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Mohammad Kazemi November 12, 2004 18:14

Discretization scheme for Convection Terms
Hi Everybody,

I am currently researching on CFX code along with Fluent to come up with a decision which one we should buy for our company. I have heard that that CFX does not include 3rd order QUICK scheme for convection terms and the highest order discretization scheme for convection terms is 2nd order which can be lowered to 1.7 order (mixed first and 2nd order schemes) if the solution tends to diverge.

Does anybody have any problem with the spatial accuracy of the code?

Glenn Horrocks November 14, 2004 17:31

Re: Discretization scheme for Convection Terms
Hi Mohammad,

CFX does have the QUICK scheme, it is just not one of the main options so does not appear in the GUI or documentation. You cannot compare the accuracy of CFX and Fluent purely on the discretisation scheme. They have fundamentally different underlying numerical methods, so behave very differently. The best (and I would suggest only) way of comparing the codes is to trial them both and test some benchmark problems relevant to what you want to study.

Glenn Horrocks

Dan November 14, 2004 20:54

Re: Discretization scheme for Convection Terms
Really? I also didn't realise that there's QUICK scheme in CFX. Can you please tell us know how to apply it if CFX does have QUICK scheme? I don't understand why the option is not shown if it's there already. Kind of weird, you know....

Glenn Horrocks November 15, 2004 17:47

Re: Discretization scheme for Convection Terms

CFX has quite a bit of stuff in it which is not documented. Generally it is because they are only recommended for use by experts who don't need documentation, or because they are not recommended options.

I can't remember how to implement QUICK in CFX, but I think you just enter the following CCL in the solver block:


Glenn Horrocks

Mohammad Kazemi November 16, 2004 15:51

Re: Discretization scheme for Convection Terms

Thanks for your comments. I just went through the CFX theory manual and realized that their approach is a hybrid of finite volume and finite element schemes. There are some issues that I do not like in CFX code:

1) The Beta factor is controlled in the program automatically to guarantee convergence. It cost the simulation low accuracy though since everybody knows that first order convection scheme is stable but diffusive. I think that is why QUICK scheme is not listed in the code since it would most likely make the code diverge: CFX struggles having a 2nd order scheme for convection terms let alone to 3rd order scheme.

2) CFX does not have any dynamic LES model. Why are they so behind of the state of the art? Even CFD-ACE has dynamic LES model.

Glenn Horrocks November 16, 2004 17:30

Re: Discretization scheme for Convection Terms

Frankly, both points you have just made are rubbish.

1) The Quick differencing scheme is well known for being unstable. I think if you do back to back testing of any other code versus CFX you will find CFX far more stable due to its fully coupled solver.

2) You can implement a dynamic LES model in CFX using expressions. Also the "state of the art" model is not just the most complicated one, but is the most accurate at describing the flow in question. A large reason dynamic LES has not been more widely accepted is because the extra complexity often does not result in more accurate answers.

Glenn Horrocks

Mohammad Kazemi November 16, 2004 19:33

Re: Discretization scheme for Convection Terms

Rubbish!! Is this a new scientific term? Perhaps not!

The Quick is the best scheme I have ever experienced. I have been a code dveloper for several years so I do not buy your first comment AT ALL based on my own experience. However, you should notice that there are different versions of QUICK scheme and some of them are pretty unstable. I can give you more information about the one that I used and had some good experiences on.

Despite many people, I dislike using those turbulence models that have some coefficients to be adjusted. I have always tried to use either a DNS or a closely-universal tubulence model (such as dynamic LES). I think that is the way to go unless you just want to create some cute animation with no accuracy behind it.

Glenn Horrocks November 16, 2004 22:58

Re: Discretization scheme for Convection Terms

Rubbish? At least it got your attention :)

Different discretisation schemes are better for different purposes. Certainly the last time I tried Quick (back in my CFX4 days) it was not good for the compressible flows with shocks I was modelling at the time. For these types of flows the second order schemes with flux limiting (eg MUSCL) are much better, and the "High Resolution" scheme in CFX5 is similar. I have seen some good results with Quick for things like natural convection flows.

With regard to dynamic LES, which model are you referring to? All the dynamic LES models I have seen have got some tuning constants.

Glenn Horrocks

Bak_Flow November 19, 2004 16:27

Re: Discretization scheme for Convection Terms

I am just curious about the specific version of Quick that you prefer. What are the details and the reasons that make it more stable than the others?

I have been under the impression that Quick, having a downstream influence always has the same tendency for dispersive errors or wiggles as CDS?

Thanks for your input.


Mohammad Kazemi November 19, 2004 18:38

Re: Discretization scheme for Convection Terms

for more information on the QUICK scheme that I prefer please see:

Hayase, T., Humphrey, J. A. C. and Greif, R. (1992) "A Consistently Formulated QUICK Scheme for Fast and Stable Convergence Using Finite-Volume Iterative Calculation Procedures," Journal of Computational Physics 98 108-118.

I used it for DNS calculations. I guess that CD/BCD would work better with LES.

Thanks Mohammad

Phil November 23, 2004 10:05

Re: Discretization scheme for Convection Terms
With the high resolution scheme, the 'beta' blend factor is not chosen based on convergence (as you suggest) but rather on boundedness. Any formally second order scheme will give overshoots/undershoots at a discontinuity for a simple scalar equation. The 'beta' factor is chosen automatically to make the scheme bounded at these discontinuities. It gives a scheme which is 'as close to second order as possible while still being bounded.' See the paper by Barth and Jesperson (referred to in the doc) for more details.


Neale December 4, 2004 13:07

Re: Discretization scheme for Convection Terms
- Quick is in CFX-5 but it's the original Leonard version. That version is not TVD and for 99% of applications it does not offer any real benefit over the standard high res scheme.

- Our High Res scheme is TVD and fully second order as long as there are not discontinuities in the flow, then it locally drops to first order to keep the solution bounded. If you are familiar with QUICK then I would think you know about monotone advection schemes (TVD schemes). Beta is not varied to guarantee convergence (your conclusion is rubbish as Glenn points out), it is varied to guarantee a monotone solution, this is different.

- It could be that running QUICK on LES calculations in CFX-5 is better than high-res. With my minimal understanding of LES calculations I think it's been clearly shown that upwind schemes suck for LES. Hence, the default in CFX-5 for LES is central difference. Maybe it might be a good idea to allow QUICK for LES. Could be.

- CFX-5 does not have dynamic LES because 99% of people using CFX-5 do not perform LES calculations. It is simply not a "production" model yet becasue they are still too expensive compared to a RANS calculations. CFX-5 does have the halfway house of DES which I know some people are using. Maybe we can add it, I'm sure it's trivial effort, but there has to be a real need, which there is not yet.

Mohammad Kazemi December 4, 2004 15:41

Re: Discretization scheme for Convection Terms
CFX is in preparation to include Dynamic LES model in the 1st quarter of 2006. You think it is useless? Well, I guess you need to attend more in roadmap meeting of your company (CFX) so you would not throw a rubbish comment with your MINIMAL understanding. :)

That is quite surprising that you mentioned DES as the CFX representative also mentioned that when I asked him about Dynamic LES. I guess it should be a fooling strategy for your guys at CFX to trick some of your customers who have less understanding about turbulence modeling. Let me tell you what I told to the direct CFX associate so you guys would be able to collaborate thinking about it and come up with a a better trick. DES has the problem of recognizing the region where the RANS and LES LES models are being integrated. The blending functions, F1 and F2, still needs more research since they are unable to deliver satisfactory results for complex problems.

Regarding the boundedness I should say that I have seen that paper and as a former code developer, who had hands on work, I know what that exactly means. I guess you need to read some fundamental materials to understand what is the problem of some discretization schemes for convections terms. Just a clue, look up "negative diffusivity" and how people try to remove it by adding some "artificial diffusivity".

I am sorry that I use the word of "rubbish" in this technical comment, but I guess that is the language that CFX associates would prefer to use to hide their shortcomes. I guess I just spoke in your language so you do not need a translator.

Good Luck selling your product; I just lost me.

JCM December 6, 2004 01:28

Re: Discretization scheme for Convection Terms
Dear Dr. Kazemi,

It is very unfortunate that what started as a technical question has been led into a biased confrontation on who holds the holy grail of advection schemes. Throwing not constructive comments at each other does not lead to a fruitul exchange of ideas. If you want to make an informed decision for your company, gather as much information as possible, scrutinize it and make the best of it. If you already made your decision, and just want to rant about it please say so first, so some in the forum realize they may be wasting their time reading it and prepare accordingly..

You support the idea that your QUICK implementation in your work (or Dr. Humphrey's 20 years experience with it) is third order accurate in space, while the CFX implementation is second order (or different depending of the variant). Well, there are well established procedures for determining the "effective" truncation order of a given implementation. Such analysis may lead to conclude that the theoretical order is not always achieved for multiple reasons which may include:

1 - Use of non-uniform meshes with a large range of aspect ratios.

2 - Use of non-orthogonal meshes with high skew angles. This probably does not apply to your work since you use orthogonal structured meshes.

3 - High density ratio throughout the solution domain, ie. high speed flows with shock waves, variable properties, combusting flows, etc..

