I am looking for a relatively simple book/paper that explains the basic Streamline Upwind Petrov Galerkin (SUPG) method for solving the incompressible unsteady Navier-Stokes equations. Most of the references I have managed to find online have been papers that more-or-less assume you already know the method well. I plan on actually implementing my own solver that uses this method, so references that provide detail on how to do this would be helpful.

Note: Preference given to references that are freely available online.


2 Answers 2


See http://www.ccpo.odu.edu/~tejada/USACM07/BrooksHughes.pdf

This is where the technique was first used for convection dominated flows.

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    $\begingroup$ Could you please elaborate a little bit on the link you posted? For instance, a full citation to the paper would be great. Links tend to go stale over time, and if that happens, having the full citation and a brief summary of the contents of the paper would be helpful in keeping this answer useful. $\endgroup$ Jul 30, 2015 at 0:35
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    $\begingroup$ The link is no longer functional. $\endgroup$ Apr 7, 2017 at 15:45

The original paper introducing the SUPG was from Brooks and Hughes, 1982 (http://www.sciencedirect.com/science/article/pii/0045782582900718). This was purposely for the convection dominated flows using the Incompressible Navier-Stokes as an emphasis.

I can recommend the monograph of Roos, Styne and Tobiska (http://www.springer.com/us/book/9783540344667). This book particularly covers this topic into great depth and will easily recommend it.

I think may be it is important to understand the Incompressible unsteady Navier-Stokes before considering the numerical discretization schemes.

  • $\begingroup$ Thanks. In regards to your last comment though, I am familiar with the incompressible Navier-Stokes equations its just the SUPG scheme that I do not know. $\endgroup$
    – James
    Jul 30, 2015 at 22:58

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