The Visual Computer

, Volume 30, Issue 6–8, pp 787–796 | Cite as

Dynamic BFECC Characteristic Mapping method for fluid simulations

  • Xiaosheng Li
  • Le Liu
  • Wen Wu
  • Xuehui Liu
  • Enhua Wu
Original Article


In this paper, we present a new numerical method for advection in fluid simulation. The method is built on the Characteristic Mapping method. Advection is solved via grid mapping function. The mapping function is maintained with higher order accuracy BFECC method and dynamically reset to identity mapping whenever an error criterion is met. Dealing with mapping function in such a way results in a more accurate mapping function and more details can be captured easily with this mapping function. Our error criterion also allows one to control the level of details of fluid simulation by simply adjusting one parameter. Details of implementation of our method are discussed and we present several techniques for improving its efficiency. Both quantitative and visual experiments were performed to test our method. The results show that our method brings significant improvement in accuracy and is efficient in capturing fluid details.


Fluid simulation Advection BFECC Characteristic Mapping 



The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper. This research is supported by NSFC Grant (61272326), HK RGC Grant (416212) and the grant of University of Macau.


  1. 1.
    Bargteil, A.W., Goktekin, T.G., O’Brien, J.F., Strain, J.A.: A semi-lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25(1), 19–38 (2006)Google Scholar
  2. 2.
    Dupont, T.F., Liu, Y.: Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function. J. Comput. Phys. 190(1), 311–324 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183(1), 83–116 (2002)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Enright, D., Marschner, S., Fedkiw, R.: Animation and rendering of complex water surfaces. ACM Trans. Graph. 21(3), 736–744 (2002)Google Scholar
  5. 5.
    Fedkiw, R., Stam, J., Jensen, H.W.: Visual simulation of smoke. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH ’01, pp. 15–22. ACM, New York (2001)Google Scholar
  6. 6.
    Hachisuka, T.: Combined lagrangian–eulerian approach for accurate advection. In: ACM SIGGRAPH 2005 Posters, SIGGRAPH ’05. ACM, New York (2005)Google Scholar
  7. 7.
    Kim, B., Liu, Y., Llamas, I., Rossignac, J.: Flowfixer: Using bfecc for fluid simulation. Proceedings of the First Eurographics Conference on Natural Phenomena. NPH’05, pp. 51–56. Eurographics Association, Aire-la-Ville (2005)Google Scholar
  8. 8.
    Kim, B., Liu, Y., Llamas, I., Rossignac, J.: Advections with significantly reduced dissipation and diffusion. IEEE Trans. Vis. Comput. Graph. 13(1), 135–144 (2007)Google Scholar
  9. 9.
    Kim, D., Song, O.Y., Ko, H.S.: A semi-lagrangian cip fluid solver without dimensional splitting. Comput. Graph. Forum 27(2), 467–475 (2008)Google Scholar
  10. 10.
    Mercier, O., Nave, J.C.: The characteristic mapping method for the linear advection of arbitrary sets. arXiv:1309.2731 (2013)
  11. 11.
    Nave, J.C., Rosales, R.R., Seibold, B.: A gradient-augmented level set method with an optimally local, coherent advection scheme. J. Comput. Phys. 229(10), 3802–3827 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Pharr, M., Humphreys, G.: Physically Based Rendering, Second Edition: From Theory To Implementation, 2nd edn. Morgan Kaufmann Publishers Inc., San Francisco (2010)Google Scholar
  13. 13.
    Selle, A., Fedkiw, R., Kim, B., Liu, Y., Rossignac, J.: An unconditionally stable maccormack method. J. Sci. Comput. 35(2–3), 350–371 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    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
  15. 15.
    Stam, J.: Stable fluids. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH ’99, pp. 121–128. ACM Press/Addison-Wesley Publishing Co., New York (1999)Google Scholar
  16. 16.
    Tessendorf, J., Pelfrey, B.: The characteristic map for fast and efficient vfx fluid simulations. In: Computer Graphics International Workshop on VFX, Computer Animation, and Stereo Movies. Ottawa, Canada (2011)Google Scholar
  17. 17.
    Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31, 335–362 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Zhu, Y., Bridson, R.: Animating sand as a fluid. ACM Trans. Graph. 24(3), 965–972 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Xiaosheng Li
    • 1
    • 2
  • Le Liu
    • 1
    • 2
  • Wen Wu
    • 3
  • Xuehui Liu
    • 1
  • Enhua Wu
    • 1
    • 3
  1. 1.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.University of MacauMacaoChina

Personalised recommendations