Abstract
This article presents a physically-based technique for simulating water. This work is motivated by the "stable fluids" method, developed by Stam [1999], to handle gaseous fluids. We extend this technique to water, which calls for the development of methods for modeling multiphase fluids and suppressing dissipation. We construct a multiphase fluid formulation by combining the Navier--Stokes equations with the level set method. By adopting constrained interpolation profile (CIP)-based advection, we reduce the numerical dissipation and diffusion significantly. We further reduce the dissipation by converting potentially dissipative cells into droplets or bubbles that undergo Lagrangian motion. Due to the multiphase formulation, the proposed method properly simulates the interaction of water with surrounding air, instead of simulating water in a void space. Moreover, the introduction of the nondissipative technique means that, in contrast to previous methods, the simulated water does not unnecessarily lose mass, and its motion is not damped to an unphysical extent. Experiments showed that the proposed method is stable and runs fast. It is demonstrated that two-dimensional simulation runs in real-time.
- Brackbill, J. U., Kothe, D. B., and Zemach, C. 1992. A continuum method for modeling surface tension. J. Comp. Phys. 100, 335--354. Google Scholar
- Carlson, M., Mucha, R. J., and Turk, G. 2004. Rigid fluid: Animating the interplay between rigid bodies and fluid. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2004) 23, 3, 377--384. Google Scholar
- Chen, J. X. and Lobo, N. D. V. 1995. Toward interactive-rate simulation of fluids with moving obstacles using Navier--Stokes equations. Graph. Models Image Process. 57, 2, 107--116. Google Scholar
- Enright, D., Marschner, S., and Fedkiw, R. 2002. Animation and rendering of complex water surfaces. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2002) 21, 3, 736--744. Google Scholar
- Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. Comput. Graph. (Proceedings of ACM SIGGRAPH 2001) 35, 15--22. Google Scholar
- Feldman, B. E., O'Brien, J. F., and Arikan, O. 2003. Animating suspended particle explosions. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2003) 22, 3, 708--715. Google Scholar
- Foster, N. and Fedkiw, R. 2001. Practical animation of liquids. Comput. Graph. (Proceedings of ACM SIGGRAPH 2001) 35, 23--30. Google Scholar
- Foster, N. and Metaxas, D. 1996. Realistic animation of liquids. Graph. Models Image Process. 58, 5, 471--483. Google Scholar
- Foster, N. and Metaxas, D. 1997a. Controlling fluid animation. In Comput. Graph. Inter. 97, 178--188. Google Scholar
- Foster, N. and Metaxas, D. 1997b. Modeling the motion of a hot, turbulent gas. Comput. Graph. (Proceedings of ACM SIGGRAPH '97) 31, Annual Conference Series, 181--188. Google Scholar
- Golub, G. H. and Loan, C. F. V. 1996. Matrix Computations. The John Hopkins Univserity Press.Google Scholar
- Harlow, F. H. and Welch, J. E. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 12, 2182--2189.Google Scholar
- Kass, M. and Miller, G. 1990. Rapid, stable fluid dynamics for computer graphics. Comput. Graph. (Proceedings of ACM SIGGRAPH '90) 24, 4, 49--57. Google Scholar
- Lorensen, W. E. and Cline, H. E. 1987. Marching cubes: A high resolution 3D surface construction algorithm. Comput. Graph. (Proceedings of ACM SIGGRAPH '87) 21, 4, 163--169. Google Scholar
- Losasso, F., Gibou, F., and Fedkiw, R. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2004) 23, 3, 457--462. Google Scholar
- McNamara, A., Treuille, A., Popović, Z., and Stam, J. 2004. Fluid control using the adjoint method. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2004) 23, 3, 449--456. Google Scholar
- Miller, G. and Pearce, A. 1989. Globular dynamics: A connected particle system for animating viscous fluids. Comput. Graph. 13, 3, 305--309.Google Scholar
- O'Brien, J. and Hodgins, J. 1995. Dynamic simulation of splashing fluids. In Proceedings of Computer Animation 95, 198--205. Google Scholar
- O'Brien, T. G. G. A. W. B. J. F. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2004) 23, 3, 463--468. Google Scholar
- Osher, S. and Fedkiw, R. 2002. The Level Set Method and Dynamic Implicit Surfaces. Springer-Verlag, New York.Google Scholar
- Osher, S. and Sethian, J. A. 1988. Fronts propagating with curvature dependent speed: Algorithms based in hamilton-jacobi formulations. J. Comp. Phys. 79, 12--49. Google Scholar
- Peng, D., Merriman, B., Osher, S., Zhao, H., and Kang, M. 1999. A pde-based fast local level set method. J. Comp. Phys. 155, 410--438. Google Scholar
- Premože, S., Tasdizen, T., Bigler, J., Lefohn, A., and Whitaker, R. T. 2003. Particle-based simulation of fluids. In Eurographics 2003 Proceedings. Blackwell Publishers, 401--410.Google Scholar
- Rasmussen, N., Nguyen, D. Q., Geiger, W., and Fedkiw, R. 2003. Smoke simulation for large scale phenomena. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2003) 22, 3, 703--707. Google Scholar
- Sethian, J. A. 1996. Fast marching level set methods for three dimensional photolithography development. SPIE 2726, 261--272.Google Scholar
- Stam, J. 1999. Stable fluids. Comput. Graph. (Proceedings of ACM SIGGRAPH '99) 33, Annual Conference Series, 121--128. Google Scholar
- Stam, J. and Fiume, E. 1995. Depicting fire and other gaseous phenomena using diffusion processes. Comput. Graph. (Proceedings of ACM SIGGRAPH '95) 29, Annual Conference Series, 129--136. Google Scholar
- Staniforth, A. and Côtè, J. 1991. Semi-lagrangian integration scheme for atmospheric model---a review. Mon. Weather Rev. 119, 12, 2206--2223.Google Scholar
- Sussman, M., Fatemi, E., Smereka, P., and Osher, S. 1998. An improved level set method for incompressible two-phase flows. Comput. Fluids 27, 663--680.Google Scholar
- Sussman, M., Smereka, P., and Osher, S. 1994. A level set approach for computing solutions to incompressible two-phase flow. J. Comp. Phys. 114, 146--159. Google Scholar
- Takahashi, T., Fujii, H., Kunimatsu, A., Hiwada, K., Saito, T., Tanaka, K., and Ueki, H. 2003. Realistic animation of fluid with splash and foam. In Eurographics 2003 Proceedings. Blackwell Publishers, 391--400.Google Scholar
- Terzopoulos, D., Platt, J., and Fleischer, K. 1989. Heating and melting deformable models (from goop to glop). In Proceedings of Graphics Interface '89. 219--226.Google Scholar
- Treuille, A., McNamara, A., Popović, Z., and Stam, J. 2003. Keyframe control of smoke simulations. ACM Trans. Graph. (Proceedings of ACM SIGGRAPH 2003) 22, 3, 716--723. Google Scholar
- Trottenberg, U., Oosterlee, C., and Schüller, A. 2001. Multigrid. Academic Press. Google Scholar
- Tsai, Y.-H. R., Cheng, L.-T., Osher, S., and Zhao, H.-K. 2003. Fast sweeping algorithms for a class of hamilton--jacobi equations. SIAM J. Numer. Anal. 41, 673--694.Google Scholar
- Xiao, F., Yabe, T., and Ito, T. 1996. Constructing oscillation preventing scheme for advection equation by rational function. Comp. Phys. Comm. 93, 1--12.Google Scholar
- Yabe, T. and Aoki, T. 1991. A universal solver for hyperbolic equations by cubic-polynomial interpolation i. one-dimensional solver. Comp. Phys. Comm. 66, 219--232.Google Scholar
- Yabe, T., Xiao, F., and Utsumi, T. 2001. The constrained interpolation profile method for multiphase analysis. J. Comp. Phys. 169, 556--593. Google Scholar
Index Terms
- Stable but nondissipative water
Recommendations
Finite volume flow simulations on arbitrary domains
We present a novel method for solving the incompressible Navier-Stokes equations that more accurately handles arbitrary boundary conditions and sharp geometric features in the fluid domain. It uses a space filling tetrahedral mesh, which can be created ...
A method for animating viscoelastic fluids
This paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian ...
Simultaneous coupling of fluids and deformable bodies
SCA '06: Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animationThis paper presents a method for simulating the two-way interaction between fluids and deformable solids. The fluids are simulated using an incompressible Eulerian formulation where a linear pressure projection on the fluid velocities enforces mass ...
Comments