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Making Animated Fluids Look More Realistic
brunascle writes "Technology Review has an article about recent advances in animated fluid dynamics made by Mathieu Desbrun, a computer science professor at Caltech. 'He and his team are developing an entirely new approach to fluid motion, based on new mathematics called discrete differential geometry, that use equations designed specifically to be solved by computers rather than people.' Desbrun explains that the currently in-use equations for animating fluid dynamics were not developed with computers in mind, and were simply reworkings of older equations. He claims that his new equations use about the same amount of computer resources, but with much better results. The article includes a 5 minute (flash) video demonstrating various results using his equations, ending with 2 fascinating and vivid displays: the first of a snowglobe, and the second of a cloud of smoke filling a volume in the shape of a bunny."
Ron Fedkiw at Stanford also has a lot of very impressive demonstrations of liquids, smoke, fire, cloth, rigid bodies, elasticity, and fracturing. The videos are definitely worth checking out: http://graphics.stanford.edu/~fedkiw/ I especially like the water being poured into the glass. It's nearly photo realistic.
No, it has nothing to do with the finite element/difference methods at all.
In fact, it's a fundamentally different approach from both of those methods. Finite element/difference means that you think of the problem as a continuous, smooth manifold. Then, you break the manifold into chunks (discretize) it, and you apply the "natural laws" like they would work on a smooth surface to the discretized approximation. The idea is that, the smaller the chunks, the errors becomes too small to notice.
However, in some cases the discretization process causes quantities (like total energy of the system) to not be conserved. The little errors add up to a lot. In fluid dynamics, non-conserved quantities cause solutions to the systems that just look wrong to the casual observer.
This team's approach is fundamentally different. Instead of discretizing a continuous problem involving a smooth manifold and continuous operators, they think of the problem as discrete to begin with and define operators on the discrete geometry. They don't say "apply the derivative to an approximation of a smooth surface", they say "apply this discrete derivative-like operator to this discrete surface". It turns out that if you define your discrete operators correctly, you can focus on conserving quantities (such as total system energy) that the normal approximation to the derivative won't.
It offers no speedup in computation time, and probably has no parallelization opportunities beyond those normally there in fluid dynamics. However, it *does* produce better-looking solutions as all of the conservation laws are met.
Very interesting research.