“Discrete viscous sheets” by Batty, Uribe, Audoly and Grinspun

  • ©Christopher Batty, Andres Uribe, Basile Audoly, and Eitan Grinspun




    Discrete viscous sheets



    We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.


    1. Ando, R., and Tsuruno, R. 2011. A particle-based method for preserving fluid sheets. In Symposium on Computer Animation, 7–16. Google ScholarDigital Library
    2. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In SIGGRAPH, vol. 32, 43–54. Google ScholarDigital Library
    3. Bargteil, A. W., Hodgins, J. K., Wojtan, C., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Trans. Graph. (SIGGRAPH) 26, 3, 16. Google ScholarDigital Library
    4. Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
    5. Batty, C., and Bridson, R. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In Symposium on Computer Animation, 219–228. Google ScholarDigital Library
    6. Batty, C., and Houston, B. 2011. A simple finite volume method for adaptive viscous liquids. In Symposium on Computer Animation, 111–118. Google ScholarDigital Library
    7. Benjamin, T. B., and Mullin, T. 1988. Buckling instabilities in layers of viscous liquid subjected to shearing. J. Fluid Mech.1 195, 523–540.Google Scholar
    8. Bergou, M., Wardetzky, M., Robinson, S., Audoly, B., and Grinspun, E. 2008. Discrete elastic rods. ACM Trans. Graph. (SIGGRAPH) 27, 3, 63. Google ScholarDigital Library
    9. Bergou, M., Audoly, B., Vouga, E., Wardetzky, M., and Grinspun, E. 2010. Discrete viscous threads. ACM Trans. Graph. (SIGGRAPH) 29, 4, 116. Google ScholarDigital Library
    10. Bertails, F., Audoly, B., Cani, M.-P., Leroy, F., Querleux, B., and Lévêque, J.-L. 2006. Super-helices for predicting the dynamics of natural hair. ACM Trans. Graph. (SIGGRAPH) 25, 3 (July), 1180–1187. Google ScholarDigital Library
    11. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In Symposium on Computer Animation, Eurographics Association, 28–36. Google ScholarDigital Library
    12. Bridson, R. 2008. Fluid Simulation for Computer Graphics. A. K. Peters, Ltd. Google ScholarDigital Library
    13. Brochu, T., and Bridson, R. 2009. Robust topological operations for dynamic explicit surfaces. SIAM J. Sci. Comput. 31, 4, 2472–2493. Google ScholarDigital Library
    14. Brochu, T., Batty, C., and Bridson, R. 2010. Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph. (SIGGRAPH) 29, 4, 47. Google ScholarDigital Library
    15. Buckmaster, J. D., A. Nachman, and Ting, L. 1975. The buckling and stretching of a viscida. J. Fluid Mech. 69, 1, 1–20.Google ScholarCross Ref
    16. Carlson, M., Mucha, P. J., Van Horn, R., and Turk, G. 2002. Melting and flowing. In Symposium on Computer Animation, 167–174. Google ScholarDigital Library
    17. Chentanez, N., Feldman, B. E., Labelle, F., O’Brien, J. F., and Shewchuk, J. R. 2007. Liquid simulation on lattice-based tetrahedral meshes. In Symposium on Computer Animation, 219–228. Google ScholarDigital Library
    18. da Silveira, R., Chaieb, S., and Mahadevan, L. 2000. Rippling instability of a collapsing bubble. Science 287, 5457, 1468–1471.Google Scholar
    19. English, R. E., and Bridson, R. 2008. Animating developable surfaces using nonconforming elements. ACM Trans. Graph. (SIGGRAPH) 27, 3, 66. Google ScholarDigital Library
    20. Erleben, K., Misztal, M., and Baerentzen, A. 2011. Mathematical foundation of the optimization-based fluid animation method. In Symposium on Computer Animation, 101–110. Google ScholarDigital Library
    21. Garg, A., Grinspun, E., Wardetzky, M., and Zorin, D. 2007. Cubic shells. In Symposium on Computer Animation, 91–98. Google ScholarDigital Library
    22. Gingold, Y., Secord, A., Han, J. Y., Grinspun, E., and Zorin, D. 2004. A discrete model for inelastic deformation of thin shells. Tech. rep., New York University.Google Scholar
    23. Grinspun, E., Hirani, A. N., Schröder, P., and Desbrun, M. 2003. Discrete shells. In Symposium on Computer Animation, Eurographics Association, 62–67. Google ScholarDigital Library
    24. Hasegawa, S., and Fujii, N. 2003. Real-time rigid body simulation based on volumetric penalty method. In HAPTICS 2003, 326. Google ScholarDigital Library
    25. Howell, P. D. 1996. Models for thin viscous sheets. European Journal of Applied Mathematics 7, 321–343.Google ScholarCross Ref
    26. Hutchinson, D., Preston, M., and Hewitt, T. 1996. Adaptive refinement for mass/spring simulations. In Eurographics Workshop on Computer Animation and Simulation, 31–45. Google ScholarDigital Library
    27. Kass, M., and Miller, G. 1990. Rapid, stable fluid dynamics for computer graphics. In SIGGRAPH, 49–57. Google ScholarDigital Library
