I'll try to give a list of the key areas that a typical university student might study to prepare for CFD research. Perhaps someone else can give some advice on where to focus for most efficient use of your time or point out specific resources.
There's a lot of background info involved in fully understanding fluid dynamics and CFD. And, as with many advanced topics, there's always more to learn. If I had to make a list of topics to study to better understand things I would divide it into two areas: Mathematical fundamentals and Physics. In rough order of sequence for learning I would propose the following lists for these topics:
- Linear algebra
- Ordinary differential equations
- Partial differential equations
- Numerical methods
- Specific CFD methods (e.g. finite difference/finite volume/finite element implementations)
- Asymptotics (maybe)
- Introductory physics
- Classical mechanics/Newtonian physics
- Transport phenomena
- Thermodynamics and/or statistical mechanics (maybe)
- Aerodynamics or other application relevant topic (e.g. ocean dynamics)
As I'm sure you know, CFD methods rely on (sometimes complex) numerical methods to solve nonlinear partial differential equations derived from physical situations. Math and physics are two subjects that build in complexity quite significantly so there is simply a lot of background material which is needed to fully understand the end processes. You could possibly skip some of these topics and still greatly improve your understanding, but I think this is a good starting list to really understand many CFD methods. In my opinion, numerical methods for scientific computing, partial differential equations, and transport phenomena are the most essential topics.