Hello all,
I was willing to know how utility of Richard Extrapolation in CFD. I know it can be used for estimation of order of scheme by running numerical simulation for 3 different grid configurations.
However what I am not clear of is how to use it to approximate results of higher order accuracy using lower order. Is it simply by the formula of Richard Extrapolation
A= 2^k A(h/2)-A(h)/ 2^k -1
where A is calculated using grid first and then 1/2^k.
In real application does this mean if I calculate some variable (say Pressure in pipe flow) with grid size 100x40 and then by 200 x 80 then using results obtained and formula I can estimate Pressure with higher order accuracy?
Is this correct or there is some other way how this is used (multi grid method or something like that)
Thank You
The standard Richardson extrapolation is for second order schemes and does not give estimates for higher order schemes, but gives estimates for infinitely small elements (or infinite number of elements) assuming second order convergence.
Hello Deewakar,
basically, you determine what your solution could be, when your grid was
infinitesimally fine using the data obtained from grids with a reasonable resolution, as stated by David,
The drawback, however, is that inaccurecies from the coarser grids will spoil the quality of the extrapolated value. Thus, it is hardly possible to improve the quality of a solution using the extrapolation. It is, however, useful to estimate the numerical uncertainty in terms of grid dependence. This is reported in e.g. "Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer" from the ASME. Check the keyword "fine grid convergence indicator".
Best regards
Bastian
Hello Bastian
Greetings.
Could please elaborate little more on what you exactly meant by Numerical Uncertainty. I also came across a text where they had mentioned to use this to check for order of Numerical Scheme.
Thanks
I found this webpage an informative source when learning how to use Richardson extrapolation:
http://www.grc.nasa.gov/WWW/wind/valid/tutorial/spatconv.html
Concerning error and uncertainly estimate using the Richardson Method you can read this report :
FACTORS OF SAFETY FOR RICHARDSON EXTRAPOLATION
by by Tao Xing and Fred Stern
IIHR Technical Report No. 476
College of Engineering
The University of Iowa
Iowa City, Iowa 52242-1585 USA
http://www.taoxing.net/web_documents/iihr-vv-2010.pdf
Concerning error and uncertainly estimate using the Richardson Method you can read this report : http://www.taoxing.net/web_documents/iihr-vv-2010.pdf
FACTORS OF SAFETY FOR RICHARDSON EXTRAPOLATION
by by Tao Xing and Fred Stern
IIHR Technical Report No. 476
College of Engineering
The University of Iowa
Iowa City, Iowa 52242-1585 USA
Anyone familiar with Richard Extrapolation in CFD? - ResearchGate. Available from: https://www.researchgate.net/post/Anyone_familiar_with_Richard_Extrapolation_in_CFD [accessed Jun 22, 2015].
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