I am recently working on computational astrophysics. My research is mainly focused on accretion processes around compact objects (black holes & neutron stars), radiative transfer and modelling of turbulent compressible flow.

I come from a background of theoretical physics and I can do programming in C/C++. So, I am looking for an expert advice on a comprehensive list of useful resources to learn the various computational techniques. Also I would like to know about the various softwares and packages that are useful in computational astrophysics.


I am not seeking an answer on resources related to theoretical aspects of astrophysical hydrodynamics or gas dynamics. Rather I am interested in the computational methods and softwares used by computational astrophysicists, for e.g., various packages and softwares used to analyse astrophysical data, techniques used to simulate accretion disks around compact objects etc.

  • $\begingroup$ Possible duplicate of Compressible gas dynamics in the context of astrophysics $\endgroup$
    – Kyle Kanos
    Nov 27, 2019 at 11:47
  • $\begingroup$ Well I’d wager that most astrophysicists write their own MHD code, as there isn’t something ubiquitous like MS Office for it. So that part of your question is largely irrelevant because it can’t be answered, the other part (text resources) are essentially the same thing as I linked $\endgroup$
    – Kyle Kanos
    Nov 27, 2019 at 13:15

1 Answer 1


At least to address the computational aspects of the turbulent, compressible flow solver parts, I will quote Kyle Kanos:

On a more programmatical aspect, Toro's Riemann Solvers and Numerical Methods and LeVeque's Finite Volume Methods for Hyperbolic Problems are pretty much the bible for how to write code that will accurately model fluid flows. In both books, vector calculus and linear algebra are needed. LeVeque's book is written more towards undergraduates, but is good for anyone interested in numerical methods; it also includes references an older version of his Fortran code Clawpack (an open-source library).

Those are good books on the numerical methods required for compressible flows. I would add to that list Computational Fluid Mechanics and Heat Transfer from Anderson, Tannehill, and Pletcher. This, with the others, should complete your computational flow needs. This book also touches on turbulence modeling aspects, but not in great detail.

To get a handle on the turbulence parts, you should look at Turbulent Flows by Pope, which has all of the theory you need plus chapters on both Large Eddy Simulation and RANS modeling. But the ultimate book on turbulence modeling will be Turbulence Modeling by Wilcox. It is out of print (and so listed at $800 on Amazon... yikes), but find a library and you'll be in good shape. This will have pretty much all of the RANS and LES closure models you will need for most flows.

If you are interested in LES specifically, then Large Eddy Simulation for Incompressible Flows and Large Eddy Simulation for Compressible Flows from Sagaut's group in France provide fantastic details. The incompressible flows one doesn't seem directly on point for what you need, but the compressible flows one builds on it and it provides details that help to understand the compressible flows book.

If multi-species and combustion are relevant for your particular applications, I recommend checking out Theoretical and Numerical Combustion by Poinsot. It has all of the tricky details needed for combustion, but it will be focused more on fundamental flames and propulsion applications. The equations and methods are still valid of course, but the focus will be different and so you'll have to keep motivated if that doesn't excite you to read about it.

(Certain flow instabilities will be important for your application as well, and these may have different modeling requirements to get correct. The Rayleigh-Taylor instability and the Richtmyer-Meshkov_instability will both be relevant in all likelihood. There are several comprehensive review papers on RTI that I will add when I get to my office -- we've cited them many times and used them to track down both physics and numerical modeling papers from their citations. Leave a comment if I haven't updated this part in a few days to remind me...)

For the more astrophysics parts (accretion, MHD, nuclear reactions), I will have to defer to others to add to this list.

  • $\begingroup$ MHD seems pretty simple compared everything else here $\endgroup$
    – Kyle Kanos
    Nov 27, 2019 at 13:34
  • $\begingroup$ @KyleKanos That's probably true... I think physically it's simpler, but computationally it was hard for us. But we were adding it to a compressible solver, so the stiffness and ensuring $\nabla \cdot B = 0$ by using a staggered grid was new for us and didn't fit well with the 20 years of development done to that point... But I guess it's probably similar in complexity to doing low Mach number flows. $\endgroup$
    – tpg2114
    Nov 27, 2019 at 14:26
  • $\begingroup$ I believe using Flux Constrained Transport method is probably easier than staggered grid. I have used it nicely for 2D simulations, probably easy enough to adapt to 3D $\endgroup$
    – Kyle Kanos
    Nov 27, 2019 at 14:29

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