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How would I go about implementing fluid dynamics in a game, such as can be seen in this video?

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Have you tried googling "2d Fluid Simulation"? – iamcreasy Nov 12 '11 at 0:55
A search term that may be useful to you is "smoothed particle hydrodynamics". Update: here is a very good introduction to the field. – DaleyPaley Apr 16 at 5:36

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It looks like the game is just using a fairly simple particle fluid simulation. Basically, the "water" consists of little balls that move according to Newtonian mechanics, fall under gravity and repel each other over short distances. The blobs of water are then drawn around the particles using something like metaballs to smooth the surface.

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Actually a good, clean answer to an otherwise overly-broad question – bobobobo Jan 28 '12 at 14:57
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Looks very similar to the water in PixelJunk shooter. There is a PDF on how the water was done:

http://www.maisonikkoku.com/yonder/SIGGRAPH2011/SlidesForADBAD.pdf ^^link has gone dead... you can get the cached version from google search, but if you're very very lazy, then you may view this copy if you need to: http://dl.dropbox.com/u/203979/SlidesForADBAD.pdf

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The link goes to a dead-end. – Todd Lehman Jan 29 '12 at 14:56
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Much like the water in the Sprinkle game, but not as good. See http://tuxedolabs.blogspot.com/2011/11/sprinkle-behind-scenes.html to understand how it was done. Particles indeed, but you probably won't get that kind of performance from a general purpose physics engine.

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Try to read great serious of articles from Intel about fluid simulation for video games http://software.intel.com/en-us/articles/fluid-simulation-for-video-games-part-1/

And also try this, fluid simulation in Alice game http://developer.nvidia.com/content/fluid-simulation-alice-madness-returns

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