参考文献:1. Bargteil, A.W., Goktekin, T.G., O鈥橞rien, J.F., Strain, J.A.: A semi-lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25(1), 19鈥?8 (2006) 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鈥?24 (2003) CrossRef 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鈥?16 (2002) 4. Enright, D., Marschner, S., Fedkiw, R.: Animation and rendering of complex water surfaces. ACM Trans. Graph. 21(3), 736鈥?44 (2002) 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 鈥?1, pp. 15鈥?2. ACM, New York (2001) 6. Hachisuka, T.: Combined lagrangian鈥揺ulerian approach for accurate advection. In: ACM SIGGRAPH 2005 Posters, SIGGRAPH 鈥?5. ACM, New York (2005) 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鈥?5, pp. 51鈥?6. Eurographics Association, Aire-la-Ville (2005) 8. Kim, B., Liu, Y., Llamas, I., Rossignac, J.: Advections with significantly reduced dissipation and diffusion. IEEE Trans. Vis. Comput. Graph. 13(1), 135鈥?44 (2007) 9. Kim, D., Song, O.Y., Ko, H.S.: A semi-lagrangian cip fluid solver without dimensional splitting. Comput. Graph. Forum 27(2), 467鈥?75 (2008) 10. Mercier, O., Nave, J.C.: The characteristic mapping method for the linear advection of arbitrary sets. arXiv:1309.2731 (2013) 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鈥?827 (2010) CrossRef 12. Pharr, M., Humphreys, G.: Physically Based Rendering, Second Edition: From Theory To Implementation, 2nd edn. Morgan Kaufmann Publishers Inc., San Francisco (2010) 13. Selle, A., Fedkiw, R., Kim, B., Liu, Y., Rossignac, J.: An unconditionally stable maccormack method. J. Sci. Comput. 35(2鈥?), 350鈥?71 (2008) CrossRef 14. Selle, A., Rasmussen, N., Fedkiw, R.: A vortex particle method for smoke, water and explosions. ACM Trans. Graph. 24(3), 910鈥?14 (2005) CrossRef 15. Stam, J.: Stable fluids. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH 鈥?9, pp. 121鈥?28. ACM Press/Addison-Wesley Publishing Co., New York (1999) 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) 17. Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31, 335鈥?62 (1979) CrossRef 18. Zhu, Y., Bridson, R.: Animating sand as a fluid. ACM Trans. Graph. 24(3), 965鈥?72 (2005) CrossRef
作者单位:Xiaosheng Li (1) (2) Le Liu (1) (2) Wen Wu (3) Xuehui Liu (1) Enhua Wu (1) (3)
1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China 2. University of Chinese Academy of Sciences, Beijing, China 3. University of Macau, Macao, China
ISSN:1432-2315
文摘
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.