Creating spherical explosions, particle beams, flame jets and debris are fairly straightforward renditions for a particle-based system, but the mathematics behind mushroom clouds are eluding me a little bit. Going by physical fundamentals is prohibitive in this case, because the distinctive shape of mushroom clouds is dependent on gravity, air pressure, thermodynamics and probably a bit of plasma physics as well, and as the parameters vary wildly over time and across the explosion's cross-section (which initially starts as a sphere or hemisphere, I believe, before becoming deformed over time), it is not a real-time operation, meaning another model has to be found instead. Anyone have any advice on this one? (At present, the colouring of particles is done by overlapping particles producing a brighter and more opaque overall colour, although this can be overridden)

If you have access to Springer through, say, a university library, you could read,

http://www.springerlink.com/content/e656l642k3662527/ .

(I have not read this; it's just the first hit that came from Google for "siggraph mushroom cloud." But it looks very topical.)

I believe Navier-Stokes equations are a pretty common method for creating vortex smoke and water effects. Google should give you some hits to get started.

Jos Stam has made plenty of documentation on really cool yet simple fluid / smoke / fire simulations. There's plenty of code samples in the doc's, which are easy to convert & tweak for whatever you need. Check out:

http://www.dgp.toronto.edu/people/stam/reality/Research/pub.html

Cheers,
Mike

It shouldn't be to hard to fake with a cylinder of vertical wind slightly larger than the explosion radius. Particles start in the center with an upward velocity after they move above the cylinder they slow and start to fall now because A) their velocity wasn't 100% vertical to begin with and B) they are hit by particles from below they spread out and start to fall. Now as the particles re-enter the cylinder they start moving up again.