Basic Sub/Super/Hypersonic CFD Code
 

Two nights ago, I started fooling around with geometric shock and pressure wave modeling in MATLAB and ended up with a little script that would geometrically plot the shape of shock and pressure waves as a function of (constant) mach number. It turned out pretty nice and generates reasonably accurate shock wave geometries. Here's the catch: there is essentially no foundation in fluid dynamics. It's purely geometric wave theory, so temperature, pressure, density effects on mach number are ignored.

While I realize that the field of computational fluid dynamics is extremely complex and involved, I would like to attempt to generate my own (simple) code to replicate this behavior, although with fluid dynamics, meshing, etc. It helps me learn more about all of it, although I recognize this is a big undertaking.

I am relatively experienced (more conceptual than analytical) with solids based FEM and have a decent understanding of basic fluid dynamics, although little experience or understanding of FVM, FDM, or fluids based FEM.

Does anyone have any recommendations as to where to start?

I'm not sure which equations and techniques are best for modeling both subsonic and supersonic flows or really where I should begin. Any tips or recommendations are most appreciated!