“Large-scale fluid simulation using velocity-vorticity domain decomposition”
Conference:
Type(s):
Title:
- Large-scale fluid simulation using velocity-vorticity domain decomposition
Session/Category Title: Dynamics
Presenter(s)/Author(s):
Abstract:
Simulating fluids in large-scale scenes with appreciable quality using state-of-the-art methods can lead to high memory and compute requirements. Since memory requirements are proportional to the product of domain dimensions, simulation performance is limited by memory access, as solvers for elliptic problems are not compute-bound on modern systems. This is a significant concern for large-scale scenes. To reduce the memory footprint and memory/compute ratio, vortex singularity bases can be used. Though they form a compact bases for incompressible vector fields, robust and efficient modeling of nonrigid obstacles and free-surfaces can be challenging with these methods.We propose a hybrid domain decomposition approach that couples Eulerian velocity-based simulations with vortex singularity simulations. Our formulation reduces memory footprint by using smaller Eulerian domains with compact vortex bases, thereby improving the memory/compute ratio, and simulation performance by more than 1000x for single phase flows as well as significant improvements for free-surface scenes. Coupling these two heterogeneous methods also affords flexibility in using the most appropriate method for modeling different scene features, as well as allowing robust interaction of vortex methods with free-surfaces and nonrigid obstacles.
References:
1. Adams, B., Pauly, M., Keiser, R., and Guibas, L. J. 2007. Adaptively sampled particle fluids. ACM Trans. Graph. 26 (July).
2. Angelidis, A., and Neyret, F. 2005. Simulation of smoke based on vortex filament primitives. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, ACM, SCA ’05, 87–96.
3. Angelidis, A., Neyret, F., Singh, K., and Nowrouzezahrai, D. 2006. A controllable, fast and stable basis for vortex based smoke simulation. In Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, SCA ’06, 25–32.
4. Barrett, R., Berry, M., Chan, T. F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and der Vorst, H. V. 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition. SIAM, Philadelphia, PA.
5. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. Graph. 26, 3, 100.
6. Bridson, R., and Müller-Fischer, M. 2007. Fluid simulation: Siggraph 2007 course notes. In ACM SIGGRAPH 2007 courses, ACM, SIGGRAPH ’07, 1–81.
7. Cantarella, J., DeTurck, D., and Gluck, H. 2002. Vector calculus and the topology of domains in 3-space. Amer. Math. Monthly 109, 5, 409–442.
8. Carlson, M. T., 2004. Rigid, melting, and flowing fluid. Ph.D. Dissertation.
9. Chentanez, N., Goktekin, T. G., Feldman, B. E., and O’Brien, J. F. 2006. Simultaneous coupling of fluids and deformable bodies. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 83–89.
10. Chentanez, N., Feldman, B. E., Labelle, F., O’Brien, J. F., and Shewchuk, J. R. 2007. Liquid simulation on lattice-based tetrahedral meshes. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, SCA ’07, 219–228.
11. Chorin, A. J. 1973. Numerical study of slightly viscous flow. Journal of Fluid Mechanics 57, 04, 785–796.
12. Cottet, G. H., and Koumoutsakos, P. D. 1998. Vortex Methods: Theory and Practice. Cambridge University Press.
13. Elcott, S., Tong, Y., Kanso, E., Schröder, P., and Desbrun, M. 2007. Stable, circulation-preserving, simplicial fluids. ACM Trans. Graph. 26 (January).
14. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, SIGGRAPH ’01, 15–22.
15. Feldman, B. E., O’Brien, J. F., and Klingner, B. M. 2005. Animating gases with hybrid meshes. In Proceedings of ACM SIGGRAPH 2005.
16. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, SIGGRAPH ’01, 23–30.
17. Foster, N., and Metaxas, D. 1996. Realistic animation of liquids. Graph. Models Image Process. 58 (September).
18. Kim, B., Liu, Y., Llamas, I., and Rossignac, J. 2007. Advections with significantly reduced dissipation and diffusion. IEEE Transactions on Visualization and Computer Graphics 13, 135–144.
19. Kim, T., Thürey, N., James, D., and Gross, M. 2008. Wavelet turbulence for fluid simulation. ACM Trans. Graph. 27 (August), 50:1–50:6.
20. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. In Proceedings of ACM SIGGRAPH 2006, 820–825.
