Dear community;
How can we assess the truncation and discretization error of CFD codes when we do not have the analytical solution? We have used the grid convergence index to assess our solution (Roache's works) but, what can we use to assess the order of our scheme?
I am more interested on state of art work to assess these type of errors. Ferziger and Peric's books also show one approach but is basically based on Roache's work.
Applied mathematician use L1, L2 and L infinity but as engineers and for more complex models how can we assess our numerical schemes?
Hallo Julio,
You can use the MMS verification technique.
The Method of Manufactured Solutions (MMS) is a very simple process and is
recommended as a general procedure for verification of codes. A manufactured solution is an exact solution to the PDE or set of PDE’s that has been constructed by solving the problem backwards. The technique can be used to estimate the accuracy of the numerical method and the order of the numerical scheme.
I have used it in my Masters and I have determined the accuracy of the used numerical method so simply.
attached is my paper where I described this method and for more detials I can send you my Master thesis.
Best regards
Mohamed
Conference Paper Sound Scattering from Acoustically Treated Bodies Using a Do...
Thanks Mohammad, I thought this technique was only for verification. In order words, to make sure your code does what you wanted it to do, but not for error estimation. I appreciate your help
Than you very much for your repose. I found your comments very useful and full of insight. !!
Your experience and knowledge is priceless for me and I am very worry how a lot of CFD practitioner do not consider these type of issues in their analysis and studies. These is very but very seldom seen in industrial related CFD analysis.
Thank you very much indeed. !!!
Hi Julio,
From the question and the answers I understand that we all are aware about distinguishing between truncation and discretization error, and the assessment of the numerical scheme. Here I exclude the consistency, stability and convergence, as they were not raised in the original question. Therefore it seems to me that it is about the accuracy.
The truncation error which is caused by truncating the Taylor series may be calculated by a Taylor series expansion for the equation which is being used in the computations, for which we can then see the order of the error for the corresponding discretized equation. Although this gives a very good estimation of the order of the error for different applications, it may become more difficult to assess when a mixed set of partial differential equations is present.
Therefore amplitude and phase error portraits are used by engineers and scientist to estimate the accuracy of the numerical schemes.
However, for the assessment of a numerical scheme, for a set of partial differential equations, the errors may be computed compared with the results of the solution of the same equations for simplified applications where the analytical solutions are available. An alternative to this and for the complicated cases an error analysis with some laboratory results may be conducted.
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