    28. Kharevych, L., Yang, W., Tong, Y., Kanso, E., Marsden, J. E., Schröder, P., and Desbrun, M. 2006. Geometric, variational integrators for computer animation. In Symposium on Computer Animation, 43–51. Google ScholarDigital Library
    29. Martin, S., Kaufmann, P., Botsch, M., Grinspun, E., and Gross, M. 2010. Unified simulation of elastic rods, shells, and solids. ACM Trans. Graph. (SIGGRAPH) 29, 4, 39. Google ScholarDigital Library
    30. Misztal, M., Bridson, R., Erleben, K., Baerentzen, A., and Anton, F. 2010. Optimization-based fluid simulation on unstructured meshes. In VRIPHYS.Google Scholar
    31. Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In Symposium on Computer Animation, 154–159. Google ScholarDigital Library
    32. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point-based animation of elastic, plastic, and melting objects. In Symposium on Computer Animation, 141–151. Google ScholarDigital Library
    33. Nealen, A., Müller, M., Keiser, R., Boxerman, E., and Carlson, M. 2006. Physically based deformable models in computer graphics. Computer Graphics Forum 25, 4, 809–836.Google ScholarCross Ref
    34. Pai, D. K. 2002. STRANDS: Interactive simulation of thin solids using Cosserat models. Computer Graphics Forum (Eurographics) 21, 3, 347–352.Google ScholarCross Ref
    35. Pearson, J. R. A., and Petrie, C. J. S. 1970. The flow of a tubular film. Part 1: Formal mathematical representation. J. Fluid Mech. 40, 1, 1–19.Google ScholarCross Ref
    36. Radovitzky, R., and Ortiz, M. 1999. Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput. Methods Appl. Mech. Eng 172, 1–4, 203–240.Google ScholarCross Ref
    37. Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In Symposium on Computer Animation, 193–202. Google ScholarDigital Library
    38. Rayleigh, J. W. S. 1945. Theory of Sound, vol. 2. Dover Publications.Google Scholar
    39. Ribe, N. 2001. Bending and stretching of thin viscous sheets. Journal of Fluid Mechanics 433, 135–160.Google ScholarCross Ref
    40. Ribe, N. 2002. A general theory for the dynamics of thin viscous sheets. J. Fluid Mech. 457, 255–283.Google ScholarCross Ref
    41. Ribe, N. 2003. Periodic folding of viscous sheets. Physical Review E 68, 3, 036305.Google ScholarCross Ref
    42. Savva, N. 2007. Viscous fluid sheets. PhD thesis, Massachusetts Institute of Technology.Google Scholar
    43. Skorobogatiy, M., and Mahadevan, L. 2000. Folding of viscous sheets and filaments. Europhysics Letters 52, 5, 532–538.Google ScholarCross Ref
    44. Spillman, J., and Teschner, M. 2007. CORDE: Cosserat rod elements for the dynamic simulation of one-dimensional elastic objects. In Symposium on Computer Animation, 63–72. Google ScholarDigital Library
    45. Stokes, G. G. 1845. On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Transactions of the Cambridge Philosophical Society. Vol. 8.Google Scholar
    46. Teichman, J., and Mahadevan, L. 2003. The viscous catenary. Journal of Fluid Mechanics 478, 71–80.Google ScholarCross Ref
    47. Teichmann, J. A. 2002. Wrinkling and sagging viscous sheets. PhD thesis, MIT.Google Scholar
    48. Villard, J., and Borouchaki, H. 2005. Adaptive meshing for cloth animation. Engineering with Computers 20, 4, 333–341. Google ScholarDigital Library
    49. Wang, H., O’Brien, J. F., and Ramamoorthi, R. 2010. Multi-resolution isotropic strain limiting. ACM Trans. Graph. (SIGGRAPH Asia) 29, 6, 156. Google ScholarDigital Library
    50. Wicke, M., Steinemann, D., and Gross, M. 2005. Efficient animation of point-sampled thin shells. Computer Graphics Forum (Eurographics) 24, 3, 667–676.Google ScholarCross Ref
    51. Wicke, M., Ritchie, D., Klingner, B. M., Burke, S., Shewchuk, J. R., and O’Brien, J. F. 2010. Dynamic local remeshing for elastoplastic simulation. ACM Trans. Graph. (SIGGRAPH) 29, 4, 49. Google ScholarDigital Library
    52. Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. ACM Trans. Graph. (SIGGRAPH) 27, 3, 47. Google ScholarDigital Library
    53. Wojtan, C., Thuerey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. (SIGGRAPH) 28, 3, 76. Google ScholarDigital Library
    54. Wojtan, C., Thuerey, N., Gross, M., and Turk, G. 2010. Physically-inspired topology changes for thin fluid features. ACM Trans. Graph. (SIGGRAPH) 29, 3. Google ScholarDigital Library
    55. Yang, H. T. Y., Saigal, S., Masud, A., and Kapania, R. K. 2000. A survey of recent shell finite elements. Int. J. Numer. Methods Eng., 47, 101–127.Google ScholarCross Ref
    56. Zhang, D., and Yuen, M. M. F. 2001. Cloth simulation using multilevel meshes. Computers and Graphics 25, 3, 383–389.Google ScholarCross Ref
    57. Zhang, Y., Wang, H., Wang, S., Tong, Y., and Zhou, K. 2011. A deformable surface model for real-time water drop animation. IEEE TVCG 99. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: