Standard for checking and testing numerical schemes?
I participated once a CFD conference in this year. A main topic of this conference was numerical schemes, e.g., high order and nonoscillating upwind schemes. Because of the high presence of theoreticians and mathematicians, the theoretical level of this conference was very high. I work in the industry and I am confronted every day with the practical application of CFD tools for the development of industry product, hence I am not very satisfied with the situation in this conference: Every author derived his scheme from the Euler equation and tested it for inviscous flows with shock wave etc.; if there are no oscillations and no obvious boundary layer caused by numerical diffusion, he said his scheme is good; but almost nobody tested his scheme for viscous flow especially for flows with boundary layer. I think, a good scheme for Euler inviscous flow can be still bad for NS viscous flow, because the numerical diffusion or artificial viscosity can confuse the physical viscosity strongly; A scheme costing much more computing time is not a good scheme; A scheme working not very stably is not a good scheme. I think, the CFD community could build a standard with typical flow cases for checking and testing numerical schemes.
X. Ye 
Re: Standard for checking and testing numerical schemes?
X. Ye, I agree that further work could be done to bring theory closer to reality. This may be among the biggest questions on a great many researchers' minds. Perhaps you have read the AIAA's 1998 general document entitled, "Guide for the Verification and Validation of Computational Fluid Dynamics Simulations" which discusses steps for answering the following two questions: 'Was the model solved correctly?' and 'Was the correct model solved?' It's not a technical document, but it is, at least, something to refer to when creating benchmark experiments for the cfd code or for considering numerical or grid convergence and so is a step forward (albeit a small one) for uniting theory and reality.

Re: Standard for checking and testing numerical schemes?
Hi,
I think you brought up some interesting points. If developers want to check there codes they normaly refer to simple single effect test cases. As a first step this is justified, because how should a code work, if it can not solve these cases. But you should have in mind, there are certain classes of problems which differ alot in physics eg. high speed flows with shocks or low speed flow with stong viscous effects. These differents in phisics might then need also different numerical methods. In practise there is a big differents if you look at the aerodynamics of a car or a fighter plane. As a results also relevant test cases differ alot, eg.: 1. driven cavity problem, 2. forward facing step problem. So we have to be very carefully when selecting test cases to test our codes. A must admid I have learned some lessons over the last years by simple try and error. For the future it would be very useful to have a kind of manual which would guide you to test your code in the area of application where you are interested in including also topics like turbulence, resolution, effectiveness, stabilty, adaptive meshes and alot more. In addition if you compare your results to others you could benchmark yourself. I am missing a procedure like this among commercial codes. I only know a first attemp published in Int. J. of Fluid a few years ago. Ciao Heinz 
Re: Standard for checking and testing numerical schemes?
Hello,
This is an interesting subject. Could you please give the exact reference for that AIAA journal? Thanks, Jan Ramboer 
Re: Standard for checking and testing numerical schemes?
Hello,
Is it possible to get the exact reference? Greetings, Jan 
Re: Standard for checking and testing numerical schemes?
No problem, I just remenbered the journal wrong, the correct reference is:
C.J. Freitas Perspective: Selected Benchmark From Commercial CFD CODES Journal of Fluid Engineering, Transactions of the ASME, Vol. 117, June 1995, pp. 208218 Hope that is useful information. Heinz 
Re: Standard for checking and testing numerical schemes?
>I think, a good scheme for Euler inviscous flow can be still bad for NS viscous flow, because the numerical diffusion or artificial viscosity can confuse the physical viscosity strongly
It is true that a good Euler solver may not be a good NS solver. However, your reasoning above is not correct/true. Numerical diffusion comes from the nonlinear convective term and has nothing to do with the linear diffusion operator in the NS equations. Since the difference between Euler and NS is only the diffusion term (forget boundaries for the sake of this argument), it is not only a good approach but advisable to check a new scheme on Euler equations. You see, if the concern is to alleviate numerical diffusion, it is much easier to analyze Euler equation. The NS equations introduce additional complications that will in no way enhance the analysis as far as the numerical diffusion issue is concerned. In fact, NS will make it even more difficult, because now you don't really know how much of the diffusion that you predict is real and how much is not. In contrast, a bad scheme applied to the Euler equation will force it to behave like NS, and you can immediately decide whether the proposed approach has a chance of doing a good job at the minimum level. To sum up, if a scheme does not do a good job predicting Euler flow, it has no chance of doing a good job predicting NS. Adrin Gharakhani 
Re: Standard for checking and testing numerical schemes?
I too was interested in this reference (Guide for the Verification and Validation of CFD Simulations". It is apparently a standard available from AIAA for about $20$30. The AIAA web site is at http://www.aiaa.org. You can search for the title, then go through to the publications catalog, then find the standard. The web site is at
http://www.aiaa.org/publications/cat...des.html#stan Hope this helps. Jeff 
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