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cynthia May 21, 2008 06:28

Richardson extrapolation
Hi guys,

usually to demonstrate the grid indipendency it is used the Richardson extrapolation. Anyway, it supposes that the refinement is homogenous...but if I have adapted my grid adjusting gradients can I still use Richardson extrapolation?



esteban June 5, 2008 06:03

Re: Richardson extrapolation
Theoretically you cannot. Richarson assumes that you refine in all directions homogeneously and methodically. That is by doubling the cell count for each new grid (you can actually multiply by any number as long as it is the same for each new grid). you can find more information on

You can also check the book by Ferziger and Peric for details.


Omar June 17, 2008 10:48

Re: Richardson extrapolation
Check this paper, C. J. Freitas, U. Ghia, I. Celik, P. Roache, and P. Raad, "ASME'S QUEST TO QUANTIFY NUMERICAL UNCERTAINTY", 41st Aerospace Sciences Meeting and Exhibit, 6-9 January 2003, Reno, Nevada.

The authors provide a nice procedure for CFD error estimation. There is a huge amount of publication in this regard .. but this paper outlines what I think is the most important part!

esteban June 20, 2008 05:16

Re: Richardson extrapolation
Very interesting paper!!! As I understand the refinement cannot be local but has done for the whole grid... Are you aware of how richarson and GCI's can be applied with local refinement only?

Thank you

Omar June 20, 2008 08:58

Re: Richardson extrapolation
Unfortunately I was not able to find such a procedure in open literature. However, I did some work on that and I calculated r locally "mesh refinement" and I used it in the same procedure .. I am not sure though if it is the right thing to do!

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