error estimation / accuracy
Hello!
I am looking for ways of estimating the numerical accuracy of a CFD simulation. I work with CFX4.4 and CFX5.4 simulating 3D combustion and heat transfer flows. As a result it is not possible to obtain a grid independent solution in most cases. Does anyone have references, subroutines or recommendations on how to efficiently estimate numerical accuracy? I am sure there are some favorite practices out there! Thanks in advance for any feedback! Regards, Michel 
Re: error estimation / accuracy
(1). I don't think so. (2). Grid independent solution can be obtained if you keep your problem simple. For complex problem, it is more difficult because you will need more mesh points. And it will take longer to converge.(3). I would strongly suggest that you simplify your problem first, and try to get the grid independent solution first. In this way, you will get the feeling you need to get the solution. (4). After that you still have to validate your solution against the test data. (5). It is important to get the mesh independent solution, because it will give you the true nature of CFD, the nonlinear side of the story.

Re: error estimation / accuracy
Hi Michel,
Have a look at the work by P Roache (in particular his book called something like "Verification and Validation for CFD"). It is an excellent way of checking your CFD solution. He breaks the errors down into two types  does your model represent the real world, and then have you solved it correctly? There are ways to put numerical values on the grid accuracy, using a "Grid Convergence Index". But I like most the way the method emphasises looking at errors from all sources. Trac. 
Re: error estimation / accuracy
Bonjour Michel,
There's an AIAA "Guide for the Verification and Validation of CFD Simulations", AIAA Guide G0771998, a 1998 publication. Very useful (about 3040 pages). Alternatively there's a 1989 paper by Roache in Journal of Spacecrafts and Rockets, Vol. 27, No. 2, pp. 90102. I usually try to abide by these principles when assessing the grid quality. Herve 
Re: error estimation / accuracy
Hi Michel,
This paper may be of help: B.R. Hutchinson, S.R. Elias, and S.D. McMillan,THE EVALUATION OF A NUMERICAL ERROR ESTIMATION TECHNIQUE FOR ENGINEERING FLOWS, Advanced Scientific Computing Ltd., Waterloo, Ontario, Canada The paper was written for presentation at CFD '96. Fourth Annual Conference of the CFD Society of Canada. It offers some simple techniques for estimating numerical error by solving on successively finer grids (but not necessarily grid doubling or converging on a mesh independant solution). The technique only applies to Hexahedral meshes. If you cannot find it, contact support directly and we can fax you a copy. Best regards, Robin 
Re: error estimation / accuracy
Try a search on "Grid Convergence Index" You will get several links where you can read about the method online.
This is just one that could help you. http://www.grc.nasa.gov/www/wind/valid/gridconv.html The GCI method atleast give you an idea on how well solved (numerical) your problem is, not the same as if you have solved the real problem/physics. Jan 
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