Maybe you're not the right person to ask, but I'll go anyway: I would like to learn the basics of CFD not because I expect to do much CFD in life, but because I believe the stuff I would have to learn in order to be able to understand CFD are very useful in other domains.
The problem is my analysis is very weak. My knowledge about linear algebra, differential equations, numerical methods, and so on is approximately limited at the level of an introductory university course. What would you suggest as a good start?
I like reading, but I also like practical exercises. The books I tried to read before to get into CFD were lacking in practical exercises, and when I tried to invent my own exercises, I didn't manage to adapt them to my current level of knowledge, so they were either too hard or too easy. (Consequently, they didn't advance my understanding much.)
This does look really good at a first glance. It seems like it uses mathematics that I'm not fully comfortable with yet -- but also takes a slow and intuitive enough approach that I may be able to infer the missing knowledge with some effort. I'll give it a shot! Big thanks.
You'll be able to understand the equations I guess. The hard part is the numerical analysis: how do you prove your computations will: 1/ reach a solution (badly managed computations will diverge and never reach any solution) 2/ reach a solution that is close to reality ?
For me that's the hard part (which I still don't get).
You could start with Saint Venant equations, although they look complicated they're actually within reach. But you'll have to understand the physics behind first (conservation of mass, of quantity of movement, etc.)
Regarding your two questions, some terms you could look up are: Courant number, von Neumann stability analysis, Kolmogorov length and time scales
With respect to 2, the standard industry practice is a mesh convergence study and comparing your solver's output to experimental data. Sadly, especially with Reynolds-averaged Navier Stokes, there is no guarantee you'll get a physically correct solution.
Yeah, I know but still had no time to dive into the theory enough to get a correct intuition of how it works on why there's no guarantee for a physically correct solution... Fortunately, my colleagues are the professors in my university who teach these, so I'll find an answer :-)
Understand the equations, yes. However, I'm sufficiently out of practise that it takes me a lot of effort to. So I guess you could say I'm not fluent to be able to grasp the meaning of these things as fast as I think I would need to in order to properly understand them.
The problem is my analysis is very weak. My knowledge about linear algebra, differential equations, numerical methods, and so on is approximately limited at the level of an introductory university course. What would you suggest as a good start?
I like reading, but I also like practical exercises. The books I tried to read before to get into CFD were lacking in practical exercises, and when I tried to invent my own exercises, I didn't manage to adapt them to my current level of knowledge, so they were either too hard or too easy. (Consequently, they didn't advance my understanding much.)