Reddit mentions of Chebyshev and Fourier Spectral Methods: Second Revised Edition (Dover Books on Mathematics)

> I want to at least give myself some experience with using CFD oriented programs

Allow me to read between the lines a little. Your original request seems to imply you want experience using commercial CFD applications. This is certainly a good sub-reddit for that, but I think you also will want/need experience with underlying CFD theory/algorithms to be successful in a graduate program on the subject (although a more industry focused Master's program might not need this at all, but I'm assuming you mean PhD programs). Academic research and advanced applications work tends to be beyond what commercial applications can provide and usually involves in-house or purpose built codes.

As suggested here Dr. Barba's "12 Steps" is a decent starting place. You'll touch on both theory, algorithms, and write code. There a couple additional recommendations I might add. There are a number of methods for CFD, the earliest one is Finite Difference methods and this is what "12 Steps" uses. However for the most part modern academic work uses either Finite Element/Volume, Discontinuous Galerkin, or Spectral methods. You'll likely branch out into one these methods depending on what your PI likes.

That isn't to say that your knowledge from "12 Steps" will be useless, there is a fair degree of overlap, but you'll likely move on from it. Having an applied math background puts you in a good place foundation-wise to quickly dive into other material. I recommend starting with Gustafsson's text Fundamentals of Scientific Computing. It's relatively simple and may cover things you already know depending on your background, but it is a comprehensive starting place that will also walk you through each of the main methods.

From there you could branch out into a method that interests you, my recommended starting texts:

Finite Volume: Leveque's "Finite Volume Methods for Hyperbolic Problems".

Finite Element: Rather than a text, I highly recommend Dr. Garikipati's online course from UMich. The video lectures are all on Youtube and are high-quality both production and layout-wise.

Discontinuous Galerkin: The defacto text is Hesthaven and Warburton's "Nodal DG Methods". I don't think it's a great intro to DG for students, but it's certainly a good reference. Shameless self-plug: I put together a set of Intro to DG video lectures that walks you through a high-order 1-D solver.

Spectral/Spectral Element: I'm least familiar with this area, but have looked through both Boyd's Chebyshev and Fourier Spectral Methods and Kopriva's Implementing Spectral Methods for Partial Differential Equations and found them to be pretty good.

Domain specific wise I'd expect you to be using a FV or DG method to deal with shock-capturing for hypersonic flow. You'll inevitably want to take a look at Toro's Riemann Solvers for shock handling and flux function related stuff. Look here last (or at all) once you actually need it.