“A stream function solver for liquid simulations” by Ando and Thürey

  • ©Ryoichi Ando and Nils Thürey




    A stream function solver for liquid simulations

Session/Category Title:   Wave-Particle Fluidity




    This paper presents a liquid simulation technique that enforces the incompressibility condition using a stream function solve instead of a pressure projection. Previous methods have used stream function techniques for the simulation of detailed single-phase flows, but a formulation for liquid simulation has proved elusive in part due to the free surface boundary conditions. In this paper, we introduce a stream function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling.Although our approach increases the dimension of the linear system necessary to enforce incompressibility, it provides interesting and surprising benefits. First, the resulting flow is guaranteed to be divergence-free regardless of the accuracy of the solve. Second, our free-surface boundary conditions guarantee divergence-free motion even in the un-simulated air phase, which enables two-phase flow simulation by only computing a single phase. We implemented this method using a variant of FLIP simulation which only samples particles within a narrow band of the liquid surface, and we illustrate the effectiveness of our method for detailed two-phase flow simulations with complex boundaries, detailed bubble interactions, and two-way solid-fluid coupling.


    1. Ando, R., Thuerey, N., and Wojtan, C. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans. Graph. 32, 4, 103. Google ScholarDigital Library
    2. Angelidis, A., and Neyret, F. 2005. Simulation of smoke based on vortex filament primitives. In Proceedings of the Symposium on Computer Animation, ACM, 87–96. Google ScholarDigital Library
    3. Barragy, E., and Carey, G. 1997. Stream function-vorticity driven cavity solution using p finite elements. Computers and Fluids 26, 5, 453–468.Google ScholarCross Ref
    4. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. 26, 3 (July). Google ScholarDigital Library
    5. Batty, C., Xenos, S., and Houston, B. 2010. Tetrahedral embedded boundary methods for accurate and flexible adaptive fluids. In Proceedings of Eurographics.Google Scholar
    6. Boyd, L., and Bridson, R. 2012. Multiflip for energetic two-phase fluid simulation. ACM Trans. Graph. 31, 2, 16:1–16:12. Google ScholarDigital Library
    7. Brecht, S. H., and Ferrante, J. R. 1989. Vortex-in-cell simulations of buoyant bubbles in three dimensions. Physics of Fluids A: Fluid Dynamics (1989–1993) 1, 7, 1166–1191.Google Scholar
    8. Bridson, R., Houriham, J., and Nordenstam, M. 2007. Curl-noise for procedural fluid flow. ACM Transactions on Graphics (TOG) 26, 3, 46. Google ScholarDigital Library
    9. Bridson, R. 2008. Fluid Simulation for Computer Graphics. AK Peters/CRC Press. Google ScholarDigital Library
    10. Brochu, T., Keeler, T., and Bridson, R. 2012. Linear-time smoke animation with vortex sheet meshes. In Proceedings of the 11th ACM SIGGRAPH/Eurographics conference on Computer Animation, Eurographics Association, 87–95. Google ScholarDigital Library
    11. Budsberg, J., Losure, M., Museth, K., and Baer, M. 2013. Liquids in “The Croods”. In ACM SIGGRAPH Digital Production Symposium (DigiPro).Google Scholar
    12. Carlson, M., Mucha, P. J., and Turk, G. 2004. Rigid fluid: Animating the interplay between rigid bodies and fluid. In ACM SIGGRAPH 2004 Papers, ACM, New York, NY, USA, SIGGRAPH ’04, 377–384. Google ScholarDigital Library
    13. Chentanez, N., Mller, M., and Kim, T.-Y. 2014. Coupling 3D Eulerian, Heightfield and Particle Methods for Interactive Simulation of Large Scale Liquid Phenomena. In Eurographics/ACM SIGGRAPH Symposium on Computer Animation, The Eurographics Association, V. Koltun and E. Sifakis, Eds.Google Scholar
    14. Da, F., Batty, C., and Grinspun, E. 2014. Multimaterial mesh-based surface tracking. ACM Trans. on Graphics (SIGGRAPH 2014) Google ScholarDigital Library
    15. de Goes, F., Crane, K., Desbrun, M., Schröder, P., et al. 2013. Digital geometry processing with discrete exterior calculus. In ACM SIGGRAPH 2013 Courses, ACM, 7. Google ScholarDigital Library
    16. Elcott, S., Tong, Y., Kanso, E., Schröder, P., and Desbrun, M. 2007. Stable, circulation-preserving, simplicial fluids. ACM Transactions on Graphics (TOG) 26, 1, 4. Google ScholarDigital Library
    17. English, R. E., Qiu, L., Yu, Y., and Fedkiw, R. 2013. Chimera grids for water simulation. In Proceedings of the Symposium on Computer Animation, 85–94. Google ScholarDigital Library
