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Old   May 27, 2013, 23:29
Default Accuracy of discretization scheme
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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 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.
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Old   May 28, 2013, 03:44
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Quote:
Originally Posted by ringtail View Post
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!!!
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Old   May 28, 2013, 04:37
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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
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Old   May 29, 2013, 20:14
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Quote:
Originally Posted by MAC88 View Post
Follow this link.
Hope you find some solution.
http://www.sharcnet.ca/Software/Flue...th/node366.htm

Best of luck!!!
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?
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Old   May 29, 2013, 20:17
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Quote:
Originally Posted by sbaffini View Post
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
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~~
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Old   May 30, 2013, 03:39
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Quote:
Originally Posted by ringtail View Post
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?
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.
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Old   May 30, 2013, 04:02
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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
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Old   May 30, 2013, 04:51
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Quote:
Originally Posted by JimKnopf View Post
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!
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Old   May 30, 2013, 06:00
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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
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Old   May 30, 2013, 21:47
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Quote:
Originally Posted by oj.bulmer View Post
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.
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Old   June 1, 2013, 08:04
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Quote:
Originally Posted by ringtail View Post

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?
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

Quote:
Originally Posted by ringtail View Post
Second, both cases have achieved a great convergence. The residuals
were all below 1e-6, and the Cd stayed still.
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.

Quote:
Originally Posted by ringtail View Post
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 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
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Old   June 2, 2013, 20:46
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Quote:
Originally Posted by JimKnopf View Post
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?
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Old   June 3, 2013, 15:03
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Quote:
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.
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.

Quote:
By the way, what do you think about the mesh requirement of LES?
For wall bounded flows: \Delta x^+\approx 100, \Delta y^+ \approx 1, \Delta z^+ \approx 20

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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