4 - Use of Rhie-Chow momemtum interpolation or similar variants for colocated finite volumes could deteriorate the truncation order. Older codes from Dr. Humphrey were on staggered meshes (typical of TEACH based codes), but I recall his group was moving to colocated meshes in the mid to late 1980's. Which one are you using?

Have you put your latest implementation through such tests to support your affirmations?, or are you supporting your comments on the theory (best minimal truncation error?) I recalled doing so in school for different numerical methods, not just advection schemes, and you would be surprised.. It is not just the theoretical, but the practical use of it.

If you are evaluating the CFX solver, I guess you have already tested it, did you not? What cases did you run? You also mentioned CFD-ACE, have you tried that one as well? How do they (CFX and CFD-ACE) compare on your tests? That is useful information.

Also, you are using 2nd order schemes for diffusion and transient terms in your work. As far as I recall, the global truncation error of the solution is determined by the largest truncation error of any of the approximated terms. Third order schemes using discretized values which already have a 2nd order error in it could lead to "not so general" conclusions.

I do not recall you doing any truncation order error analysis of your implementation in your DNS work for disk drives (perhaps I missed it). For example, the ASME Journal of Heat Transfer will require such study for numerical predictions, not only mesh size estimation.

During the late 1990's, there were some publications of 3D unsteady flow within rotating cylindrical enclosures from The University of Texas at Austin using spectral methods. I do not recall the title of the works at the moment, but authors were Hill, R. and Ball, K. Perhaps, Dr. Humphrey already knows about them and help you. Since spectral methods have a much high order of approximation than traditional finite volume methods, that could help you as a baseline for your truncation error analysis.

Please try keeping the discussion as technical and helpful as possible, so more people like Glenn, Phil, Dan and Neale contribute to it. Comments from the heart (everybody already know you are passionate about DNS) sometimes derail the conversation.. I personally doubt that cute animations have been able to support the research on RANS equations for more than 40 years across the globe. Every problem has its own priorities. You have yours..

Good luck,


Mohammad Kazemi December 6, 2004 15:39

Re: Discretization scheme for Convection Terms
Thanks for your polite reply. As you said everybody has his own priorities but i suggest you to share an important priority when somebody makes some inquiries in here: AVOID USING OFFENSIVE WORDS SUCH AS RUBBISH.

Offending people when you cannot address the inquires is not a healthy policy unless you don't mind losing more potential customers.

Neale December 7, 2004 23:33

Re: Discretization scheme for Convection Terms
Hello Mohammed.

1st quarter of 2006 is a long way off. I can assure you that plans are not made that far into the future.

A consultant may implement Dynamic LES for a development contract or research project but this does not mean that it will be a releasable production model anytime soon. If it is done as a contract by 2006, it will be the end of 2006 before it is released, so at least 2 years off which may as well be infinity because a lot can change in 2 years.

LES is a useful model as a research tool but it's not a useful engineering tool no matter what subgrid model one invokes. If it was a useful engineering tool then more clients would use it for that, but they simply don't. Very few clients are regularily using LES to design and analyse their products yet, that's the reality. Hence the timeframe for possibly implementing and releasing a Dynamic LES model.

For production models many clients use DES in the meantime because it's runtimes are more tractable. Yes, the blending functions are somewhat of a "cooking" process but so are all turbulence models, so really, does it matter?

I assume by "negative diffusivity" you probably mean advection schemes which attempt to add "antidiffision" where they can to get greater than first order accuracy while maintaining boundedness. The first of non-linear advection scheme that did this was Flux Corrected Transport, invented in by Jay Boris and David Book in 1972. PPM/MUSCL/TVD/High Res in CFX-5 etc.... all follow a similar approach with various degrees of the problem physics directly cast into the discretisation. I personally implemented PPM, MUSCL and FCT in my past life and they all do very similar things.

The word "rubbish" was chosen to point out the fact that one of your original statements, i.e. that CFX-5 varies beta to ensure a converged solution, was incorrect, that's all. It was not intended to be an insult.

Please feel free to continue to point out all of our shortcomings as I will gladly acknowledge them if what you point out is true and based in fact.

I have no problem if you don't use CFX-5. It's a free world, for the most part, after all.


Neale December 7, 2004 23:38

Re: Discretization scheme for Convection Terms
Hmm, you seem a bit sensitive about this word.

I always thought that rubbish was considered normal language.

Would you be offended if Glenn or myself had simply stated "You are incorrect because of ..." instead of "That is rubbish because ...", or would that still have offended you?

I will gladly address all of your enquiries, without using the word rubbish.

Hopefully my other post answers all of your questions.

Please let me know if anything is unclear.


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