Christopher Batty
Andres Uribe
Skip Abstract Section
Skip Supplemental Material SectionAbstract
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.
Supplemental Material
Available for Download
zip
a113-batty.zip (125.7 MB)
Supplemental material.
- Ando, R., and Tsuruno, R. 2011. A particle-based method for preserving fluid sheets. In Symposium on Computer Animation, 7--16. Google Scholar
Digital Library
- Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In SIGGRAPH, vol. 32, 43--54. Google ScholarDigital Library
- 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
- Batchelor, G. K. 1967. An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Bridson, R. 2008. Fluid Simulation for Computer Graphics. A. K. Peters, Ltd. Google ScholarDigital Library
- Brochu, T., and Bridson, R. 2009. Robust topological operations for dynamic explicit surfaces. SIAM J. Sci. Comput. 31, 4, 2472--2493. Google ScholarDigital Library
- 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
- 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
- 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
- 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
- da Silveira, R., Chaieb, S., and Mahadevan, L. 2000. Rippling instability of a collapsing bubble. Science 287, 5457, 1468--1471.Google Scholar
- English, R. E., and Bridson, R. 2008. Animating developable surfaces using nonconforming elements. ACM Trans. Graph. (SIGGRAPH) 27, 3, 66. Google ScholarDigital Library
- 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
- Garg, A., Grinspun, E., Wardetzky, M., and Zorin, D. 2007. Cubic shells. In Symposium on Computer Animation, 91--98. Google ScholarDigital Library
- 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
- 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
- Hasegawa, S., and Fujii, N. 2003. Real-time rigid body simulation based on volumetric penalty method. In HAPTICS 2003, 326. Google ScholarDigital Library
- Howell, P. D. 1996. Models for thin viscous sheets. European Journal of Applied Mathematics 7, 321--343.Google ScholarCross Ref
- 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
- Kass, M., and Miller, G. 1990. Rapid, stable fluid dynamics for computer graphics. In SIGGRAPH, 49--57. Google ScholarDigital Library
- 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
- 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
- Misztal, M., Bridson, R., Erleben, K., Baerentzen, A., and Anton, F. 2010. Optimization-based fluid simulation on unstructured meshes. In VRIPHYS.Google Scholar
- 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
- 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
- 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
- Pai, D. K. 2002. STRANDS: Interactive simulation of thin solids using Cosserat models. Computer Graphics Forum (Eurographics) 21, 3, 347--352.Google ScholarCross Ref
- 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
- 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
- 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
- Rayleigh, J. W. S. 1945. Theory of Sound, vol. 2. Dover Publications.Google Scholar
- Ribe, N. 2001. Bending and stretching of thin viscous sheets. Journal of Fluid Mechanics 433, 135--160.Google ScholarCross Ref
- Ribe, N. 2002. A general theory for the dynamics of thin viscous sheets. J. Fluid Mech. 457, 255--283.Google ScholarCross Ref
- Ribe, N. 2003. Periodic folding of viscous sheets. Physical Review E 68, 3, 036305.Google ScholarCross Ref
- Savva, N. 2007. Viscous fluid sheets. PhD thesis, Massachusetts Institute of Technology.Google Scholar
- Skorobogatiy, M., and Mahadevan, L. 2000. Folding of viscous sheets and filaments. Europhysics Letters 52, 5, 532--538.Google ScholarCross Ref
- 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
- 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
- Teichman, J., and Mahadevan, L. 2003. The viscous catenary. Journal of Fluid Mechanics 478, 71--80.Google ScholarCross Ref
- Teichmann, J. A. 2002. Wrinkling and sagging viscous sheets. PhD thesis, MIT.Google Scholar
- Villard, J., and Borouchaki, H. 2005. Adaptive meshing for cloth animation. Engineering with Computers 20, 4, 333--341. Google ScholarDigital Library
- 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
- 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
- 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
- Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. ACM Trans. Graph. (SIGGRAPH) 27, 3, 47. Google ScholarDigital Library
- 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
- 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
- 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
- Zhang, D., and Yuen, M. M. F. 2001. Cloth simulation using multilevel meshes. Computers and Graphics 25, 3, 383--389.Google ScholarCross Ref
- 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
Index Terms
Discrete viscous sheets
Recommendations
Lagrangian vortex sheets for animating fluids
Buoyant turbulent smoke plumes with a sharp smoke-air interface, such as volcanic plumes, are notoriously hard to simulate. The surface clearly shows small-scale turbulent structures which are costly to resolve. In addition, the turbulence onset is ...
A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains
We present a new numerical methodology for simulating fluid-structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet-Neumann partitioning technique. The curvilinear immersed ...
ISPH–PBD: coupled simulation of incompressible fluids and deformable bodies
AbstractWe present an efficient and stable method for simulating the two-way coupling of incompressible fluids and deformable bodies. In our method, the fluid is represented by particles, and simulated using divergence-free incompressible smoothed-...
Comments