“Codimensional surface tension flow on simplicial complexes” by Zhu, Quigley, Cong, Solomon and Fedkiw

  • ©Bo Zhu, Ed Quigley, Matthew D Cong, Justin M. Solomon, and Ronald Fedkiw

Conference:


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Title:

    Codimensional surface tension flow on simplicial complexes

Session/Category Title: Mesh-Based Simulation


Presenter(s)/Author(s):


Moderator(s):



Abstract:


    Many visually interesting natural phenomena are characterized by thin liquid sheets, long filaments, and droplets. We present a new Lagrangian-based numerical method to simulate these codimensional surface tension driven phenomena using non-manifold simplicial complexes. Tetrahedra, triangles, segments, and points are used to model the fluid volume, thin films, filaments, and droplets, respectively. We present a new method for enforcing fluid incompressibility on simplicial complexes along with a physically-guided meshing algorithm to provide temporally consistent information for interparticle forces. Our method naturally allows for transitions between codimensions, either from tetrahedra to triangles to segments to points or vice versa, regardless of the simulation resolution. We demonstrate the efficacy of this method by simulating various natural phenomena that are characterized by thin fluid sheets, filaments, and surface tension effects.

References:


    1. Adams, B., Pauly, M., Keiser, R., and Guibas, L. J. 2007. Adaptively sampled particle fluids. ACM Trans. Graph. (SIGGRAPH Proc.) 26, 3. Google ScholarDigital Library
    2. Akinci, N., Akinci, G., and Teschner, M. 2013. Versatile surface tension and adhesion for SPH fluids. ACM Trans. Graph. 32, 6 (Nov.), 182:1–182:8. Google ScholarDigital Library
    3. Alduán, I., and Otaduy, M. A. 2011. SPH granular flow with friction and cohesion. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, ACM, SCA ’11, 25–32. Google ScholarDigital Library
    4. Ando, R., Thurey, N., and Tsuruno, R. 2012. Preserving fluid sheets with adaptively sampled anisotropic particles. Visualization and Computer Graphics, IEEE Transactions on 18, 8, 1202–1214. Google ScholarDigital Library
    5. Ando, R., Thürey, N., and Wojtan, C. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans. Graph. (Proc. SIGGRAPH 2013) 32, 4, 103:1–103:10. Google ScholarDigital Library
    6. Batty, C., Xenos, S., and Houston, B. 2010. Tetrahedral embedded boundary methods for accurate and flexible adaptive fluids. In Proceedings of Eurographics, vol. 29, 695–704.Google ScholarCross Ref
    7. Batty, C., Uribe, A., Audoly, B., and Grinspun, E. 2012. Discrete viscous sheets. ACM Trans. Graph. (TOG) 31, 4, 113. Google ScholarDigital Library
    8. Becker, M., and Teschner, M. 2007. Weakly compressible SPH for free surface flows. In Proc. of the 2007 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 209–217. Google ScholarDigital Library
    9. Bergou, M., Audoly, B., Vouga, E., Wardetzky, M., and Grinspun, E. 2010. Discrete viscous threads. ACM Transactions on Graphics (TOG) 29, 4, 116. Google ScholarDigital Library
    10. Bonet, J., and Burton, A. 1998. A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications. Comm. Num. Meth. Eng. 14, 437–449.Google ScholarCross Ref
    11. Brochu, T., and Bridson, R. 2009. Robust topological operations for dynamic explicit surfaces. SIAM Journal on Scientific Computing 31, 4, 2472–2493. Google ScholarDigital Library
    12. Brochu, T., Batty, C., and Bridson, R. 2010. Matching fluid simulation elements to surface geometry and topology. ACM Trans. Graph. (SIGGRAPH Proc.), 47:1–47:9. Google ScholarDigital Library
    13. Buckingham, R., and Bush, J. W. M. 2001. Fluid polygons. Physics of Fluids (1994-present) 13, 9, S10–S10.Google Scholar
