Accuracy of discretization scheme
 

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 third-order 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.

Follow this link.
Hope you find some solution.
http://www.sharcnet.ca/Software/Flue...th/node366.htm

Best of luck!!!
:)

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

thanks for your reply.
I have read the introduction for schemes on User's Guide. and it says :

"The QUICK and third-order 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 second-order 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?

Hi, sbaffini.
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~~

As far as, I know QUICK scheme also work good in unsteady conditions.
So it varies from case to case.
QUICK scheme is also not good for unstructured meshing.

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

Hi all, thanks for the replies.
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 1e-6, 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!

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

Thanks~
The reference is fabulous.

That probably is the main point, that you don't have a steady state in your case. You are trying to simulate some kind of bluff body, don't you? Well in my opinion you should stick to the averaged result of a LES, if you did it in an apropiate way - the LES and the averaging

Well, 1e-6 I wouldn't call a great convergence, at least in Fluent. If you have a stable steady state and a mesh of good quality, then residuals might go down to 1e-12 to 1e-15. This can be the case for Fluent.

What I meant was, that the mesh has a influence of the interpolation, if it skewed or in some other way not the best quality. I'm quite sure that Fluent has some technique to handle bad cells, so if you have bad cells, you get slightly different results for every interpolation scheme.

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

Greetz
Jim

Hi Jim, thanks.
By the way, what do you think about the mesh requirement of LES?

Residual values are not the best way to judge the convergence. It is wise to use surface/point monitors of parameters of interest, along with volumetric imbalances.

For wall bounded flows:

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