    18. Enright, D., Nguyen, D., Gibou, F., and Fedkiw, R. 2003. Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free-Surface Flows. Proc. of the 4th ASME-JSME Joint Fluids Engineering Conference.Google Scholar
    19. Ferstl, F., Westermann, R., and Dick, C. 2014. Large-scale liquid simulation on adaptive hexahedral grids. IEEE Trans. Vis. Comput. Graph. 20, 10, 1405–1417.Google ScholarCross Ref
    20. Foster, N., and Metaxas, D. N. 1997. Controlling fluid animation. In Computer Graphics International, 178–188. Google ScholarDigital Library
    21. G. Guj, F. S. 1993. A vorticity-velocity method for the numerical solution of 3d incompressible flows. Journal of Computational Physics 106, 2, 286–298. Google ScholarCross Ref
    22. Gamito, M. N., Lopes, P. F., and Gomes, M. R. 1995. Two-dimensional simulation of gaseous phenomena using vortex particles. In In Proceedings of the 6th Eurographics Workshop on Computer Animation and Simulation, Citeseer.Google Scholar
    23. Gibou, F., Fedkiw, R. P., Cheng, L.-T., and Kang, M. 2002. A second-order-accurate symmetric discretization of the poisson equation on irregular domains. Journal of Computational Physics 176, 1, 205–227. Google ScholarDigital Library
    24. Golas, A., Narain, R., Sewall, J., Krajcevski, P., Dubey, P., and Lin, M. 2012. Large-scale fluid simulation using velocity-vorticity domain decomposition. ACM Trans. Graph. 31, 6 (Nov.), 148:1–148:9. Google ScholarDigital Library
    25. Harlow, F., and Welch, E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (12), 2182–2189.Google ScholarCross Ref
    26. Hong, J.-M., and Kim, C.-H. 2005. Discontinuous fluids. In ACM SIGGRAPH 2005 Papers, ACM, New York, NY, USA, SIGGRAPH ’05, 915–920. Google ScholarDigital Library
    27. Ihmsen, M., Orthmann, J., Solenthaler, B., Kolb, A., and Teschner, M. 2014. SPH fluids in computer graphics. In Eurographics – State of the Art Reports, Eurographics Association, 21–42.Google Scholar
    28. Kang, N., Park, J., Yong Noh, J., and Shin, S. Y. 2010. A Hybrid Approach to Multiple Fluid Simulation using Volume Fractions. Computer Graphics Forum 29, 685–694.Google ScholarCross Ref
    29. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. ACM Trans. Graph. 25, 3, 820–825. Google ScholarDigital Library
    30. Lorensen, W. E., and Cline, H. E. 1987. Marching cubes: A high resolution 3d surface construction algorithm. In Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, ACM, New York, NY, USA, SIGGRAPH ’87, 163–169. Google ScholarDigital Library
    31. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. ACM Trans. Graph. 25, 3, 812–819. Google ScholarDigital Library
    32. Müller, M., Solenthaler, B., Keiser, R., and Gross, M. H. 2005. Particle-based fluid-fluid interaction. In Proceedings of the Symposium on Computer Animation, ACM, 237–244. Google ScholarDigital Library
    33. Pfaff, T., Thuerey, N., and Gross, M. H. 2012. Lagrangian vortex sheets for animating fluids. ACM Trans. Graph. 31, 4, 112. Google ScholarDigital Library
    34. Ren, B., Li, C., Yan, X., Lin, M. C., Bonet, J., and Hu, S. 2014. Multiple-fluid SPH simulation using a mixture model. ACM Trans. Graph. 33, 5, 171. Google ScholarDigital Library
    35. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. ACM Trans. Graph. 24, 3 (July), 910–914. Google ScholarDigital Library
    36. Stam, J. 1999. Stable fluids. In Proceedings of SIGGRAPH ’99, ACM, 121–128. Google ScholarDigital Library
    37. Stock, M. J., Dahm, W. J., and Tryggvason, G. 2008. Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method. Journal of Computational Physics 227, 21, 9021–9043. Google ScholarDigital Library
    38. Vines, M., Houston, B., Lang, J., and Lee, W.-S. 2014. Vortical inviscid flows with two-way solid-fluid coupling. IEEE Transactions on Visualization and Computer Graphics 20, 2 (Feb.), 303–315. Google ScholarDigital Library
    39. Wang, S., and Zhang, X. 2011. An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows. Journal of Computational Physics 230, 9, 3479–3499. Google ScholarDigital Library
    40. Weissmann, S., and Pinkall, U. 2010. Filament-based smoke with vortex shedding and variational reconnection. ACM Transactions on Graphics (TOG) 29, 4, 115. Google ScholarDigital Library
    41. Wong, A. K., and Reizes, J. A. 1984. An effective vorticity-vector potential formulation for the numerical simulation of three-dimensional duct flow problems. Journal of Computational Physics 55, 98–114.Google ScholarCross Ref
    42. Zhu, Y., Sifakis, E., Teran, J., and Brandt, A. 2010. An efficient multigrid method for the simulation of high-resolution elastic solids. ACM Trans. Graph. 29, 2. Google ScholarDigital Library

ACM Digital Library Publication:

Overview Page: