“Closest-Point Turbulence for Liquid Surfaces” by Kim, Thuerey and Tessendorf

  • ©Theodore Kim, Nils Thuerey, and Jerry Tessendorf




    Closest-Point Turbulence for Liquid Surfaces

Session/Category Title: Voxels & Liquids




    We propose a method of increasing the apparent spatial resolution of an existing liquid simulation. Previous approaches to this “up-resing” problem have focused on increasing the turbulence of the underlying velocity field. Motivated by measurements in the free surface turbulence literature, we observe that past certain frequencies, it is sufficient to perform a wave simulation directly on the liquid surface, and construct a reduced-dimensional surface-only simulation. We sidestep the considerable problem of generating a surface parameterization by employing an embedding technique known as the Closest Point Method (CPM) that operates directly on a 3D extension field. The CPM requires 3D operators, and we show that for surface operators with no natural 3D generalization, it is possible to construct a viable operator using the inverse Abel transform. We additionally propose a fast, frozen core closest point transform, and an advection method for the extension field that reduces smearing considerably. Finally, we propose two turbulence coupling methods that seed the high-resolution wave simulation in visually expected regions.


    1. Adalsteinsson, D. and Sethian, J. 2003. Transport and diffusion of material quantities on propagating interfaces via level set methods. J. Comput. Phys. 185, 1, 271–288.
    2. Angelidis, A., Anon, J., Bruins, G., Reisch, J., and Varagnolo, E. 2011. Ocean mission on Cars 2. In ACM SIGGRAPH Talks. 17:1–17:1.
    3. Angst, R., Thurey, N., Botsch, M., and Gross, M. 2008. Robust and efficient wave simulations on deforming meshes. Comput. Graph. Forum 27, 6, 1895–1900.
    4. Auer, S., MacDonald, C., Treib, M., Schneider, J., and Westermann, R. 2012. Real-Time fluid effects on surfaces using the closest point method. Comput. Graph. Forum 31, 6, 1909–1923.
    5. Bargteil, A. W., Goktekin, T. G., O’Brien, J. F., and Strain, J. A. 2006a. A semi-Lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25, 19–38.
    6. Bargteil, A. W., Sin, F., Michaels, J. E., Goktekin, T. G., and O’Brien, J. F. 2006b. A texture synthesis method for liquid animations. In Proceedings of the ACM/Eurographics Symposium on Computer Animation. 345–351.
    7. Bergou, M., Mathur, S., Wardetzky, M., and Grinspun, E. 2007. Tracks: Toward directable thin shells. ACM Trans. Graph. 26, 3.
    8. Bertalmio, M., Cheng, L.-T., Osher, S., and Sapiro, G. 2001. Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys. 174, 2, 759–780.
    9. Bracewell, R. 1999. The Fourier Transform and Its Applications. McGraw-Hill.
    10. Brocchini, M. and Peregrine, D. H. 2001. The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225–254.
    11. Carlson, D. 2007. Wave displacement effects for surf’s up. In ACM SIGGRAPH Sketches. ACM Press, New York.
    12. Chentanez, N. and Muller, M. 2010. Real-Time simulation of large bodies of water with small scale details. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 197–206.
    13. Chentanez, N. and Muller, M. 2011. Real-Time eulerian water simulation using a restricted tall cell grid. ACM Trans. Graph. 30, 82:1–82:10.
    14. Chuang, M., Luo, L., Brown, B. J., Rusinkiewicz, S., and Kazhdan, M. 2009. Estimating the laplace-beltrami operator by restricting 3d functions. In Proceedings of the Eurographics Symposium on Geometry Processing. 1475–1484.
