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May 19, 2010, 05:05 
Explanation bounding k and bounding epsilon

#1 
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Claus Meister
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Hey Foamers,
I have no idea what is bounding k and bounding epsilon supposed to mean. Can anybody explaing, please? Druing my simulation I am getting such messages with even negative values. Cheers in advance 

May 19, 2010, 06:06 

#2 
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Moritz Wied
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Hi Claus,
as i understood it, bounding means, that the actual calculated values are limited not to get too huge. bounding then should mean that the calculated value was the bounded amount higher than it is being used for the next iteration/timestep. hope this is right, if not please anyone correct me . bye, mo 

May 20, 2010, 02:21 

#3  
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Mark Olesen
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Quote:
Having really large values for k/epsilon may not be great, but avoiding dividebyzero is the real issue: Code:
// source in k or epsilon equations have this: rho_*epsilon_/k_ // mut calculation has this: rho_*Cmu_*sqr(k_)/epsilon_ The source code is found under src/finiteVolume/cfdTools/general/bound/bound.C 

May 21, 2010, 01:33 

#4 
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Claus Meister
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Thanks for your replies!
When the minimum bound value for k is e.g. 136 do I have to worry about something? I think the value should never fall below 0. Cheers 

May 21, 2010, 02:27 

#5 
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Mark Olesen
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The k/epsilon are bounded with SMALL (1e15 for double) so that will stop the dividebyzero issues. If your problem always produces negative values throughout the solution, it could indicate that something else needs attention  eg, system needs more relaxation or something.


May 21, 2010, 03:17 

#6 
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Claus Meister
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It was obvious to me that something is wrong! Okay, I used Gauss linear for all convection terms, because I wanted to keep accuracy as best as possible. I changed to limitedLinear(V) 1; know the negative min values increases toward to zero and, eventually, they vanished.
Cheers 

May 21, 2010, 03:33 

#7 
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Claus Meister
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Now, there is no occurrence of bounding k or epsilon anymore. However, it crossed my mind: can I use a better scheme instead of limitedLinear 1 for the approximation of epsilon and k, respectively?


May 22, 2010, 03:46 

#8 
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To explain your problem, we need to look at the boundness of the differencing scheme of the convection term. Upwind differencing scheme usually gives bounded results, but introduces a numerical diffusion which is not good for the accuracy. However, the secondorder central differencing scheme, i.e. Gauss linear, does not assure the boundness of the result. That is why you got a unbounded result in your earlier calculation.
The limitedLinear scheme you are using now is a blended one of the upwind and central differencing, I guess. (I am now considering the same problem to increase the accuracy of the calculation) So you can obtain a bounded result with it. The limitedLinear scheme may have a accuracy between first and second order??? I am looking forward to a discussion about this. Thanks for reading.
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Jinbiao 

May 24, 2010, 08:10 

#9 
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Claus Meister
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Hallo JinBiao!
Actually, I am not really sure about the usage of lmitedLinear 1; I spotted it in a tutorial. Basically, I tend to use schemes which are both of high order and bounded. However, as we both know there a no higher order bounded schemes, therefore, I would like to know which schemes gives the best results? Which e.g. TVD scheme would you prefere? I simulation twophase flows (waterair) through bendend pipe with a maximal velocity of 9.6 m/s. Additionally, in this pipes there holes where the water can flow out. Cheers in advance 

May 24, 2010, 21:57 

#10 
Member

Hi there,
I was also struggling to find out a scheme for the convection term. But now I think no method will solve all the problems. One solution will be refining your mesh at the location where you are expecting a peak value or a large gradient. It improves the boundness of the result, I think. The reason is, from my understanding, that the face value is more inclined to fall into the range between the value of the two neighbor points, if your mesh is refined. The scheme I am now using is SFCD and QUICK. I am not sure it is good for you. I have no experience with two phase flow simulation, so I cannot provide more information. Good luck.
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May 25, 2010, 02:51 

#11  
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Alberto Passalacqua
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Hello,
just a quick clarification. The limitedLinear scheme is the linear scheme with a limiter (if I remember correctly, it uses Sweby's limiter). It's not a blended version of the "linear" scheme and the "upwind" scheme, which would be "linearUpwind" in OpenFOAM. So limitedLinear is a TVD scheme (take a look at ../OpenFOAM1.6.x/src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes/limitedLinear), as also written in the user's guide. Quote:
For your application, you can either use the default works fine. You can try linearUpwind / linearUpwindV with the cellLimited option to have what many would call "second order upwind". Best, 

May 25, 2010, 02:55 

#12  
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Alberto Passalacqua
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Quote:
In my experience, QUICK doesn't offer any particular advantage (it's either second or first order on general grids, more diffusive than limitedLinear). Best, 

