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Old   June 8, 2007, 07:24
Default Uncertainty
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Hello everybody!

I am a spanish engineer doing a Master by Research in United kingdom and I am starting my research about uncertainty and error in CFD. My background is Industrial Engineering and my mayor is Industrial Management, so I haven't wide experience in CFD field.

That's why I need your help in order to FIND INFORMATION ABOUT THE UNCERTAINTY IN CFD. If I am not wrong, I should understand the probabilistic methods and the next theories: Fuzzy set, evidence, upper and lower previsions. Is it correct? Do you know where could I find easyly understandable information about it and related to CFD? Thank you very much for your answers. I have a meeting with the company very soon and I need help!!!
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Old   June 9, 2007, 01:40
Default Re: Uncertainty
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"uncertainty in CFD": it is completely general concept, it can relate to:

- error in physical modeling and simplification (is always present), a good way for studing this is experimental mesurment (consider uncertainty of experiment too).

- error and uncertainty due to approximate geometrical modeling, physical properties and limited accuracy computer arithmatic. For analysis such behaviour a good way is sensitivity analysis (this mean that studing variation of parameter under study, desired parameter, with variation of an especial parameter (uncertain), e.g. physical properties or geometry perturbation).

There are several methods for sencitivity and uncertainty analysis from this veiwpoint, some of them are stochastic (simple but usually computationally expencive) and some of them are deterministic (e.g. adjoint sencitivity analysis, arised form functional analysis) the later methods relay on some deep mathematical basis.

There are some book on this concept, one of them that i konw is: Sensitivity and Uncertainty Analysis (vol. I and II) by D.G. Cacuci. (i have an e-copy if u need), this book is more mathematically oriented (need some background) and has clos connection to numerical optimization, probably better books for u are availible.

>I should understand the probabilistic methods and the next theories: Fuzzy set, evidence, upper and lower previsions. Is it correct?

in my opinion, not all of your mentioned field are essential (especially Fuzzy set), but based on selection of your method you sholud select one category.

>Do you know where could I find easyly understandable information about it and related to CFD?

i don't know any that is easy to catch, but recomment to google about sensitivity analysis

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Old   June 9, 2007, 14:26
Default Re: Uncertainty
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Thank you very much for your help! I feel me quite alone and worried because I don't manage to make progress in the research, so your answer helps me a lot. I am just starting, but on 21st of June I have to explain my Research situation and I need to have more knowledge and more interesting information.

After reading some papers, I considered this division between error, uncertainty and variability in CFD:

ERROR ≡ "A RECOGNIZABLE deficiency in any phase or activity of modelling and simulation that is NOT due to lack of knowledge."

EPISTEMIC UNCERTAINTY≡ "A POTENTIAL deficiency in any phase or activity of the modeling process that is due to the LACK OF KNOWLEDGE."

VARIABILITY (or aleatory uncertainty) ≡ "Physical variation present in the system or its environment." It is not due to a lack of knowledge and can not be reduced.

Then, the error could be:





USAGE ERROR (including mistakes and blunders)

And the uncertainty:

STRUCTURAL or MODEL FORM (only epistemic): Due to differences between the model and the true

PARAMETRIC (Epistemic and variability): Due to the precise data for the analysis is not available.

I read somewhere that to analyze the uncertainty the "traditional" methods were the probabilistic ones, but these methods can be used only when we have enough information for it, and it is not usual. That's why I mentioned Fuzzy set, evidence, upper and lower previsions theories, thinking that these are the alternative theories that we can use, but I can't find information enough to can understand this theories in CFD.

So what I need before 21st of June really is to know is all that I said here is correct, to know is this theories are useful to understand the uncertainty (what do you mean with select one category?), and to find the way to understand this theories.

After that I should learn more about it and about CFD to develop a novel computational framework for the characterisation and representation of error and uncertainty in computational fluid mechanics simulations this is the aim of my Research).

Ones more I would like to thank you for your help and to apologize for the mistakes that I could make because of my limited English skills.

Please, I'd be so grateful if you could be so kind to send me the book that you speak about, all the help that I can get is important for me.

Thank you very much again.


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Old   June 11, 2007, 14:36
Default Re: Uncertainty
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Try looking at the Best Practices for Marine Applications of CFD (there is a link to it on this board). You will see that Section 3 is General Errors and Uncertainties and Section 4 is Method Independent Errors and Uncertainites.

AIAA 2002-5531 is titled Observations on CFD Simulation Uncertainties and can be found on the internet, also MAD Center Report 2003-02-01 Remarks on CFD Simulation Uncertainies, NASA -aiaa-2003-0411, Best Practices for Reduction of Uncertainty in CFD Results. These were found with a simple GOOGLE search.

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Old   June 12, 2007, 01:45
Default Re: Uncertainty
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>>what do you mean with select one category?

in my previous message, i count at least three categories:

1) experimentally (usually interpreted by probebility and..., sometimes used as snapshot for stablisihng basis for proper orthogonal decomposition for reduced order modeling)

2) stochastic simulation base (based on probability)

3) diterminestic simulation base (usually under context of sensitivity analysis)

you talk about quite general concept if you limit your area it is better, e.g. uncertinity analysis of what CFD analysis is subject of your study (with details)?

my background on Uncertainty analysis (is limited) is related to adjoint sensitivity analysis for using in gradient base optimization methods, if you work in this field i can give help !

also i have some study related to effect of accuracy physical properties on result of various aspect of casting simulation.

>>Please, I'd be so grateful if you could be so kind to send me the book that you speak about

please give your email

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Old   June 12, 2007, 11:42
Default Re: Uncertainty
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this proceeding (from Los Alamos) may be interesting for u to be familiar with various aspect of sensitivity analysis:

Sensitivity Analysis of Model Output (

complete PDF:

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Old   June 12, 2007, 11:55
Default Re: Uncertainty
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You should definitely have a look at:


Roache, P.J., Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico, 1998.

These are very useful references.

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