    15. Darles, E., Crespin, B., Ghazanfarpour, D., and Gonzato, J. 2011. A survey of ocean simulation and rendering techniques in computer graphics. Comput. Graph. Forum 30, 43–60.
    16. Dias, F. and Kharif, C. 1999. Nonlinear gravity and capillary-gravity waves. Ann. Rev. Fluid Mech. 31, 301–346.
    17. Dubey, P., Hanrahan, P., Fedkiw, R., Lentine, M., and Schroeder, C. 2011. PhysBAM: Physically based simulation. In ACM SIGGRAPH Courses. 10:1–10:22.
    18. Falcon, E. 2010. Laboratory experiments on wave turbulence. Discr. Cont. Dyn. B13, 819–840.
    19. Flores, L. and Horsley, D. 2009. Underground cave sequence for Land of the Lost. In ACM SIGGRAPH Talks. ACM Press, New York, 6:1–6:1.
    20. Foster, N. and Fedkiw, R. 2001. Practical animation of liquids. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’01). 23–30.
    21. Greer, J. B. 2006. An improvement of a recent Eulerian method for solving pdss on general geometrics. J. Sci. Comput. 29, 3, 321–352.
    22. Heo, N. and Ko, H.-S. 2010. Detail-Preserving fully-Eulerian interface tracking framework. ACM Trans. Graph. 29, 176:1–176:8.
    23. Hong, Y., Zhu, D., Qiu, X., and Wang, Z. 2010. Geometry-Based control of fire simulation. Vis. Comput. 26.
    24. Huang, R., Melek, Z., and Keyser, J. 2011. Preview-Based sampling for controlling gaseous simulations. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 177–186.
    25. Jang, T., Kim, H., Bae, J., Seo, J., and Noh, J. 2010. Multilevel vorticity confinement for water turbulence simulation. Vis. Comput. 26, 873–881.
    26. Johnson, R. S. 1997. A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press.
    27. Kim, D., Song, O.-Y., and Ko, H.-S. 2009. Stretching and wiggling liquids. ACM Trans. Graph. 28, 5, 120:1–120:7.
    28. Kim, T., Thurey, N., James, D., and Gross, M. 2008. Wavelet turbulence for fluid simulation. ACM Trans. Graph. 27, 50:1–50:6.
    29. Komori, S., Murakami, Y., and Ueda, H. 1989. The relationship between surface-renewal and bursting motions in an open channel flow. J. Fluid Mech. 203, 103–123.
    30. Kwatra, V., Adalsteinsson, D., Kim, T., Kwatra, N., Carlson, M., and Lin, M. 2007. Texturing fluids. IEEE Trans. Vis. Comput. Graph. 13, 5, 939–952.
    31. Lait, J. 2011. Correcting low frequency impulses in distributed simulations. In ACM SIGGRAPH Talks. 53:1–53:2.
    32. Lentine, M., Zheng, W., and Fedkiw, R. 2010. A novel algorithm for incompressible flow using only a coarse grid projection. ACM Trans. Graph. 29, 114:1–114:9.
    33. Losasso, F., Fedkiw, R., and Osher, S. 2006. Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids 35, 10, 995–1010.
    34. Ma, C., Wei, L.-Y., Guo, B., and Zhou, K. 2009. Motion field texture synthesis. ACM Trans. Graph. 28, 5, 110:1–110:8.
    35. MacDonald, C. B., Brandman, J., and Ruuth, S. J. 2011. Solving eigenvalue problems on curved surfaces using the closest point method. J. Comput. Phys. 230, 22.
    36. MacDonald, C. B. and Ruuth, S. J. 2008. Level set equations on surfaces via the closest point method. J. Sci. Comput. 35, 2-3, 219–240.
    37. MacDonald, C. B. and Ruuth, S. J. 2009. The implicit closest point method for the numerical solution of partial differential equations on surfaces. J. Sci. Comput. 31, 6, 4330–4350.
    38. Mauch, S. 2003. Efficient algorithms for solving static Hamilton-Jacobi equations. Ph.D. thesis, California Institute of Technology, Pasadena, CA.
    39. McNamara, A., Treuille, A., Popovic, Z., and Stam, J. 2004. Fluid control using the adjoint method. ACM Trans. Graph. 23, 449–456.
    40. Miller, K. and Ross, B. 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley & Sons.
    41. Museth, K., Breen, D. E., Whitaker, R. T., and Barr, A. H. 2002. Level set surface editing operators. ACM Trans. Graph. 21, 330–338.
