Wavelet turbulence for fluid simulation

Abstract

We present a novel wavelet method for the simulation of fluids at high spatial resolution. The algorithm enables large- and small-scale detail to be edited separately, allowing high-resolution detail to be added as a post-processing step. Instead of solving the Navier-Stokes equations over a highly refined mesh, we use the wavelet decomposition of a low-resolution simulation to determine the location and energy characteristics of missing high-frequency components. We then synthesize these missing components using a novel incompressible turbulence function, and provide a method to maintain the temporal coherence of the resulting structures. There is no linear system to solve, so the method parallelizes trivially and requires only a few auxiliary arrays. The method guarantees that the new frequencies will not interfere with existing frequencies, allowing animators to set up a low resolution simulation quickly and later add details without changing the overall fluid motion.

References

1. Angelidis, A., Neyret, F., Singh, K., and Nowrouzezahrai, D. 2006. A controllable, fast and stable basis for vortex based smoke simulation. In ACM SIGGRAPH/EG Symposium on Computer Animation (SCA).
2. Basu, S., Foufoula-Georgiou, E., and Porte-Agel, F. 2004. Synthetic turbulence, fractal interpolation, and large-eddy simulation. Physical Review E, 026310.
3. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. In Proceedings of ACM SIGGRAPH.
4. Bridson, R., Hourihan, J., and Nordenstam, M. 2007. Curl-noise for procedural fluid flow. In Proceedings of ACM SIGGRAPH.
5. Cook, R., and DeRose, T. 2005. Wavelet noise. In Proceedings of ACM SIGGRAPH.
6. Elcott, S., Tong, Y., Kanso, E., Schröder, P., and Desbrun, M. 2007. Stable, circulation-preserving, simplicial fluids. ACM Transactions on Graphics.
7. Farge, M., Kevlahan, N., Perrier, V., and Goirand, E. 1996. Wavelets and turbulence. Proceedings of the IEEE 84, 4, 639--669.
8. Fattal, R., and Lischinski, D. 2004. Target-driven smoke animation. In Proceedings of SIGGRAPH.
9. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Proceedings of ACM SIGGRAPH, 15--22.
10. Frisch, U. 1995. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
11. Kim, B., Liu, Y., Llamas, I., and Rossignac, J. 2005. Flow-fixer: Using BFECC for fluid simulation. In Proceedings of Eurographics Workshop on Natural Phenomena.
12. Klingner, B. M., Feldman, B. E., Chentanez, N., and O'Brien, J. F. 2006. Fluid animation with dynamic meshes. In Proceedings of ACM SIGGRAPH.
13. Lamorlette, A., and Foster, N. 2002. Structural modeling of flames for a production environment. In Proceedings of ACM SIGGRAPH.
14. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. Proceedings of ACM SIGGRAPH, 457--462.
15. McNamara, A., Treuille, A., Popovic, Z., and Stam, J. 2004. Fluid control using the adjoint method. In Proceedings of SIGGRAPH.
16. Neyret, F. 2003. Advected textures. In ACM SIGGRAPH/EG Symposium on Computer Animation (SCA).
17. Perlin, K. 1985. An image synthesizer. In Proceedings of ACM SIGGRAPH, 287--296.
18. Perrier, V., Philipovitch, T., and Basdevant, C. 1995. Wavelet spectra compared to fourier spectra. Journal of Mathematical Physics 36.
19. Rasmussen, N., Nguyen, D. Q., Geiger, W., and Fedkiw, R. 2003. Smoke simulation for large scale phenomena. In Proceedings of ACM SIGGRAPH.
20. Scotti, A., and Meneveau, C. 1999. A fractal model for large eddy simulation of turbulent flows. Physica D, 198--232.
21. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In Proceedings of SIGGRAPH.
22. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. 2008. An unconditionally stable MacCormack method. Journal of Scientific Computing (in press).
23. Shraiman, B., and Siggia, E. 2000. Scalar turbulence. Nature, 405, 639--646.
24. Stam, J., and Fiume, E. 1993. Turbulent wind fields for gaseous phenomena. In Proceedings of ACM SIGGRAPH.
25. Stam, J. 1999. Stable fluids. In Proceedings of ACM SIGGRAPH.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation

    • Shape modeling

  • Modeling and simulation

    • Simulation types and techniques

      • Simulation by animation

• Mathematics of computing

  • Continuous mathematics

    • Topology

      • Geometric topology