May 25, 2010, 03:39 

#13 
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In my case, QUICK converges better than TVD and NVA schemes. I am not quite sure about the reason. One of the explanations can be NVA and TVD has artificial switch which cause nonsmooth change of the coefficient matrix.
This can be particular in my case because I am simulating a backwardfacing step flow. There is large gradient at the edge of the step. Regards,
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Jinbiao 

May 25, 2010, 11:38 

#14 
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Alberto Passalacqua
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Interesting, because QUICK is known to have some trouble due to the possibility of having coefficients that change sign.
Did you try to estimate the influence of the numerical diffusion (QUICK is quite diffusive for what I know). This could explain the improved stability. 

May 25, 2010, 21:50 

#15 
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Hi Alberto,
Up to now, I have not analysed the numerical diffusion because it is difficult to find out a scheme to compare with. I think an ideal counterpart for comparison should be CDS, with which it is hard to obtain the bounded result. Also, I think TVD schemes, such as limitedLinear, have a better boundness because they introduce numerical diffusion. So it does not make sense to compare with them. It is also good to know there are some defects in QUICK. I will be more careful when I am using it. I also tried to find some comments on QUICK in the textbooks. Mainly, people think QUICK has about the same accuracy with CDS because the integration on the surface is usually secondorder in accuracy. I have another question about TVD schemes. Does the prefix "limited" mean that Sweby's limit function is applied to the scheme indicated by the second half of the name. For example, limitedLinear is a limited CDS scheme? Thanks for your discussion. Regards,
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Jinbiao 

May 26, 2010, 00:11 

#16  
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Alberto Passalacqua
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Quote:
To compare with CDS you don't have to run a huge practical case. Just compare in a realistic but small test case, where you don't have problems to use the appropriate discretization. After all it's not so hard to obtain a solution with CDS, being it one of the schemes used in LES due to its central nature (=> no dissipation) Quote:
QUICK might have the same formal order of accuracy (not always), but CDS have zero dissipation error (only the dispersion error is present in central schemes). Quote:
About the implementation of the limiter, OF allows the implementation of generic limiter functions, so take a look at ~/OpenFOAM/OpenFOAM1.6.x/src/finiteVolume/interpolation/surfaceInterpolation/limitedSchemes where you find the implementation of the abstract limited class and of the schemes. Best, 

May 26, 2010, 02:53 

#17 
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Claus Meister
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Hallo alberto!
Actually, I really like to use central differencing, but I am facing ocillations when I am using it. Therefore, I used linearLimited(V) 1 successfully, however, there sill a question: Is there yet a better scheme? Since limiters switches between UD and CD, I would like to use a limiter which switches in that moment to UD when it is really necessary. As far as I understand, the limiter switches depending on "r" and I think that limiters switches often to early. Is this correct? Cheers Claus 

May 26, 2010, 03:00 

#18 
Member

Thanks a lot for your patient explanation.
I am sorry but I really got confused about the words, diffusion, dispersion and dissipation. I have not read the code quite in detail. It just come out in my mind that the limit function introduces nonlinearity which can be the reason for poor convergence of TVD scheme. How do you think? But I still think the limitedLinear scheme falls into the blend of upwind and linear. Please see Hrvoje's doctor thesis page 98 eq.(3.66). The limit function performs as the blend factor. However, the blend factor goes larger than one, according to Sweby's constraint. Thanks.
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Jinbiao 

May 26, 2010, 09:59 

#19  
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Alberto Passalacqua
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Quote:
Quote:
Best, 

May 26, 2010, 13:02 

#20 
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Moritz Wied
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Hi Foamers,
as i also try to tune the solvers in the fvSchemes at the moment, i'd be great if you might answer if i the system works like this: in the divSchemes dictionary i defined like that: div(phi,U) Gauss upwind Gauss limitedLinear 0.7; is it right that is is defined like that: Gauss <interpolationScheme> Gauss upwind <gradScheme> Gauss upwind Gauss <interpolationScheme> Gauss upwind Gauss limitedLinear 0.5 <interpolationScheme> > upwind <gradScheme> <gradScheme> > Gauss <interpolationScheme> <interpolationScheme> > limitedLinear 0.5 Another question: how can scalars be strictly bounded? As i understood the manual, the specific interpolation schemes are not defined in the interpolationSchemes dictionary, but in the divSchemes dictionary. I dont understand how to limit scalar values, when divergence is calculated. Would it maybe work like hits? div(phi,k) Gauss limitedLinear Gauss linear 1e10 30; All the best, Moritz 

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