    42. Narain, R., Kwatra, V., Lee, H.-P., Kim, T., Carlson, M., and Lin, M. C. 2007. Feature-Guided dynamic texture synthesis on continuous flows. In Proceedings of the Eurographics Symposium on Rendering. 361–370.
    43. Narain, R., Sewall, J., Carlson, M., and Lin, M. C. 2008. Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans. Graph. 27, 166:1–166:8.
    44. Nielsen, M. B. and Bridson, R. 2011. Guide shapes for high resolution naturalistic liquid simulation. ACM Trans. Graph. 30, 83:1–83:8.
    45. Nielsen, M. B., Christensen, B. B., Zafar, N. B., Roble, D., and Museth, K. 2009. Guiding of smoke animation through variational coupling of simulations at different resolutions. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 217–226.
    46. Patel, S., Tessendorf, J., and Molemaker, J. 2009. Monocoupled 3D and 2D river simulations. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Posters Session.
    47. Pharr, M. and Humphreys, G. 2010. Physically-Based Rendering: From Theory to Implementation. Morgan Kaufmann, San Fransisco, CA.
    48. Podlubny, I. 1999. Fractional Differential Equations. Academic Press.
    49. Ruuth, S. J. and Merriman, B. 2008. A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys. 227, 3, 1943–1961.
    50. Savelsberg, R. and van de Water, W. 2008. Turbulence of a free surface. Physical Rev. Lett. 100, 034501.
    51. Schechter, H. and Bridson, R. 2008. Evolving sub-grid turbulence for smoke animation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 1–7.
    52. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. 2008. An unconditionally stable maccormack method. J. Sci. Comput. 35, 2-3, 350–371.
    53. Shi, L. and Yu, Y. 2005. Taming liquids for rapidly changing targets. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 229–236.
    54. Stam, J. 1999. Stable fluids. In Proceedings of the Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH’99). 121–128.
    55. Tessendorf, J. 2004a. Interactive water surfaces. In Game Programming Gems 4. Charles River Media.
    56. Tessendorf, J. 2004b. Simulating ocean water. In ACM SIGGRAPH Courses.
    57. Tessendorf, J. 2008. Vertical derivative math for iwave. http://people. clemson.edu/~jtessen/papers_files/verticalderivativesforiwave.pdf.
    58. Tessendorf, J. 2011. Resolution independent volumes. In ACM SIGGRAPH Courses.
    59. Thurey, N., Wojtan, C., Gross, M., and Turk, G. 2010. A multiscale approach to mesh-based surface tension flows. ACM Trans. Graph. 29, 48:1–48:10.
    60. Wardetzky, M., Mathur, S., Kalberer, F., and Grinspun, E. 2007. Discrete laplace operators: No free lunch. In Proceedings of the Eurographics Symposium on Geometry Processing. 33–37.
    61. Wojtan, C., Thurey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. 28, 3, 9.
    62. Yu, J., Wojtan, C., Turk, G., and Yap, C. 2012. Explicit mesh surfaces for particle based fluids. Comput. Graph. Forum 31, 2, 815–824.
    63. Yuan, Z., Chen, F., and Zhao, Y. 2011. Pattern-Guided smoke animation with lagrangian coherent structure. ACM Trans. Graph. 30, 136:1–136:8.
    64. Yuan, Z., Zhao, Y., and Chen, F. 2012. Incorporating stochastic turbulence in particle-based fluid simulation. Vis. Comput., 435–444.
    65. Yuksel, C., House, D. H., and Keyser, J. 2007. Wave particles. ACM Trans. Graph. 26.
    66. Zakharov, V. E., L’Vov, V. S., and Falkovich, G. 1992. Kolmogorov Spectra of Turbulence 1: Wave Turbulence. Springer.
    67. Zhu, Y. and Bridson, R. 2005. Animating sand as a fluid. ACM Trans. Graph. 24, 965–972.

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