The Visual Computer

, Volume 28, Issue 5, pp 425–434 | Cite as

Fluid simulation with adaptively sharpening and embedded boundary conditions

  • Meng YangEmail author
  • Wenjuan Chen
Original Article


In this paper, we present a physically based technique for simulating inviscid fluids. Our contribution is concerned with two issues. First, for solving the advection equation, we introduce a hybrid scheme that couples the FLIP scheme with the semi-Lagrangian scheme by adaptively distributing implicit particles and using a transition layer to propagate information. Secondly, for solving pressure, we develop a flux based scheme that can embed arbitrary solid boundaries into a Poisson equation. And based on this scheme we make further improvement to achieve two-way fluid/solid coupling on an octree structure with second-order accuracy. Finally, the experimental results demonstrate that our hybrid scheme for advection can preserve relatively fine surface details with less computation expenditure; and simultaneously our robust pressure solver can handle both stationary and moving obstacles more efficiently compared with unstructured meshes.


Numerical dissipation Hybrid scheme Particle Boundary condition Flux Two-way coupling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Stam, J.: Stable fluids. In: SIGGRAPH 1999, August 1999, pp. 121–128 (1999) CrossRefGoogle Scholar
  2. 2.
    Foster, N., Fedkiw, R.: Practical animation of liquids. In: SIGGRAPH 2001, August 2001, pp. 23–30 (2001) CrossRefGoogle Scholar
  3. 3.
    Enright, D., Marschner, S., Fedkiw, R.: Animation and rendering of complex water surfaces. In: SIGGRAPH 2002, August 2002, pp. 736–744 (2002) CrossRefGoogle Scholar
  4. 4.
    Nguyen, D.Q., Fedkiw, R., Jensen, H.W.: Physically based modeling and animation of fire. ACM Trans. Graph. 21(3), 721–728 (2002) CrossRefGoogle Scholar
  5. 5.
    Kim, J., Cha, D., Chang, B.: Practical animation of turbulent splashing water. In: Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium, pp. 335–344 (2006) Google Scholar
  6. 6.
    Losasso, F., Shinar, T., Selle, A., Fedkiw, R.: Multiple interacting liquids. In: SIGGRAPH06, ACM Trans. Graph., vol. 25, pp. 812–819 (2006) Google Scholar
  7. 7.
    Fedkiw, R., Stam, J., Jensen, H.W.: Visual simulation of smoke. In: SIGGRAPH 2001, August 2001, pp. 15–22 (2001) CrossRefGoogle Scholar
  8. 8.
    Selle, A., Rasmussen, N., Fedkiw, R.: A vortex particle method for smoke, water and explosions. ACM Trans. Graph. 24(3), 910–914 (2005) CrossRefGoogle Scholar
  9. 9.
    Kim, B., Liu, Y., Llamas, I., et al.: FlowFixer: using BFECC for fluid simulation. In: Eurographics Workshop on Natural Phenomena (2005) Google Scholar
  10. 10.
    Molemaker, J., Cohen, M.J., Patel, S., et al.: Low viscosity flow simulations for animation. In: Symposium on Computer Animation 2008, (2008) Google Scholar
  11. 11.
    Osher, S., Fedkiw, R.: Level-Set Methods and Dynamic Implicit Surfaces. Springer, New York (2003) zbMATHGoogle Scholar
  12. 12.
    Song, O.-Y., Shin, H., Ko, H.-S.: Stable but nondissipative water. ACM Trans. Graph. 24(1), 81–97 (2005) CrossRefGoogle Scholar
  13. 13.
    Harlow, F.H.: The particle-in-cell method for numerical solution of problems in fluid dynamics. In: Experimental Arithmetic, High-Speed Computations and Mathematics (1963) Google Scholar
  14. 14.
    Brackbill, J.U., Ruppel, H.M.: FLIP: a method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J. Comput. Phys. 65, 314–343 (1986) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Patrick, M., Keenan, C., Dmitry, P., Yiying, T., Mathieu, D.: Energy-preserving integrators for fluid animation. In: SIGGRAPH 2009, August 2009 Google Scholar
  16. 16.
    Kim, T., Thürey, N., James, D.: Wavelet turbulence for fluid simulation. In: SIGGRAPH 2008, August 2008 Google Scholar
  17. 17.
    Houston, B., Bond, C., Wiebe, M.: A unified approach for modeling complex occlusions in fluid simulations. In: Proc. SIGGRAPH Sketches & Applications (2003) Google Scholar
  18. 18.
    Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., Fedkiw, R.: Directable photorealistic liquids. In: Proceedings of the 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 195–200 (2004) Google Scholar
