“Lagrangian vortex sheets for animating fluids” by Pfaff, Thuerey and Gross

  • ©Tobias Pfaff, Nils Thuerey, and Markus Gross




    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 directly visible at the interface, and is not captured by commonly used turbulence models. We present a novel approach that employs a triangle mesh as a high-resolution surface representation combined with a coarse Eulerian solver. On the mesh, we solve the interfacial vortex sheet equations, which allows us to accurately simulate buoyancy induced turbulence. For complex boundary conditions we propose an orthogonal turbulence model that handles vortices caused by obstacle interaction. In addition, we demonstrate a re-sampling scheme to remove surfaces that are hidden inside the bulk volume. In this way we are able to achieve highly detailed simulations of turbulent plumes efficiently.


    1. Angelidis, A., Neyret, F., Singh, K., and Nowrouzezahrai, D. 2006. A controllable, fast and stable basis for vortex based smoke simulation. In ACM SIGGRAPH/EG Symposium on Computer Animation. Google ScholarDigital Library
    2. Bargteil, A. W., Goktekin, T. G., O’Brien, J. F., and Strain, J. A. 2006. A semi-lagrangian contouring method for fluid simulation. ACM Transactions on Graphics 25, 1. Google ScholarDigital Library
    3. Brady, M., Leonard, A., and Pullin, D. I. 1998. Regularized vortex sheet evolution in three dimensions. J. Comput. Phys. 146, 520–545. Google ScholarDigital Library
    4. Brochu, T., and Bridson, R. 2009. Animating smoke as a surface. SCA posters.Google Scholar
    5. Chentanez, N., and Mueller, M. 2011. Real-time eulerian water simulation using a restricted tall cell grid. ACM Trans. Graph. 30, 82:1–82:10. Google ScholarDigital Library
    6. Chorin, A. J., and Bernard, P. S. 1973. Discretization of a vortex sheet on a roll-up. J. Comp. Phys. 13, 423–429.Google ScholarCross Ref
    7. Cowper, G. 1973. Gaussian quadrature formulas for triangles. Int. J. Num. Methods 7, 3, 405–408.Google ScholarCross Ref
    8. Desbrun, M., Meyer, M., Schröder, P., and Barr, A. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. Proc. SIGGRAPH, 317–324. Google ScholarDigital Library
    9. Enright, D., Fedkiw, R., Ferziger, J., and Mitchell, I. 2002. A hybrid particle level set method for improved interface capturing. J. Comp. Phys. 183, 83–116. Google ScholarDigital Library
    10. Kim, T., Thuerey, N., James, D., and Gross, M. 2008. Wavelet turbulence for fluid simulation. ACM SIGGRAPH Papers 27, 3 (Aug), Article 6. Google ScholarDigital Library
    11. Kim, D., Song, O.-Y., and Ko, H.-S. 2009. Stretching and wiggling liquids. ACM Transactions on Graphics 28, 5, 120. Google ScholarDigital Library
    12. Kolluri, R. 2005. Provably good moving least squares. In Proceedings of ACM-SIAM Symposium on Discrete Algorithms, 1008–1018. Google ScholarDigital Library
    13. Launder, B. E., and Sharma, D. B. 1974. Applications of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transf. 1, 1031–138.Google ScholarCross Ref
    14. Leonard, A. 1980. Vortex methods for flow simulation. J. Comput. Phys. 37, 289–335.Google ScholarCross Ref
    15. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. Proceedings of ACM SIGGRAPH, 457–462. Google ScholarDigital Library
    16. Lozano, A., Garca-Olivares, A., and Dopazo, C. 1998. The instability growth leading to a liquid sheet breakup. Phys. Fluids 10, 9, 2188–2197.Google ScholarCross Ref
    17. Meng, J. C. S. 1978. The physics of vortex-ring evolution in a stratified and shearing environment. J. Fluid Mech., 3, 455–469.Google ScholarCross Ref
    18. Mullen, P., Crane, K., Pavlov, D., Tong, Y., and Desbrun, M. 2009. Energy-Preserving Integrators for Fluid Animation. ACM SIGGRAPH Papers 28, 3 (Aug), Article 38. Google ScholarDigital Library
    19. Müller, M., Solenthaler, B., Keiser, R., and Gross, M. 2005. Particle-based fluid-fluid interaction. ACM SIGGRAPH/EG Symposium on Computer Animation. Google ScholarDigital Library
    20. Narain, R., Sewall, J., Carlson, M., and Lin, M. C. 2008. Fast animation of turbulence using energy transport and procedural synthesis. ACM SIGGRAPH Asia papers, Article 166. Google ScholarDigital Library
    21. Pfaff, T., Thuerey, N., Selle, A., and Gross, M. 2009. Synthetic turbulence using artificial boundary layers. ACM Transactions on Graphics 28, 5, 121:1–121:10. Google ScholarDigital Library
    22. Pfaff, T., Thuerey, N., Cohen, J., Tariq, S., and Gross, M. 2010. Scalable fluid simulation using anisotropic turbulence particles. SIGGRAPH Asia papers, 174:1–174:8. Google ScholarDigital Library
    23. Pope, S. B. 2000. Turbulent Flows. Cambridge University Press.Google Scholar
    24. Rasmussen, N., Nguyen, D. Q., Geiger, W., and Fedkiw, R. 2003. Smoke simulation for large scale phenomena. In Proceedings of ACM SIGGRAPH. Google ScholarDigital Library
    25. Rosenhead, L. 1931. The formation of vorticies from a surface of discontinuity. Proc. Roy. Soc. London 134, 170–192.Google ScholarCross Ref
    26. Schechter, H., and Bridson, R. 2008. Evolving sub-grid turbulence for smoke animation. In Proceedings of the 2008 ACM/Eurographics Symposium on Computer Animation. Google ScholarDigital Library
    27. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. Proceedings of ACM SIGGRAPH 24, 3, 910–914. Google ScholarDigital Library
    28. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing. Google ScholarDigital Library
    29. Spalart, P. R., and Allmaras, S. R. 1992. A one-equation turbulence model for aerodynamic flows. AIAA Paper 92, 0439.Google Scholar
    30. Stam, J., and Fiume, E. 1993. Turbulent wind fields for gaseous phenomena. In Proceedings of ACM SIGGRAPH. Google ScholarDigital Library
    31. Stam, J. 1999. Stable fluids. In Proceedings of ACM SIGGRAPH. Google ScholarDigital Library
    32. Stock, M., Dahm, W., and Tryggvason, G. 2008. Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method. J. Comp. Phys. 227, 9021–9043. Google ScholarDigital Library
    33. Tryggvason, G., and Aref, H. 1983. Numerical experiments on hele-shaw flow with a sharp interface. J. Fluid Mech., 1–30.Google Scholar
    34. Weissmann, S., and Pinkall, U. 2010. Filament-based smoke with vortex shedding and variational reconnection. ACM Transactions on Graphics 29, 4. Google ScholarDigital Library
    35. Wojtan, C., Thuerey, N., Gross, M., and Turk, G. 2010. Physics-inspired topology changes for thin fluid features. ACM Transactions on Graphics 29, 3 (July), 8. Google ScholarDigital Library
    36. Wu, J.-Z. 1995. A theory of three-dimensional interfacial vorticity dynamics. Phys. Fluids 7, 10, 2375–2395.Google ScholarCross Ref
    37. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. Proceedings of ACM SIGGRAPH 24, 3, 965–972. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: