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A multi-layer grid approach for fluid animation

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Abstract

Real fluid phenomena often present multi-scale behavior, such as tiny splashes and foams in the ocean and small vortexes near the bank of a wide river, which requires sufficiently fine grids and long computational time in the simulation to get adequately resolved solution. We present a new method to address this issue by solving Navier-Stokes equation on multiple layers of grids with different resolutions or categories. The governing equations are solved on different layers in successive passes. And the velocity and pressure fields are synchronized between adjacent layers through the processes of prolongation and restriction. The multi-layer approach enables combining the respective advantages of various grid types, catching the multi-scale behavior of fluids and optimizing the computational resources. Two simple examples, the regular-tetrahedral and the coarse-fine bi-layer grids, are given to illustrate the powerfulness of the multi-layer framework.

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References

  1. Irving G, Guendelman E, Losasso F, et al. Efficient simulation of large bodies of water by coupling two and three dimensional techniques. ACM Trans Graph, 2006, 25: 805–811

    Article  Google Scholar 

  2. Losasso F, Gibou F, Fedkiw R. Simulating water and smoke with an octree data structure. In: Proceedings of SIGGRAPH’ 04, New York: ACM, 2004. 457–462

    Chapter  Google Scholar 

  3. Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids, 1965, 8: 2182–2189

    Article  MATH  Google Scholar 

  4. Klingner B M, Feldman B E, Chentanez N, et al. Fluid animation with dynamic meshes. ACM Trans Graph, 2006, 25: 820–825

    Article  Google Scholar 

  5. Batty C, Bertails F, Bridson R. A fast variational framework for accurate solid-fluid coupling. In: Proceedings of SIGGRAPH’07, New York: ACM, 2007. 100

    Google Scholar 

  6. Feldman B E, O’Brien J F, Klingner B M. Animating gases with hybrid meshes. In: Proceedings of SIGGRAPH’05, New York: ACM, 2005. 904–909

    Google Scholar 

  7. Tan J, Yang X B. Physically-based fluid animation: A survey. Sci China Inf Sci, 2009, 52: 723–740

    Article  Google Scholar 

  8. Foster N, Metaxas D. Realistic animation of liquids. Graph Models Image Process, 1996, 58: 471–483

    Article  Google Scholar 

  9. Stam J. Stable fluids. In: Proceedings of the 26th annual conference on computer graphics and interactive techniques, New York: ACM Press/Addison-Wesley Publishing Co, 1999. 121–128

    Google Scholar 

  10. Foster N, Metaxas D. Modeling the motion of a hot, turbulent gas. In: Proceedings of the 24th annual conference on computer graphics and interactive techniques, New York: ACM Press/Addison-Wesley Publishing Co, 1997. 181–188

    Google Scholar 

  11. Fedkiw R, Stam J, Jensen H W. Visual simulation of smoke. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques, New York: ACM, 2001. 15–22

    Google Scholar 

  12. Foster N, Fedkiw R. Practical animation of liquids. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques, New York: ACM, 2001. 23–30

    Google Scholar 

  13. Enright D, Marschner S, Fedkiw R. Animation and rendering of complex water surfaces. In: Proceedings of the 29th annual conference on computer graphics and interactive techniques, New York: ACM, 2002. 736–744

    Google Scholar 

  14. Carlson M, Mucha P J, Van-Horn III R B, et al. Melting and flowing. In: Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on computer animation, New York: ACM, 2002. 167–174

    Chapter  Google Scholar 

  15. Nguyen D C, Fedkiw R, Jensen H W. Physically based modeling and animation of fire. ACM Trans Graph, 2002, 21: 721–728

    Article  Google Scholar 

  16. Carlson M, Mucha P J, Turk G. Rigid fluid: animating the interplay between rigid bodies and fluid. In: Proceedings of SIGGRAPH’04, New York: ACM, 2004. 377–384

    Google Scholar 

  17. Goktekin T G, Bargteil A W, O’Brien J F. A method for animating viscoelastic fluids. In: Proceedings of SIGGRAPH’04, New York: ACM, 2004. 463–468

    Google Scholar 

  18. Hong J M, Kim C H. Discontinuous fluids. ACM Trans Graph, 2005, 24: 915–920

    Article  Google Scholar 

  19. Wang H M, Mucha P J, Turk G. Water drops on surfaces. In: Proceedings of SIGGRAPH’05, New York: ACM, 2005. 921–929

    Google Scholar 

  20. Kim B, Liu Y J, Llamas I, et al. Simulation of bubbles in foam with the volume control method. ACM Trans Graph, 2007, 26: 98

    Article  Google Scholar 

  21. Müller M, Charypar D, Gross M. Particle-based fluid simulation for interactive applications. In: Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on computer animation, Switzerland, 2003. 154–159

  22. Müller M, Keiser R, Nealen A, et al. Point based animation of elastic, plastic and melting objects. In: Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, Switzerland, 2004. 141–151

  23. Monaghan J J. Smoothed particle hydrodynamics. Annual Rev Astron Astrophys, 1992, 30: 543–574

    Article  Google Scholar 

  24. Premoze S, Tasdizen T, Bigler J, et al. Particle-based simulation of fluids. Comput Graph Forum, 2003, 22: 401–410

    Article  Google Scholar 

  25. Adams B, Pauly M, Keiser R, et al. Adaptively sampled particle fluids. In: Proceedings of SIGGRAPH’07, New York: ACM, 2007. 48

    Google Scholar 

  26. Chentanez N, Feldman B E, Labelle F, et al. Liquid simulation on lattice-based tetrahedral meshes. In: Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on computer animation, Switzerland, 2007. 219–228

  27. Berger M J, Oliger J E. Adaptive mesh refinement for hyperbolic partial differential equations. J Comput Phys, 1984, 53: 484–512

    Article  MathSciNet  MATH  Google Scholar 

  28. Berger M J, Colella P. Local adaptive mesh refinement for shock hydrodynamics. J Comput Phys, 1989, 82: 64–84

    Article  MATH  Google Scholar 

  29. Blackburn H M, Elston J R, Niclasen D A, et al. A hybrid method for simulation of axial flow impeller driven mixing vessels. Appl Math Model, 2000, 24: 795–805

    Article  MATH  Google Scholar 

  30. Bechmann A, Sørensen N N, Johansen J, et al. Hybrid RANS/LES method for high reynolds numbers, applied to atmospheric flow over complex terrain. J Phys Conference Ser, 2007, 75, 012054

    Article  Google Scholar 

  31. Breuer M, Jaffrézic B, Arora K. Hybrid LES-RANS technique based on a one-equation near-wall model. Theor Comput Fluid Dyn, 200622: 157–187

    Article  Google Scholar 

  32. Hamba F. A hybrid RANS/LES simulation of high-reynolds-number channel flow using additional filtering at the interface. Theor Comput Fluid Dyn, 2006, 20: 89–101

    Article  MATH  Google Scholar 

  33. Temmerman L, Hadziabdi M, Leschziner M, et al. A hybrid two-layer URANS-LES approach for large eddy simulation at high reynolds numbers. J Heat Fluid Flow, 2004, 26: 173–190

    Article  Google Scholar 

  34. Celik I. The future prospects of turbulence modeling. J Fluids Eng, 2005, 127: 829

    Article  Google Scholar 

  35. Martin D, Cartwright K. Solving poisson’s equation using adaptive mesh refinement. Technical Report M96/66, University of California, Berkeley Electronic Research Laboratory. http://citeseer.ist.psu.edu/article/martin96solving.html, 1996

  36. Alliez P, Cohen-Steiner D, Yvinec M, et al. Variational tetrahedral meshing. In: Proceedings of SIGGRAPH’05, New York: ACM, 2005. 617–625

    Google Scholar 

  37. Lorensen W E, Cline H E. Marching cubes: A high resolution 3d surface construction algorithm. ACM SIGGRAPH Comput Graph, 1987, 21: 163–169

    Article  Google Scholar 

  38. Bridson R, Müller-Fischer M. Fluid simulation: Siggraph 2007 course notes. In: ACM SIGGRAPH 2007 courses, New York: ACM, 2007. 1–81

    Google Scholar 

  39. Bargteil A W, Goktekin T G, O’brien J F, et al. A semi-lagrangian contouring method for fluid simulation. ACM Trans Graph, 2006, 25: 19–38

    Article  Google Scholar 

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Authors and Affiliations

  1. MOE-Microsoft Key Lab for Intelligent Computing and System, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jie Tan & XuBo Yang

  2. Digital Art Lab, School of Software, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jie Tan, XuBo Yang, Xin Zhao & ZhanXin Yang

Authors
  1. Jie Tan
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  2. XuBo Yang
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  3. Xin Zhao
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  4. ZhanXin Yang
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Correspondence to XuBo Yang.

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Tan, J., Yang, X., Zhao, X. et al. A multi-layer grid approach for fluid animation. Sci. China Inf. Sci. 54, 2269–2278 (2011). https://doi.org/10.1007/s11432-011-4276-x

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  • DOI: https://doi.org/10.1007/s11432-011-4276-x

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