I have good background of finite element methods and continuum mechanics and I am familiar with fluid mechanics. My aim is to understand the required theory and to write my own simple codes using finite element, finite volume or other methods.

I am looking for references for computational fluid dynamics. I am beginner in this field, so I am looking for 'beginner references.' The reference should also outline necessary background in an accessible manner for computational fluid dynamics, such as Navier-Stokes equations, finite volume method derivation etc. (I personally think many books outline prerequisites before going for advance topics.)

I did search and found out two books:

  • T. J. Chung, computational fluid dynamics
  • Versteeg and Malalasekera, An Introduction to Computational Fluid Dynamics

Chung's book seems to give a lot of background information on FEM, FDM, FVM. But I am not sure how the book will turn out after investing time and efforts. Suggestions are welcome.

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    $\begingroup$ The book my Versteeg and Malasekera is a good reference, it is easy to read and follow and is actually relatively modern. However, they rarely use tensor notation which makes it highly tedious for some parts. I highly recommend the book by Ferziger and Peric ( springer.com/gp/book/9783540420743) . It is a bit dated, but it is the best reference in my opinion. $\endgroup$
    – BlaB
    Mar 21, 2017 at 12:20
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    $\begingroup$ For FVM I can warmly recommend E. Toro's book 'Riemann solvers and numerical methods for fluid dynamics'. Goes through the math in great detail, gives many examples and at the beginning of each chapter re-references all needed prior knowledge. $\endgroup$ Nov 17, 2017 at 10:50
  • $\begingroup$ Would you be interested in incompressible flow (versus compressible flow)? Methods and analysis tend to be simpler in this case. $\endgroup$
    – hardmath
    Feb 15, 2018 at 22:24

2 Answers 2


Unfortunately this is a vast question and can have many responses.

Most CFD books tend to focus more on the author's interests. In addition most books would only do either finite volume or finite difference, and that too on (mostly) Cartesian grids. There are a few reasons for this but probably the most obvious reason would be that they are conceptually the simplest, and probably easiest to implement (for Cartesian grids).

In terms of personal preferences, for finite volume I would recommend Computational Fluid Dynamics: Principles and Applications by Blazek since it helped me when I needed to implement a finite volume method. I am making a generalization here, but Blazek, and other books will only get you started. When I needed to implement WENO schemes, which are really not that complicated, I had to go straight to papers. To go further, at least for compressible flows you would definitely have to go through Riemann Solvers and Numerical Methods for Fluid Dynamics by Toro.

For finite difference and more generally as a reference I would recommend Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics - Hirsch since it covers most topics in a reasonable amount of detail. Also CFD by J. D Anderson would be good as well.

I don't know about finite element methods, but if you want to use Discontinuous Galerkin methods, Nodal Discontinuous Galerkin Methods by Hesthaven, Warburton is a great book that includes sections on how to write the code, although its in Matlab.


For finite element method in fluids " Finite Element Methods for Flow Problems" https://g.co/kgs/H6ZVpQ

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    $\begingroup$ This could use more elaboration. Why do you recommend it? $\endgroup$
    – J. M.
    Sep 18, 2017 at 15:35

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