    14. Bush, J. W., and Hasha, A. E. 2004. On the collision of laminar jets: fluid chains and fishbones. Journal of fluid mechanics 511, 285–310.Google ScholarCross Ref
    15. Chen, X., Ma, D., and Yang, V. 2012. Dynamics and stability of impinging jets. ILASS Americas, 24th Annual Conference on Liquid Atomization and Spray Systems.Google Scholar
    16. Clanet, C. 2007. Waterbells and liquid sheets. Annu. Rev. Fluid Mech. 39, 469–496.Google ScholarCross Ref
    17. Clausen, P., Wicke, M., Shewchuk, J. R., and O’brien, J. F. 2013. Simulating liquids and solid-liquid interactions with lagrangian meshes. ACM Trans. Graph. 32, 2 (Apr.), 17:1–17:15. Google ScholarDigital Library
    18. Durikovic, R. 2001. Animation of soap bubble dynamics, cluster formation and collision. Comput. Graph. Forum 20, 3, 67–76.Google ScholarCross Ref
    19. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In Proc. of ACM SIGGRAPH 2001, 23–30. Google ScholarDigital Library
    20. Gerszewski, D., and Bargteil, A. W. 2013. Physics-based animation of large-scale splashing liquids. ACM Trans. Graph. 32, 6 (Nov.), 185:1–185:6. Google ScholarDigital Library
    21. Golub, G., and Loan, C. 1996. Matrix Computations. The John Hopkins University Press, Baltimore. Google ScholarDigital Library
    22. Guendelman, E., Bridson, R., and Fedkiw, R. 2003. Non-convex rigid bodies with stacking. ACM Trans. Graph. (SIGGRAPH Proc.) 22, 3, 871–878. Google ScholarDigital Library
    23. Hasha, A. E., and Bush, J. W. M. 2002. Fluid fishbones. Physics of Fluids (1994-present) 14, 9, S8–S8.Google Scholar
    24. Idelsohn, S., Onate, E., and Del Pin, F. 2004. The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. International Journal For Numerical Methods in Engineering 61, 964–989.Google ScholarCross Ref
    25. Irving, G., Schroeder, C., and Fedkiw, R. 2007. Volume conserving finite element simulations of deformable models. ACM Trans. Graph. (SIGGRAPH Proc.) 26, 3, 13.1–13.6. Google ScholarDigital Library
    26. Kim, B., Liu, Y., Llamas, I., Jiao, X., and Rossignac, J. 2007. Simulation of bubbles in foam with the volume control method. In Proc. of ACM SIGGRAPH 2007, 98:1–98:10. Google ScholarDigital Library
    27. Kim, D., Song, O.-y., and Ko, H.-S. 2009. Stretching and wiggling liquids. ACM Trans. Graph. (SIGGRAPH Asia Proc.) 28, 5, 120:1–120:7. Google ScholarDigital Library
    28. Klingner, B. M., and Shewchuk, J. R. 2008. Aggressive tetrahedral mesh improvement. In Proceedings of the 16th International Meshing Roundtable, Springer, 3–23.Google Scholar
    29. Loop, C. 1987. Smooth subdivision surfaces based on triangles. Master’s thesis, The University of Utah. Google ScholarDigital Library
    30. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. (SIGGRAPH Proc.) 23, 457–462. Google ScholarDigital Library
    31. Losasso, F., Talton, J., Kwatra, N., and Fedkiw, R. 2008. Two-way coupled SPH and particle level set fluid simulation. IEEE TVCG 14, 4, 797–804. Google ScholarDigital Library
    32. Martin, S., Kaufmann, P., Botsch, M., Grinspun, E., and Gross, M. 2010. Unified simulation of elastic rods, shells, and solids. ACM Trans. Graph. 29, 4, 39:1–39:10. Google ScholarDigital Library
    33. Misztal, M. K., Bridson, R., Erleben, K., Bærentzen, J. A., and Anton, F. 2010. Optimization-based fluid simulation on unstructured meshes. In Proc. of the 7th Workshop on Virtual Reality Interactions and Physical Simulations (VRIPhys2010), 11–20.Google Scholar
    34. Misztal, M. K., Erleben, K., Bargteil, A., Fursund, J., Christensen, B., Bærentzen, J. A., and Bridson, R. 2012. Multiphase flow of immiscible fluids on unstructured moving meshes. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Eurographics Association, 97–106. Google ScholarDigital Library
