“A fast variational framework for accurate solid-fluid coupling” by Batty, Bertails and Bridson

  • ©Christopher Batty, Florence Bertails-Descoubes, and Robert Bridson

Conference:


Type:


Title:

    A fast variational framework for accurate solid-fluid coupling

Presenter(s)/Author(s):


Abstract:


    Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.

References:


    1. Angelidis, A., Neyret, F., Singh, K., and Nowrouzezahrai, D. 2006. A controllable, fast and stable basis for vortex based smoke simulation. In ACM-EG Proc. Symposium on Computer Animation, 25–32. 
    2. Baraff, D. 1996. Linear-time dynamics using Lagrange multipliers. In Computer Graphics Proc. (Proc. SIGGRAPH), 137–146. 
    3. Bridson, R., Müller-Fischer, M., and Guendelman, E. 2006. Fluid simulation. In ACM SIGGRAPH Course Notes.
    4. Carlson, M., Mucha, P. J., and Turk, G. 2004. Rigid fluid: animating the interplay between rigid bodies and fluid. ACM Trans. Graph. (Proc. SIGGRAPH) 23, 377–384. 
    5. Chentanez, N., Goktekin, T. G., Feldman, B. E., and O’Brien, J. F. 2006. Simultaneous coupling of fluids and deformable bodies. In ACM-EG Proc. Symposium on Computer Animation, 83–89. 
    6. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Computer Graphics Proc. (Proc. SIGGRAPH), 13–22. 
    7. Feldman, B. E., O’Brien, J. F., and Klingner, B. M. 2005. Animating gases with hybrid meshes. ACM Trans. Graph. (Proc. SIGGRAPH) 24, 3, 904–909. 
    8. Ferris, M. C., and Munson, T. S. 1998. Complementarity problems in GAMS and the PATH solver. Tech. Rep. Mathematical Programming 98–12, Computer Sciences Dept., University of Madison.
    9. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In Computer Graphics Proc. (Proc. SIGGRAPH), 23–30. 
    10. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graphical models and image processing: GMIP 58, 5, 471–483. 
    11. Génevaux, O., Habibi, A., and Dischler, J.-M. 2003. Simulating fluid-solid interaction. In Graphics Interface, 31–38.
    12. Gibou, F., Fedkiw, R., Cheng, L.,-T., and Kang, M. 2002. A second order accurate symmetric discretization of the Poisson equation on irregular domains. J. Comput. Phys. 176, 205–227. 
    13. Guendelman, E., Bridson, R., and Fedkiw, R. 2003. Non-convex rigid bodies with stacking. ACM Trans. Graph. (Proc. SIGGRAPH) 22, 871–878. 
    14. Guendelman, E., Selle, A., Losasso, F., and Fedkiw, R. 2005. Coupling water and smoke to thin deformable and rigid shells. ACM Trans. Graph. (Proc. SIGGRAPH) 24, 3, 973–981. 
    15. Harlow, F. H., and Welch, J. E. 1965. Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface. Phys. Fluids 8, 2182–2189.
    16. Hirt, C. W., Amsden, A. A., and Cook, J. L. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 3, 227–253.
    17. Houston, B., Bond, C., and Wiebe, M. 2003. A unified approach for modeling complex occlusions in fluid simulations. In Proc. SIGGRAPH Sketches & applications. 
    18. Irving, G., Guendelman, E., Losasso, F., and Fedkiw, R. 2006. Efficient simulation of large bodies of water by coupling two and three dimensional techniques. ACM Trans. Graph. (Proc. SIGGRAPH) 25, 805–811. 
    19. Johansen, H., and Colella, P. 1998. A Cartesian grid embedded boundary method for Poison’s equation on irregular domains. J. Comput. Phys. 147, 1, 60–85. 
    20. Keiser, R., Adams, B., Gasser, D., Bazzi, P., Dutré, P., and Gross, M. 2005. A unified Lagrangian approach to solid-fluid animation. In Eurographics Symposium on Point-Based Graphics, 125–148. 
    21. Kirkpatrick, M. P., Armfield, S. W., and Kent, J. H. 2003. A representation of curved boundaries for the solution of the Navier-Stokes equations on a staggered three-dimensional Cartesian grid. J. Comput. Phys. 184, 1–36. 
    22. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. In ACM Trans. Graph. (Proc. SIGGRAPH), 820–825. 
    23. Le, D. V., Khoo, B. C., and Peraire, J. 2006. An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries. J. Comp. Phys. 220, 109–138. 
    24. Liu, H., Krishnan, S., Marella, S., and Udaykumar, H. 2005. Sharp interface Cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape. J. Comput. Phys. 210, 1, 32–54. 
    25. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. (Proc. SIGGRAPH) 23, 3, 457–462. 
    26. Marella, S., Krishnan, S., Liu, H., and Udaykumar, H. 2005. Sharp interface Cartesian grid method I: An easily implemented technique for 3D moving boundary computations. J. Comput. Phys. 210, 1, 1–31. 
    27. Peskin, C. S. 2002. The immersed boundary method. Acta Numerica 11, 479–517.
    28. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In ACM-EG Proc. Symposium on Computer Animation, 193–202. 
    29. Roble, D., Bin Zafar, N., and Falt, H. 2005. Cartesian grid fluid simulation with irregular boundary voxels. In Proc. SIGGRAPH Sketches & applications. 
    30. Schwartz, P., Barad, M., Colella, P., and Ligocki, T. 2006. A Cartesian grid embedded boundary method for the heat equation and Poisson’s equation in three dimensions. J. Comput. Phys. 211, 2, 531–550. 
    31. Takahashi, T., Heihachi, U., and Kunimatsu, A. 2002. The simulation of fluid-rigid body interaction. In Proc. SIGGRAPH Sketches & applications. 
    32. Tam, D., Radovitzky, R., and Samtaney, R. 2005. An algorithm for modelling the interaction of a flexible rod with a two-dimensional high-speed flow. Int. J. Numer. Meth. Engng 64, 1057–1077.
    33. Thürey, N., Iglberger, K., and Rüde, U. 2006. Free surface flows with moving and deforming objects with LBM. In Vision, Modeling, and Visualization.
    34. Udaykumar, H. S., Mittal., R., Rampunggoon, P., and Khanna, A. 2001. A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys. 174, 345–380. 
    35. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans. Graph. (Proc. SIGGRAPH) 24, 3, 965–972. 

Overview Page: