Stable fluids

Jos Stam
Alias wavefront, 1218 Third Ave, 8th Floor, Seattle, WA 98101, U.S.A
In SIGGRAPH ’99: Proceedings of the 26th annual conference on Computer graphics and interactive techniques (1999), pp. 121-128.


   title={Stable fluids},

   author={Stam, J.},

   booktitle={Proceedings of the 26th annual conference on Computer graphics and interactive techniques},




   organization={ACM Press/Addison-Wesley Publishing Co.}


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Building animation tools for fluid-like motions is an important and challenging problem with many applications in computer graphics. The use of physics-based models for fluid flow can greatly assist in creating such tools. Physical models, unlike key frame or procedural based techniques, permit an animator to almost effortlessly create interesting, swirling fluid-like behaviors. Also, the interaction of flows with objects and virtual forces is handled elegantly. Until recently, it was believed that physical fluid models were too expensive to allow real-time interaction. This was largely due to the fact that previous models used unstable schemes to solve the physical equations governing a fluid. In this paper, for the first time, we propose an unconditionally stable model which still produces complex fluid-like flows. As well, our method is very easy to implement. The stability of our model allows us to take larger time steps and therefore achieve faster simulations. We have used our model in conjuction with advecting solid textures to create many fluid-like animations interactively in two- and three-dimensions.
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