  19. 19.
    Losasso, F., Gibou, F., Fedkiw, R.: Simulating water and smoke with an octree data structure. ACM Trans. Graph. 23(3), 457–462 (2004) (Proc. SIGGRAPH 2004) CrossRefGoogle Scholar
  20. 20.
    Feldman, B.E., O’brien, J.F., Klingner, B.M.: Animating gases with hybrid meshes. ACM Trans. Graph. 24(3), 904–909 (2005) (Proc. SIGGRAPH 2005) CrossRefGoogle Scholar
  21. 21.
    Klingner, B.M., Feldman, B.E., Chentanez, N., O’Brien, J.F.: Fluid animation with dynamic meshes. ACM Trans. Graph. 25(3), 820–825 (2006) (Proc. SIGGRAPH 2006) CrossRefGoogle Scholar
  22. 22.
    Jie, T., Xubo, Y.: Physically-based fluid animation: a survey. Sci. China Ser. F 25(1), 1–17 (2008) Google Scholar
  23. 23.
    Müller, M., Schirm, S., Teschner, M., Heidelberger, B., Gross, M.: Interaction of fluids with deformable solids. Computer Animation and Virtual World 15(3), 159–171 (2004) CrossRefGoogle Scholar
  24. 24.
    Carlson, M., Mucha, P.J., Turk, G.: Rigid fluid: animating the interplay between rigid bodies and fluid. ACM Trans. Graph. 23, 377–384 (2004) (Proc. SIGGRAPH 2004) CrossRefGoogle Scholar
  25. 25.
    Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479–517 (2002) MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Chentanez, N., Goktekin, T.G., Feldman, B.E., O’Brien, J.F.: Simultaneous coupling of fluids and deformable bodies. In: Proceedings of the 2006 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 83–89 (2006) Google Scholar
  27. 27.
    Batty, C., Bertails, F., Bridson, R.: A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. 26(3), 100–107 (2007) (Proc. SIGGRAPH 2007) CrossRefGoogle Scholar
  28. 28.
    Robinson-Mosher, A., Shinar, T., Gretarsson, J., Su, J., Fedkiw, R.: Two-way coupling of fluids to rigid and deformable solids and shells. ACM Trans. Graph. 27(46), 1–9 (2008) CrossRefGoogle Scholar
  29. 29.
    Li, W., Wei, X.M., Kaufman, A.: Implementing lattice and Boltzmann computation on graphics hardware. Vis. Comput. 19, 444–456 (2003) Google Scholar
  30. 30.
    Guendelman, E., Selle, A., Losasso, F., Fedkiw, R.: Coupling water and smoke to thin deformable and rigid shells. ACM Trans. Graph. 24(3), 973–981 (2005) (Proc. SIGGRAPH 2005) CrossRefGoogle Scholar
  31. 31.
    Williams, B.W.: Fluid surface reconstruction from particles. Master thesis, The University of British Columbia, 1–57 February 2008 Google Scholar
  32. 32.
    Zhu, Y., Bridson, R.: Animating sand as a fluid. ACM Trans. Graph. 24(3), 965–972 (2005) (Proc. SIGGRAPH 2005) CrossRefGoogle Scholar
  33. 33.
    NG, Y.T., Min, C., Gibou, F.: An efficient fluid–solid coupling algorithm for single-phase flows. J. Comput. Phys. 228, 8807–8829 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Min, C., Gibou, F., Ceniceros, H.: A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids. J. Comput. Phys. 218, 123–140 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Losasso, F., Fedkiw, R., Osher, S.: Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids 35, 995–1010 (2005) MathSciNetCrossRefGoogle Scholar
  36. 36.
    Batty, C., Bridson, R.: Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In: Proc. Symposium on Computer Animation 2008, pp. 219–228, July 2008, (2008) Google Scholar
  37. 37.
    Enright, D., Nguyen, D., Gibou, F., Fedkiw, R.: Using the particle level set method and a second order accurate pressure boundary condition for free surface flows. In: Proc. of the 4th ASME-JSME Joint Fluids Engineering Conference (2003) Google Scholar
  38. 38.
    Sallee, J.F.: The middle-cut triangulations of the n-cube. SIAM J. Algebr. Discrete Methods 5, 407–419 (1984) MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Wojtan, C., Thürey, N., Gross, M., Turk, G.: Physics-inspired topology changes for thin fluid features. In: SIGGRAPH 2010, August 2010 Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingChina
  2. 2.Join Faculty of Computer Scientific ResearchCapital Normal UniversityBeijingChina
  3. 3.Graduate University of Chinese Academy of ScienceBeijingChina

Personalised recommendations