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This is not a technical question, and is asked just out of curiosity.

Are computational fluid dynamics (CFD) simulations used in animation movies? (something like shallow water equations, explosion problem etc.)

In other words, can computational simulations of real world problems be used in art?

(I have tagged the question with simulation, but please feel free to retag it as I can't find appropriate tags)

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There was a paper in Notices of the American Mathematical Society on this subject: Crashing Waves, Awesome Explosions, Turbulent Smoke and Beyond: Applied Mathematics and Scientific Computing in the Visual Effects Industry. In particular, these commercial packages constitute examples of simulation software used in the film industry.

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One of the leaders in the field of using CFD for animation, Ron Fedkiw, had a web page with some fantastic examples, including references to the relevant publications.

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  • $\begingroup$ wow! That really is awesome... $\endgroup$
    – Subodh
    May 21, 2013 at 4:52
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After a bit of search, I discovered that CFD is heavily used in films, games and special effects in media. Here is the wiki page of the relevant topic, references therein are helpful as well.

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Yes a lot. See for example FumeFx (3ds max plugin, grid based simulation) or RealFlow (SHP simulation) and more.

And there is still research going on in this field. See Siggraph papers. My favorite this year is snow simulation.

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