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Links - Modeling and Numerics

This section contains links to selected resources covering physical modeling and numerics. The intent is to give the best starting points available within each subject. To suggest a link to be included in this section please use the online link suggestion form. You are of course also welcome to contact us directly via email at



Introduction to Turbulence, CFD-Wiki [GOOD]
A comprehensive textbook about turbulence. Based on "Lectures in Turbulence for the 21st Century" by Professor William K. George. Added to CFD-Wiki by Michail Kirichkov.
Turbulence Modeling, CFD-Wiki [GOOD]
Contains a lot of information about many different turbulence models. Also help on how to set turbulent boundary conditions. Please help to improve CFD-Wiki by adding and reviewing information yourself!
Turbulence Modeling Resource [GOOD]
A turbulence modeling page maintained by the Turbulence Model Benchmarking Working Group by the Fluid Dynamics Technical Committee at AIAA. Has detailed descriptions of many turbulence models. You can also find many validation cases, including grids. This looks like a very good resource if you want to implement and validate a turbulence model.
Turbulence at Wikipedia
A growing page of information about turbulence.
Turbulence Links
A comprehensive summary of turbulence information on the net by George B. Ross. It isn't always up-to-date, but it is still the most complete source of turbulence information on the net.
Bibliography Of Turbulent Flows
A list of over 9000 references on turbulence and associated numerical and experimental techniques. Compiled by Prof. Peter Bradshaw.
Turbulence Models and Their Application to Complex Flows, by R. H. Nichols [GOOD]
A very nice book that contains a fairly complete overview of RANS and LES turbulence models. More than 200 pages long. Also contains chapters on wall functions and transition prediction. We just found this book, but after a quick look it seems very interesting (Jan 2012).
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Combustion, CFD-Wiki [GOOD]
A very impressing summary of combustion modeling in CFD-Wiki. Written by volunteers. Please help to add information and review the information in CFD-Wiki, everyone can help!
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Discretization Schemes

Finite Volume Methods: Foundation and Analysis
A 57-page report on finite volume methods by Timothy Barth and Mario Ohlberger. The focus is on compressible flows and it describes classical schemes like TVD, ENO and Muscl as well as modern multi-dimensional higher-order schemes. Nice!
Numerical Methods and Error Estimation for Conservation Laws on Structured and Unstructured Meshes
Timothy Barth's lecture notes from his 2003 VKI lecture series. Good stuff!
Finite Volume Methods by Eymard, Gallouet and Herbin
A 249 page document originally published in Handbook of Numerical Analysis, September 1997.
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For software libraries see the Programming and Computing > Software Libraries section.
Templates for the Solution of Linear Systems [GOOD]
A hypertext book focused on iterative methods for solving large sparse systems of linear equations. Algorithms are presented in a language independent "template" form. Basically the same routines are available in the C++ libraries SparseLib++, IML++, MV++ .
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Multigrid Methods

Has a long history on the net.
A repository for information related to the multigrid, multilevel, and domain decomposition methods. Has a large bibtex database, reports, preprints, tutorials and a lot of free software. Also publishes a monthly newsletter. Highly recommended!
CFD-Wiki: Multigrid methods, Geometric Multigrid - FAS, Algebraic Multigrid - AMG
A few pages in CFD-Wiki to give you an overview of multigrid methods. You can improve these pages yourself!
Wikipedia Multigrid Methods
A brief introduction to multigrid methods, not very exisiting yet (2012), but you can find a few good references at least.
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Finite Element Methods

Internet Finite Element Resources [GOOD]
An excellent annotated collection of links to information related to FEM. Has been on the net for a long time. This site is rarely updated any more, but it is still a valuable resource.
FEMur - The Finite Element Method Universal Resource
An introduction to FEM and a collection of FEM resources. Has a lot of educational information. This is a site that has been on the net since 1995!
Finite Element People
This list is getting old and many links are dead, but we do not have anything better so we will leave the link here. This list includes links to home pages of people working with finite element methods.
Wikipedia Finite Element Method
A growing page with basic information about FEM. Not focused on only CFD.

Selected Projects

FEAT is a general purpose software system for solving PDEs with the finite element method. The system includes a lot of tools and an incompressible fluid-flow package called FEATFLOW. The software is available freely with source (F77) and the site has a lot of further information available online. The FEAT group are from the University of Heidelberg.
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Cartiesian Grid Methods & Adaptive Mesh Refinement (AMR)

Home Page of Michael J. Aftosmis, NASA Ames Research Center [GOOD]
Working on Cartesian Grid Methods and the Cart3D code. Has many publications available online, including leture notes from a VKI course on cartesian grid methods.
Home Page of Marsha J. Berger, Courant Institute [GOOD]
One of the leading researchers on cartesian grid methods. Has several highly relevant publications available directly online.
AMR at Wikipedia
A growing resource that gives a good introduction to AMR methods.
Adaptive Mesh Refinement for Structured Grids
A portal for AMR by Tomasz Plewa. This site has been online for more than 15 years. It is focused on astrophysics, but can also be a good general resource.
AMRITA is a system for communicating software-based ideas and information by James J. Quirk. AMRITA in a cross between a document preparation system, a computational engine, and a programming language. The kit includes compressible CFD examples using AMR.
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Numerical Analysis

Numerical Methods, CFD-Wiki [GOOD]
CFD-Wiki contains a lot of information about numerical methods used in CFD. Please take the time to review and add information yourself!
An online forum for numerical analysts. Provides an email database, a whitepage database and a weekly digest.
NAFEMS is an organization aimed at fostering quality and standards in the numerical analysis of engineering problems. They have a CFD working group which hosts seminars and develops CFD training documentation.
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