skip to main content
article

Fluid control using the adjoint method

Published: 01 August 2004 Publication History

Abstract

We describe a novel method for controlling physics-based fluid simulations through gradient-based nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of free-surface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.

Supplementary Material

MOV File (pps031.mov)

References

[1]
ADALSTEINSSON, D., AND SETHIAN, J. 1998. The Fast Construction of Extension Velocities in Level Set Methods. Journal of Computational Physics 148, 2--22.
[2]
BRAZEL, R., HUGHES, J. F., AND WOOD, D. 1996. Plausible motion simulation for computer animation. In EGCAS '96: Seventh International Workshop on Computer Animation and Simulation.
[3]
BEWLEY, T. R., MOIN, P., AND TEMAM, R. 2001. Dns-based predictive control of turbulence: an optimal benchmark for feedback algorithms. Journal of Fluid Mechanics 447, 179--225.
[4]
BEWLEY, T. R. 2002. The emerging roles of model-based control theory in fluid mechanics. In Advances in Turbulence IX. Proceedings of the Ninth European Turbulence Conference.
[5]
CHENNEY, S., AND FORSYTH, D. A. 2000. Sampling Plausible Solutions to Multi-body Constraint Problems. In Computer Graphics (SIGGRAPH 2000), ACM, 219--228.
[6]
ENRIGHT, D., MARSCHNER, S., AND FEDKIW, R. 2002. Animation and Rendering of Complex Water Surfaces. In Computer Graphics (SIGGRAPH 2002), ACM, 736--744.
[7]
FATTAL, R., AND LISCHINSKI, D. 2004. Target-driven smoke animation. ACM Transactions on Graphics 23, 3 (Aug.).
[8]
FEDKIW, R., STAM, J., AND JENSEN, H. 2001. Visual Simulation of Smoke. In Computer Graphics (SIGGRAPH 2001), ACM, 15--22.
[9]
FOSTER, N., AND FEDKIW, R. 2001. Practical Animation of Liquids. In Computer Graphics (SIGGRAPH 2001), ACM, 23--30.
[10]
FOSTER, N., AND METAXAS, D. 1996. Realistic Animation of Liquids. Graphical Models and Image Processing 58, 5, 471--483.
[11]
FOSTER, N., AND METAXAS, D. 1997. Controlling fluid animation. Computer Graphics International, 178--188.
[12]
FOSTER, N., AND METAXAS, D. 1997. Modeling the Motion of a Hot, Turbulent Gas. In Computer Graphics (SIGGRAPH 97), ACM, 181--188.
[13]
GHIL, M., IDE, K., BENNETT, A. F., COURTIER, P., KIMOTO, M., AND (EDS.), N. S. 1997. Data Assimilation in Meteorology and Oceanography: Theory and Practice. Meteorological Society of Japan and Universal Academy Press.
[14]
GILES, M. B., AND PIERCE, N. A. 2000. An introduction to the adjoint approach to design. Flow, Turbulence and Combustion 65, 393--415.
[15]
GRIEWANK, A. 2000. Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation. SIAM.
[16]
KAJIYA, J. T., AND VON HERZEN, B. P. 1984. Ray Tracing Volume Densities. Computer Graphics (SIGGRAPH 84) 18, 3 (July), 165--174.
[17]
KASS, M., AND MILLER, G. 1990. Rapid, Stable Fluid Dynamics for Computer Graphics. ACM Computer Graphics (SIGGRAPH '90) 24, 4 (August), 49--57.
[18]
KUNIMATSU, A., WATANABE, Y., FUJII, H., SAITO, T., AND HIWADA, K. 2001. Fast simulation and rendering techniques for fluid objects. Computer Graphics Forum (Proceedings of Eurographics) 20, 3, 357--367.
[19]
LIONS, J. P. 1971. Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, New York.
[20]
MUELLER, M., CHARYPAR, D., AND GROSS, M. 2003. Particle-based fluid simulation for interactive applications. In Proceedings of ACM SIGGRAPH Symposium on Computer Animation SCA 2003, 154--159.
[21]
OSHER, S., AND SETHIAN, J., 1988. Fronts Propagating with Curvature Dependant Speed: Alogorithms Based on Hamilton-Jacobi Formulations.
[22]
POPOVIĆ, J., SEITZ, S. M., ERDMANN, M., POPOVIĆ, Z., AND WITKIN, A. 2000. Interactive Manipulation of Rigid Body Simulations. In Computer Graphics (SIGGRAPH 2000), ACM, 209--218.
[23]
POPOVIĆ, J. 2001. Interactive Design of Rigid-Body Simulatons for Computer Animation. PhD thesis, Carnegie Mellon University.
[24]
PREMOZE, S., TASDIZEN, T., BIGLER, J., LEFOHN, A., AND WHITAKER, R. 2003. Particle Based Simlation of Fluids. Computer Graphics Forum (Proceedings of Eurographics) 22, 3, 401--410.
[25]
STAM, J. 1999. Stable Fluids. In Computer Graphics (SIGGRAPH 99), ACM, 121--128.
[26]
TREUILLE, A., MCNAMARA, A., POPOVIĆ, Z., AND STAM, J. 2003. Keyframe control of smoke simulations. ACM Transactions on Graphics 22, 3 (July), 716--723.
[27]
ZHU, C., BYRD, R., LU, P., AND NOCEDAL, J., 1994. Lbfgs-b: Fortran subroutines for large-scale bound constrained optimization.

Cited By

View all

Index Terms

  1. Fluid control using the adjoint method

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 23, Issue 3
    August 2004
    684 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/1015706
    Issue’s Table of Contents
    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]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 01 August 2004
    Published in TOG Volume 23, Issue 3

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Adjoint Method
    2. Inverse Control
    3. Optimization

    Qualifiers

    • Article

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)110
    • Downloads (Last 6 weeks)14
    Reflects downloads up to 28 Dec 2024

    Other Metrics

    Citations

    Cited By

    View all

    View Options

    Login options

    Full Access

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media