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PDEs, for Graphics programmers

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I am considering adding some very noddy simulation code using to my game for doing real-time interactive water, fire, etc. effects (possibly doomed to failed, but I want to give it a go). My problem is that while I use pretty complex matrix+vector math every day, the last time I tried to solve a differential equation was at college. I rapidly get out of my depth in papers on PDEs, Fast fourier transform, multigrids, etc. I'm sure alot of it is just a notation issue (or possibly all those brain cells I've killed with beer since college :-). Could anyone suggest a good book for getting a handle on this kind of thing ? Thanks all.

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I find the following book to be a most excellent introduction to numerical methods. Although it is specialized, it does provide a good, general-purpose introduction, with examples, that is easy to read in my opinion.

Computational Fluid Dynamics - John D. Anderson

For more detail, try this one:

Computational Fluid Mechanics And Heat Transfer - Tannehill et al.

The latter one is a bit more advanced, but still good.

With either of these, you need to be comfortable with math!

Sorry the books aren't cheaper!

Jos Stam's papers on stable fluids are possibly useful, though somewhat light on details and not introductory.

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