“Two-way coupling of fluids to rigid and deformable solids and shells” by Robinson-Mosher, Shinar, Gretarsson, Su and Fedkiw

  • ©Avi Robinson-Mosher, Tamar Shinar, Jon Gretarsson, Jonathan Su, and Ronald Fedkiw




    Two-way coupling of fluids to rigid and deformable solids and shells



    We propose a novel solid/fluid coupling method that treats the coupled system in a fully implicit manner making it stable for arbitrary time steps, large density ratios, etc. In contrast to previous work in computer graphics, we derive our method using a simple back-of-the-envelope approach which lumps the solid and fluid momenta together, and which we show exactly conserves the momentum of the coupled system. Notably, our method uses the standard Cartesian fluid discretization and does not require (moving) conforming tetrahedral meshes or ALE frameworks. Furthermore, we use a standard Lagrangian framework for the solid, thus supporting arbitrary solid constitutive models, both implicit and explicit time integration, etc. The method is quite general, working for smoke, water, and multiphase fluids as well as both rigid and deformable solids, and both volumes and thin shells. Rigid shells and cloth are handled automatically without special treatment, and we support fully one-sided discretizations without leaking. Our equations are fully symmetric, allowing for the use of fast solvers, which is a natural result of properly conserving momentum. Finally, for simple explicit time integration of rigid bodies, we show that our equations reduce to form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though four spatial dimensions rather than three.


    1. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. SIGGRAPH 98, 43–54. Google ScholarDigital Library
    2. Bargteil, A. W., Wojtan, C., Hodgins, J. K., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Trans. Graph. (SIGGRAPH Proc.) 26, 3. Google ScholarDigital Library
    3. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. (SIGGRAPH Proc.) 26, 3, 100. Google ScholarDigital Library
    4. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In Proc. of the 2003 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 28–36. Google ScholarDigital Library
    5. Carlson, M., Mucha, P., Van Horn, R., and Turk, G. 2002. Melting and flowing. In ACM Trans. Graph. (SIGGRAPH Proc.), vol. 21, 167–174. Google ScholarDigital Library
    6. Carlson, M., Mucha, P. J., and Turk, G. 2004. Rigid fluid: Animating the interplay between rigid bodies and fluid. ACM Trans. Graph. (SIGGRAPH Proc.) 23, 377–384. Google ScholarDigital Library
    7. Chentanez, N., Goktekin, T. G., Feldman, B., and O’Brien, J. 2006. Simultaneous coupling of fluids and deformable bodies. In SCA ’06: Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, 325–333. Google ScholarDigital Library
    8. Choi, S.-C. 2006. Iterative Methods for Singular Linear Equations and Least-Squares Problems. PhD thesis, Stanford University.Google Scholar
    9. Demmel, J. W. 1997. Applied numerical linear algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. Google ScholarDigital Library
    10. Faure, F., Allard, J., and Nesme, M. 2007. Eulerian contact for versatile collision processing. Tech. rep., INRIA. http://hal.inria.fr/inria-00149706.Google Scholar
    11. Génevaux, O., Habibi, A., and Dischler, J.-M. 2003. Simulating fluid-solid interaction. In Graph. Interface, 31–38.Google Scholar
    12. Goktekin, T. G., Bargteil, A. W., and O’Brien, J. F. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. (SIGGRAPH Proc.) 23, 463–468. Google ScholarDigital Library
    13. Guendelman, E., Selle, A., Losasso, F., and Fedkiw, R. 2005. Coupling water and smoke to thin deformable and rigid shells. ACM Trans. Graph. (SIGGRAPH Proc.) 24, 3, 973–981. Google ScholarDigital Library
    14. Hadap, S., and Magnenat-Thalmann, N. 2001. Modeling dynamic hair as a continuum. Comput. Graph. Forum 20, 3.Google ScholarCross Ref
    15. Keiser, R., Adams, B., Gasser, D., Bazzi, P., Dutré, P., and Gross, M. 2005. A unified Lagrangian approach to solid-fluid animation. In Eurographics Symp. on Point-Based Graph. Google ScholarCross Ref
    16. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. In ACM Trans. Graph. (SIGGRAPH Proc.), vol. 25, 820–825. Google ScholarDigital Library
    17. Losasso, F., Irving, G., Guendelman, E., and Fedkiw, R. 2006. Melting and burning solids into liquids and gases. IEEE Trans. on Vis. and Comput. Graph. 12, 3, 343–352. Google ScholarDigital Library
    18. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. ACM Trans. Graph. (SIGGRAPH Proc.) 25, 3, 812–819. Google ScholarDigital Library
    19. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In Proc. of the 2004 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 141–151. Google ScholarDigital Library
    20. Müller, M., Schirm, S., Teschner, M., Heidelberger, B., and Gross, M. 2004. Interaction of fluids with deformable solids. J. Comput. Anim. and Virt. Worlds 15, 3–4 (July), 159–171. Google ScholarDigital Library
    21. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In Proc. of the 2004 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 193–202. Google ScholarDigital Library
    22. Sifakis, E., Shinar, T., Irving, G., and Fedkiw, R. 2007. Hybrid simulation of deformable solids. In Proc. of ACM SIGGRAPH/Eurographics Symp. on Comput. Anim. (in press). Google ScholarDigital Library
    23. Stam, J. 1999. Stable fluids. In Proc. of SIGGRAPH 99, 121–128. Google ScholarDigital Library
    24. Terzopoulos, D., Platt, J., and Fleischer, K. 1989. Heating and melting deformable models (from goop to glop). In Graph. Interface, 219–226.Google Scholar
    25. Yngve, G., O’Brien, J., and Hodgins, J. 2000. Animating explosions. In Proc. of ACM SIGGRAPH 2000, 29–36. Google ScholarDigital Library
    26. Yuksel, C., House, D. H., and Keyser, J. 2007. Wave particles. ACM Trans. Graph. (SIGGRAPH Proc.) 26, 3, 99. Google ScholarDigital Library

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