implementation is straightforward.

References

[1]
ABRAHAM, R., MARSDEN, J., AND RATIU, T., Eds. 1988. Manifolds, Tensor Analysis, and Applications, vol. 75 of Applied Mathematical Sciences. Springer.
[2]
ALLIEZ, P., COHEN-STEINER, D., YVINEC, M., AND DESBRUN, M. 2005. Variational tetrahedral meshing. ACM Transactions on Graphics 24, 3, 617-625.
[3]
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.
[4]
BOSSAVIT, A. 1998. Computational Electromagnetism. Academic Press, Boston.
[5]
CHANG, W., GIRALDO, F., AND PEROT, B. 2002. Analysis of an exact fractional step method. Journal of Computational Physics 180, 3 (Nov.), 183-199.
[6]
CHORIN, A., AND MARSDEN, J. 1979. A Mathematical Introduction to Fluid Mechanics, 3rd edition ed. Springer-Verlag.
[7]
DESBRUN, M., KANSO, E., AND TONG, Y. 2006. Discrete differential forms for computational sciences. In Discrete Differential Geometry, E. Grinspun, P. Schröder, and M. Desbrun, Eds., Course Notes. ACM SIGGRAPH.
[8]
ELCOTT, S., AND SCHRÖDER, P. 2006. Building your own dec at home. In Discrete Differential Geometry, E. Grinspun, P. Schröder, and M. Desbrun, Eds., Course Notes. ACM SIGGRAPH.
[9]
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.
[10]
FELDMAN, B. E., O'BRIEN, J. F., AND KLINGNER, B. M. 2005. Animating gases with hybrid meshes. ACM Transactions on Graphics 24, 3, 904-909.
[11]
FOSTER, N., AND FEDKIW, R. 2001. Practical animation of liquids. In Proceedings of ACM SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 23-30.
[12]
FOSTER, N., AND METAXAS, D. 1997. Modeling the motion of a hot, turbulent gas. In Proceedings of SIGGRAPH, Computer Graphics Proceedings, Annual Conference Series, 181-188.
[13]
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.
[14]
GUENDELMAN, E., SELLE, A., LOSASSO, F., AND FEDKIW, R. 2005. Coupling water and smoke to thin deformable and rigid shell. ACM Transactions on Graphics 24, 3, 973-981.
[15]
HIRANI, A. 2003. Discrete Exterior Calculus. PhD thesis, California Institute of Technology.
[16]
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.
[17]
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.
[18]
MARSDEN, J. E., AND WENSTEIN, A. 1983. Coadjoint orbits, vortices and Clebsch variables for incompressible fluids. Physica D 7, 305-323.
[19]
MARSDEN, J. E., AND WEST, M. 2001. Discrete mechanics and variational integrators. Acta Numerica 10, 357-515.
[20]
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.
[21]
MUNKRES, J. R. 1984. Elements of Algebraic Topology. Addison-Wesley.
[22]
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.
[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]
SHI, L., AND YU, Y. 2005. Controllable smoke animation with guiding objects. ACM Transactions on Graphics 24, 1, 140-164.
[25]
STAM, J. 1999. Stable fluids. In Proceedings of ACM SIGGRAPH , Computer Graphics Proceedings, Annual Conference Series, 121-128.
[26]
STAM, J. 2001. A simple fluid solver based on the fft. Journal of Graphics Tools 6, 2, 43-52.
[27]
STAM, J. 2003. Flows on surfaces of arbitrary topology. ACM Transactions on Graphics 22, 3 (July), 724-731.
[28]
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.
[29]
TONG, Y., LOMBEYDA, S., HIRANI, A. N., AND DESBRUN, M. 2003. Discrete multiscale vector field decomposition. ACM Transactions on Graphics 22, 3, 445-452.
[30]
TREUILLE, A., MCNAMARA, A., POPOVI¿, 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 ACM SIGGRAPH) 20 4, 85-93.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SIGGRAPH '06: ACM SIGGRAPH 2006 Courses
July 2006
83 pages
ISBN:1595933646
DOI:10.1145/1185657
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 July 2006

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Article

Conference

SIGGRAPH06
Sponsor:

Acceptance Rates

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)2
  • Downloads (Last 6 weeks)1
Reflects downloads up to 19 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2009)Modular bases for fluid dynamicsACM SIGGRAPH 2009 papers10.1145/1576246.1531345(1-8)Online publication date: 27-Jul-2009
  • (2009)Modular bases for fluid dynamicsACM Transactions on Graphics10.1145/1531326.153134528:3(1-8)Online publication date: 27-Jul-2009
  • (2009)Toward Real-Time Simulation of Blood-Coil Interaction during Aneurysm EmbolizationProceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I10.1007/978-3-642-04268-3_25(198-205)Online publication date: 2-Oct-2009
  • (2007)Level set driven flowsACM Transactions on Graphics10.1145/1289603.128960626:4(15-es)Online publication date: 1-Oct-2007
  • (2007)Finite volume flow simulations on arbitrary domainsGraphical Models10.1016/j.gmod.2006.05.00469:1(19-32)Online publication date: 1-Jan-2007
  • (2006)A controllable, fast and stable basis for vortex based smoke simulationProceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation10.5555/1218064.1218068(25-32)Online publication date: 2-Sep-2006
  • (2006)Model reduction for real-time fluidsACM SIGGRAPH 2006 Papers10.1145/1179352.1141962(826-834)Online publication date: 30-Jul-2006
  • (2006)Edge subdivision schemes and the construction of smooth vector fieldsACM Transactions on Graphics10.1145/1141911.114199125:3(1041-1048)Online publication date: 1-Jul-2006
  • (2006)Model reduction for real-time fluidsACM Transactions on Graphics10.1145/1141911.114196225:3(826-834)Online publication date: 1-Jul-2006

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media