
[Sponsors] 
May 27, 2013, 23:29 
Accuracy of discretization scheme

#1 
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
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  
New Member

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

May 28, 2013, 04:37 

#3 
Senior Member

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 

#4  
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
Quote:
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 

#5  
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
Quote:
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  
New Member

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

May 30, 2013, 04:02 

#7 
Member
Jim Knopf
Join Date: Dec 2010
Posts: 60
Rep Power: 7 
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 

#8  
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
Quote:
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 
Senior Member
OJ
Join Date: Apr 2012
Location: United Kindom
Posts: 475
Rep Power: 11 
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 

#10  
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
Quote:
The reference is fabulous. 

June 1, 2013, 08:04 

#11  
Member
Jim Knopf
Join Date: Dec 2010
Posts: 60
Rep Power: 7 
Quote:
Quote:
Quote:
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 

#12  
Member
Join Date: Dec 2009
Location: China
Posts: 79
Rep Power: 8 
Quote:
By the way, what do you think about the mesh requirement of LES? 

June 3, 2013, 15:03 

#13  
Senior Member
OJ
Join Date: Apr 2012
Location: United Kindom
Posts: 475
Rep Power: 11 
Quote:
Quote:
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 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
TVD scheme in unstructured finite volume discretization  abcdef123  Main CFD Forum  2  January 16, 2013 01:26 
Accuracy problem of HO schemes on unstructured mesh, HO scheme gives 1st order result  gemini  Main CFD Forum  12  December 27, 2011 22:01 
Time discretization scheme  HaKu  Main CFD Forum  1  June 12, 2011 02:06 
Discretization scheme for Convection Terms  Mohammad Kazemi  CFX  16  December 7, 2004 23:38 
MARS discretization scheme  raymond  CDadapco  3  February 1, 2002 06:33 