I've alluded to this in other comments but a lot of the mathematics is linear algebra. As gaius mentions, check out the wikipedia article. There are plenty of linear algebra books out there. Recently I've really enjoyed the book by Meyer which is free although it does get quite advanced and is mostly theorem / proof-style. It's also free so who can complain.
I've take a quick look through it and it seems pretty good. It introduces many of the most important ideas of solving PDEs. Obviously there are huge tomes on various techniques to solve the Navier-Stokes equations but this link, I think, does a pretty good elementary introduction. A more comprehensive treatment would require a more thorough background in mathematics (e.g. I wrote a 2D NS solver using the vorticity formulation and FFTs but to understand the equivalence requires a greater background).
As for the cool visualisation, I cannot help you. I don't know any fancy graphics programming since I normally use the built-in plotting tools of Python and Matlab.
http://matrixanalysis.com/DownloadChapters.html
Here is a link I found yesterday which gets you solving the 2D NS equations.
http://lorenabarba.com/blog/cfd-python-12-steps-to-navier-st...
I've take a quick look through it and it seems pretty good. It introduces many of the most important ideas of solving PDEs. Obviously there are huge tomes on various techniques to solve the Navier-Stokes equations but this link, I think, does a pretty good elementary introduction. A more comprehensive treatment would require a more thorough background in mathematics (e.g. I wrote a 2D NS solver using the vorticity formulation and FFTs but to understand the equivalence requires a greater background).
As for the cool visualisation, I cannot help you. I don't know any fancy graphics programming since I normally use the built-in plotting tools of Python and Matlab.