Finite difference methods still form the basis of finite volume methods. Within an FVM implementation, you use finite differences to approximate things like gradients of point-valued functions. The difference is that then FVM uses those FDM approximations and integrates them on surfaces or volumes which gives nice properties like conservation and geometric flexibility. Alternatively you can use Green-Gauss (an integral form) to compute gradients, and that's not really FDM. FDM methods are all about approximating derivatives, which happens everywhere, so it's a proper place to start an intro CFD course. (My first CFD course did go into FVM, many do.)

@Anirudh Diwakar @Ahmed Zaid @Walid Badawy @Michał Murzyn an overview here

@Anirudh Diwakar So 100% of the code is present in the text writeup and the accompanying github repository. You can literally just download and build the final project, or turn your brain off and copy-paste all the code (learning nothing in the process). It's something I've found difficult in the writing process and I'm curious how a reader like yourself would experience it, hence seeking feedback before I release it all publicly. So in theory you could have zero C++ experience at all, but I've also shown this to seasoned C++ experts in the field who still learn something from the architecture. I'll figure out how to do this; either I'll give you access to the currently-private repository or just email early drafts of the HTML docs.

I'm just here because I was curious how it works, but I'm gainfully employed :) NASA now, formerly Siemens and Cadence. Iowa State undergrad, Princeton PhD. Primarily solver development in FV and DG, and HPC solver architecture.

@Mohamed Sayed well I started in computer science at Iowa state as an undergrad for no reason other than I was "good with computers" but that didn't really work out. Found aerospace engineering and loved how diverse the curriculum was. I had never heard of CFD at the time. Eventually was taking an aerodynamics course with Ganesh rajagopalan and he found out I could do some c++, and he asked me to work for his small rotorcraft company doing development. Decided to stay for an MS with him starting 2008, he let me pick any topic I wanted, so I developed GPU CFD code in the early days. Enjoyed the field and wanted more, so I found myself starting a PhD at Princeton. Initially worked on structured multi block FV solvers with some wind energy applications. Eventually wrote a fairly advanced high order DG code for the bulk of my thesis. A job opportunity came up at Siemens / former CD adapco, as a physics developer for STAR-CCM+ where I developed some key stuff and also started the GPU port. Was there for 5 years, then got an opportunity at Cadence during their acquisitions of CFD companies. Worked on solvers there for 2 years til an opportunity came up in the computational aerosciences branch at NASA Langley and I've been there for 6 months now working on their cfd codes. Tldr wrote a ridiculous amount of CFD code for 15+ years and got decent at it :)

I can't speak to Europe, but I would say as long as it's a reputable university, you won't be passed over and you'll be judged on your work/skills. Although I have seen some UK postdoc listings which specified they wanted phds from top universities, which I found a little odd. That said, you might find better resources at "better" universities.