21. Lentine, M., Zheng, W., and Fedkiw, R. 2010. A novel algorithm for incompressible flow using only a coarse grid projection. In ACM SIGGRAPH 2010 papers, ACM, SIGGRAPH ’10, 114:1–114:9.
22. Lentine, M., Aanjaneya, M., and Fedkiw, R. 2011. Mass and momentum conservation for fluid simulation. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, ACM, 91–100.
23. Lindsay, K., and Krasny, R. 2001. A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow. J. Comput. Phys. 172 (September), 879–907.
24. Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. In ACM SIGGRAPH 2004 Papers, ACM, SIGGRAPH ’04, 457–462.
25. Losasso, F., Talton, J., Kwatra, N., and Fedkiw, R. 2008. Two-way coupled sph and particle level set fluid simulation. IEEE Transactions on Visualization and Computer Graphics 14 (July), 797–804.
26. Mullen, P., Crane, K., Pavlov, D., Tong, Y., and Desbrun, M. 2009. Energy-preserving integrators for fluid animation. ACM Trans. Graph. 28 (July), 38:1–38:8.
27. Müller, M., Charypar, D., and Gross, M. 2003. Particle-based fluid simulation for interactive applications. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, SCA ’03, 154–159.
28. Narain, R., Sewall, J., Carlson, M., and Lin, M. C. 2008. Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans. Graph. 27 (December), 166:1–166:8.
29. Park, S. I., and Kim, M. J. 2005. Vortex fluid for gaseous phenomena. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, ACM, SCA ’05, 261–270.
30. Pfaff, T., Thuerey, N., Cohen, J., Tariq, S., and Gross, M. 2010. Scalable fluid simulation using anisotropic turbulence particles. In ACM SIGGRAPH Asia 2010 papers, ACM, New York, NY, USA, SIGGRAPH ASIA ’10, 174:1–174:8.
31. Robinson-Mosher, A., Shinar, T., Gretarsson, J., Su, J., and Fedkiw, R. 2008. Two-way coupling of fluids to rigid and deformable solids and shells. ACM Trans. Graph. 27 (August), 46:1–46:9.
32. Schechter, H., and Bridson, R. 2008. Evolving sub-grid turbulence for smoke animation. In Proceedings of the 2008 ACM/Eurographics Symposium on Computer Animation.
33. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In ACM SIGGRAPH 2005 Papers, ACM, SIGGRAPH ’05, 910–914.
34. Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac, J. 2008. An unconditionally stable maccormack method. J. Sci. Comput. 35 (June), 350–371.
35. Sin, F., Bargteil, A. W., and Hodgins, J. K. 2009. A point-based method for animating incompressible flow. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation.
36. Solenthaler, B., and Pajarola, R. 2009. Predictive-corrective incompressible sph. ACM Trans. Graph. 28 (July), 40:1–40:6.
37. Stam, J. 1999. Stable fluids. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques, SIGGRAPH ’99, 121–128.
38. Toselli, A., and Widlund, O. 2004. Domain Decomposition Methods – Algorithms and Theory, vol. 34 of Springer Series in Computational Mathematics. Springer.
39. Treuille, A., Lewis, A., and Popović, Z. 2006. Model reduction for real-time fluids. In ACM SIGGRAPH 2006 Papers, ACM, SIGGRAPH ’06, 826–834.
40. Weissmann, S., and Pinkall, U. 2009. Real-time interactive simulation of smoke using discrete integrable vortex filaments. In Workshop in VRIPS 2009, Eurographics Association.
41. Weissmann, S., and Pinkall, U. 2010. Filament-based smoke with vortex shedding and variational reconnection. In ACM SIGGRAPH 2010 papers, ACM, SIGGRAPH ’10, 115:1–115:12.
42. Wendt, J. D., Baxter, W., Oguz, I., and Lin, M. C. 2007. Finite volume flow simulations on arbitrary domains. Graph. Models 69 (January), 19–32.
43. Wicke, M., Stanton, M., and Treuille, A. 2009. Modular bases for fluid dynamics. In ACM SIGGRAPH 2009 papers, ACM, SIGGRAPH ’09, 39:1–39:8.
44. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. In ACM SIGGRAPH 2005 Papers, ACM, New York, NY, USA, SIGGRAPH ’05, 965–972.
