“Model reduction for real-time fluids” by Treuille, Lewis and Popovic

  • ©Adrien Treuille, Andrew Lewis, and Zoran Popovic

Conference:


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Title:

    Model reduction for real-time fluids

Presenter(s)/Author(s):



Abstract:


    We present a new model reduction approach to fluid simulation, enabling large, real-time, detailed flows with continuous user interaction. Our reduced model can also handle moving obstacles immersed in the flow. We create separate models for the velocity field and for each moving boundary, and show that the coupling forces may be reduced as well. Our results indicate that surprisingly few basis functions are needed to resolve small but visually important features such as spinning vortices.

References:


    1. Ausseur, J., Pinier, J., Glauser, M., and Higuchi, H. 2004. Predicting the Dynamics of the Flow over a NACA 4412 using POD. APS Meeting Abstracts (Nov.), D8.]]Google Scholar
    2. Barbič, J., and James, D. 2005. Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM Transactions on Graphics 24, 3 (Aug.), 982–990.]] Google ScholarDigital Library
    3. Bolz, J., Farmer, I., Grinspun, E., and Schröder, P. 2003. Sparse matrix solvers on the gpu: Conjugate gradients and multigrid. ACM Transactions on Graphics 22, 3 (July), 917–924.]] Google ScholarDigital Library
    4. Couplet, M., Basdevant, C., and Sagaut, P. 2005. Calibrated reduced-order POD-Galerkin system for fluid flow modelling. J. Comput. Phys. 207, 1, 192–220.]] Google ScholarDigital Library
    5. Elcott, S., Tong, Y., Kanso, E., Schröder, P., and Desbrun, M. 2005. Stable, circulation-preserving, simplicial fluids. In Discrete Differential Geometry, Chapter 9 of Course Notes. ACM SIGGRAPH.]] Google ScholarDigital Library
    6. Feldman, B. E., O’Brien, J. F., and Klingner, B. M. 2005. Animating gases with hybrid meshes. ACM Transactions on Graphics 24, 3 (Aug.), 904–909.]] Google ScholarDigital Library
    7. Fogleman, M., Lumley, J., Rempfer, D., and Haworth, D. 2004. Application of the proper orthogonal decomposition to datasets of internal combustion engine flows. Journal of Turbulence 5, 23 (June).]]Google ScholarCross Ref
    8. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graphical Models and Image Processing 58, 5, 471–483.]] Google ScholarDigital Library
    9. Goodnight, N., Woolley, C., Luebke, D., and Humphreys, G. A. 2003. Multigrid solver for boundary value problems using programmable graphics hardware. In Proceeding of Graphics Hardware, 102.]] Google ScholarDigital Library
    10. Harris, M. J., Coombe, G., Scheuermann, T., and Lastra, A. 2002. Physically-based visual simulation on graphics hardware. In Graphics Hardware 2002, 109–118.]] Google ScholarDigital Library
    11. Holmes, P., Lumley, J. L., and Berkooz, G. 1996. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press, Cambridge, MA.]]Google Scholar
    12. James, D. L., and Fatahalian, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Transactions on Graphics 22, 3 (July), 879–887.]] Google ScholarDigital Library
    13. Krüger, J., and Westermann, R. 2003. Linear algebra operators for GPU implementation of numerical algorithms. ACM Transactions on Graphics 22, 3 (July), 908–916.]] Google ScholarDigital Library
    14. Li, W., Wei, X., and Kaufman, A. 2003. Implementing lattice Boltzmann computation on graphics hardware. The Visual Computer 19, 7–8, 444–456.]]Google ScholarDigital Library
    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.]] Google ScholarDigital Library
    16. Lumley, J. L. 1970. Stochastic Tools in Turbulence, vol. 12 of Applied Mathematics and Mechanics. Academic Press, New York.]]Google Scholar
    17. Marion, M., and Temam, R. 1989. Nonlinear Galerkin methods. SIAM J. Numer. Anal. 26, 5, 1139–1157.]] Google ScholarDigital Library
    18. Maurel, S., Boree, J., and Lumley, J. 2001. Extended proper orthogonal decomposition: Application to jet/vortex interaction. Flow, Turbulence and Combustion 67, 2 (June), 125–36.]]Google Scholar
    19. Park, S. I., and Kim, M. J. 2005. Vortex fluid for gaseous phenomena. In 2005 ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 261–270.]] Google ScholarDigital Library
    20. Rowley, C. W., and Marsden, J. E. 2000. Reconstruction equations and the Karhunen-Loéve expansion for systems with symmetry. Phys. D 142, 1–2, 1–19.]] Google ScholarDigital Library
    21. Rowley, C. W., Kevrekidis, I. G., Marsden, J. E., and Lust, K. 2003. Reduction and reconstruction for self-similar dynamical systems. Nonlinearity 16 (July), 1257–1275.]]Google ScholarCross Ref
    22. Rowley, C., Williams, D., Colonius, T., Murray, R., and MacMartin, D. 2006. Linear models for control of cavity flow oscillations. J. Fluid Mech. (Jan.).]]Google Scholar
    23. Schmit, R., and Glasuer, M. 2002. Low dimensional tools for flow-structure interaction problems: Application to micro air vehicles. APS Meeting Abstracts (Nov.), D1+.]]Google Scholar
    24. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. ACM Transactions on Graphics 24, 3 (Aug.), 910–914.]] Google ScholarDigital Library
    25. Sirisup, S., and Karniadakis, G. E. 2004. A spectral viscosity method for correcting the long-term behavior of POD models. J. Comput. Phys. 194, 1, 92–116.]] Google ScholarDigital Library
    26. Sirovich, L. 1987. Turbulence and the dynamics of coherent structures. I – Coherent structures. II – Symmetries and transformations. III – Dynamics and scaling. Quarterly of Applied Mathematics 45 (Oct.), 561–571.]]Google ScholarCross Ref
    27. Stam, J. 1999. Stable Fluids. In Computer Graphics (SIGGRAPH 99), ACM, 121–128.]] Google ScholarDigital Library
    28. Stam, J. 2001. A simple fluid solver based on the fft. Journal of graphics tools 6, 2, 43–52.]] Google ScholarDigital Library
    29. Wang, H., Wu, Q., Shi, L., Yu, Y., and Ahuja, N. 2005. Out-of-core tensor approximation of multi-dimensional matrices of visual data. ACM Transactions on Graphics 24, 3 (Aug.), 527–535.]] Google ScholarDigital Library
    30. Wu, E., Liu, Y., and Liu, X. 2005. An improved study of realtime fluid simulation on GPU. Computer Animation and Virtual Worlds 15, 3–4, 139–146.]] Google ScholarDigital Library


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