    35. Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In Proc. of the 2003 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 154–159. Google ScholarDigital Library
    36. Narain, R., Golas, A., Curtis, S., and Lin, M. C. 2009. Aggregate dynamics for dense crowd simulation. In ACM Transactions on Graphics (TOG), vol. 28, ACM, 122. Google ScholarDigital Library
    37. Oefner, F., 2013. Orchid. http://fabianoefner.com/?portfolio=orchid.Google Scholar
    38. Patkar, S., Aanjaneya, M., Karpman, D., and Fedkiw, R. 2013. A hybrid Lagrangian-Eulerian formation for bubble generation and dynamics. In Proceedings of 2013 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 105–114. Google ScholarDigital Library
    39. Pfaff, T., Thuerey, N., and Gross, M. 2012. Lagrangian vortex sheets for animating fluids. ACM Trans. Graph. 31, 4, 112:1–112:8. Google ScholarDigital Library
    40. Premžoe, S., Tasdizen, T., Bigler, J., Lefohn, A., and Whitaker, R. T. 2003. Particle-based simulation of fluids. In Computer Graphics Forum, vol. 22, Wiley Online Library, 401–410.Google Scholar
    41. 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
    42. Ribe, N. 2002. A general theory for the dynamics of thin viscous sheets. Journal of Fluid Mechanics 457, 255–283.Google ScholarCross Ref
    43. Ribe, N. M. 2004. Coiling of viscous jets. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 460, 2051, 3223–3239.Google Scholar
    44. Saye, R. I., and Sethian, J. A. 2013. Multiscale modeling of membrane rearrangement, drainage, and rupture in evolving foams. Science 340, 6133, 720–724.Google Scholar
    45. Sin, F., Bargteil, A. W., and Hodgins, J. K. 2009. A point-based method for animating incompressible flow. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., ACM, New York, NY, USA, SCA ’09, 247–255. Google ScholarDigital Library
    46. Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., and Seidel, H.-P. 2004. Laplacian surface editing. In Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, ACM, 175–184. Google ScholarDigital Library
    47. Stam, J. 2009. Nucleus: Towards a unified dynamics solver for computer graphics. In Computer-Aided Design and Computer Graphics, 2009. CAD/Graphics’ 09. 11th IEEE International Conference on, IEEE, 1–11.Google ScholarCross Ref
    48. Thürey, N., Wojtan, C., Gross, M., and Turk, G. 2010. A multiscale approach to mesh-based surface tension flows. ACM Trans. Graph. (TOG) 29, 4, 1–10. Google ScholarDigital Library
    49. Wicke, M., Ritchie, D., Klingner, B., Burke, S., Shewchuk, J., and O’Brien. 2010. Dynamic local remeshing for elastoplastic simulation. In Proc. of ACM SIGGRAPH 2010, 49:1–49:11. Google ScholarDigital Library
    50. Wojtan, C., Thürey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. In ACM Trans. Graph. (TOG), vol. 28, ACM, 76. Google ScholarDigital Library
    51. Yu, J., and Turk, G. 2010. Reconstructing surfaces of particle-based fluids using anisotropic kernels. In Proc. of the 2010 ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 217–225. Google ScholarDigital Library
    52. Yu, J., Wojtan, C., Turk, G., and Yap, C. 2012. Explicit mesh surfaces for particle based fluids. Comp. Graph. Forum 31, 2pt4 (May), 815–824. Google ScholarDigital Library
    53. Zhang, Y., Wang, H., Wang, S., Tong, Y., and Zhou, K. 2012. A deformable surface model for real-time water drop animation. Visualization and Computer Graphics, IEEE Transactions on 18, 8, 1281–1289. Google ScholarDigital Library
    54. Zheng, W., Zhu, B., Kim, B., and Fedkiw, R. 2013. A new incompressibility discretization for a hybrid particle MAC grid representation with surface tension. (submitted).Google Scholar


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