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May 27, 2013, 23:29 
Accuracy of discretization scheme

#1 
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Dear all,
I am simulating a flow model using FLUENT. There are two cases I have done for the same model. The settings of the cases are similar. They are steady using SST model. The only difference between them is the discretization scheme. The one is second order upwind, and the other is thirdorder MUSCL. The results for Cd are 8.48 and 8.37, respectively. Unfortunately, I have no available physical test data. So, my problem is how to tell which one is a bit more accurate? Thanks in advance. 

May 28, 2013, 03:44 

#2  
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Hope you find some solution. http://www.sharcnet.ca/Software/Flue...th/node366.htm Best of luck!!! 

May 28, 2013, 04:37 

#3 
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You need to perform a grid convergence analysis with, at least, 3 different solutions on sufficiently fine grids.
Useful references: http://www.stanford.edu/group/uq/docs/roache.pdf http://champs.cecs.ucf.edu/Library/J...%20studies.pdf 

May 29, 2013, 20:14 

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I have read the introduction for schemes on User's Guide. and it says : "The QUICK and thirdorder MUSCL discretization schemes may provide better accuracy than the secondorder scheme for rotating or swirling flows. The QUICK scheme is applicable to quadrilateral or hexahedral meshes, while the MUSCL scheme is used on all types of meshes. In general, however, the secondorder scheme is sufficient and the QUICK scheme will not provide significant improvements in accuracy." But, all of this is just a general guideline (as well as the theory guide). Is there any other explicit methods to tell accuracy? 

May 29, 2013, 20:17 

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Sure, I will do mesh convergence analysis, but even for a fine and suitable grid, different schemes come out different results. Thanks for your references, they looks really great~~ 

May 30, 2013, 03:39 

#6  
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So it varies from case to case. QUICK scheme is also not good for unstructured meshing. 

May 30, 2013, 04:02 

#7 
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Jim Knopf
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Hi,
some remarks on your question. First, think about the solution, is it really a stable steady state? If not, you might end up with two different solutions. Second, think about the convergence, did both cases converge two very low values? At last you should think about error sources. First there is the model error, which you can cancel out since your model stays the same. Then there is the iteration error which is reflected in the residuals. Finally there is the discretization error, which is due to the meshing, due to the interpolation scheme, i.e. MUSCL and some other stuff in the solver. If you perform a Richardson Extrapolation for both of your cases you could get a fealing for discretization error. It should come up with a second order accuracy for the second order upwind and as far as I with 3rd order for the MUSCL. But if you have such a big differenz in a integral value  drag coefficient  then you should first think about your model and the mesh. Greetz Jim 

May 30, 2013, 04:51 

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And to Jim: First, As for the real physical flow, actually, it's not a steady flow. I even have carried out LES simulation for the model, and according to the results, there were vortices shedding from the boudary of geometry model. The RANS simulation is carrying out in order to get an average flow results. If I average the results of LES, is it a more accurate average flow results than the RANS? Second, both cases have achieved a great convergence. The residuals were all below 1e6, and the Cd stayed still. The geometry model and numerical mesh are identical for both cases. The only difference between the cases is the discretization scheme. Maybe, different schemes require different mesh density to achieve a accurate result? What's more, I am really puzzled by the Richardson Extrapolation, could you give me details how to perform a Richardson Extrapolation. Regards! 

May 30, 2013, 06:00 

#9 
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OJ
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This is the easiest link to understand all about Richardson's extrapolation and Roche's method for Grid Convergence Index. The latter is recommended over former to judge the grid independence.
http://www.grc.nasa.gov/WWW/wind/val.../spatconv.html Please understand that though the order of accuracy of the discretization scheme on stencil (theoretical) may be 2 and 3 for second order and MUSCL, the actual accuracy depends on many things! Richardson's extrapolation helps you find the actual order of accuracy. LES is a different ball game. You need to make sure that your grid cell size is small enough (of the order of Taylor's lengthscale) and your turbulent energy spectrum is well established to make sure the larger lengthscales are resolved, and not modelled using SGS models. OJ 

May 30, 2013, 21:47 

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The reference is fabulous. 

June 1, 2013, 08:04 

#11  
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Jim Knopf
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Finally the difference in your results is less than 2%, which I would say isn't that much. Greetz Jim 

June 2, 2013, 20:46 

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By the way, what do you think about the mesh requirement of LES? 

June 3, 2013, 15:03 

#13  
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OJ
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For inner regions: Taylor's lengthscale However, to have legitimate results from LES, it is extremely important to make sure that the larger lengthscales are resolved and smaller ones are modeled. You need to make this sure by plotting a turbulent energy spectrum, such that your filtering size falls within inertial subrange, such that below which the energy decay is 5/3. Only then you are sure that you have resolved your timescales and lengthscales adequately, and the only the isotopic lengthscales are passed on to SGS models. Otherwise, the results you have for LES are just a gimmick OJ 

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