Hello,
where can I find refer
Hello,
where can I find references for the limitedLinear scheme to cite in a paper? Thanks in advance, Alberto 
There is no printed reference
There is no printed reference but it is Henry's application of the Sweby limiter to central differencing.

Thanks Mattijs.
Alberto
Thanks Mattijs.
Alberto 
After looking into the code I
After looking into the code I found in limitedLinear.H:
... return max(min(twor, 1), 0); ... with "twor" beeing equal to 2*r for default setup, e.g. "div(phi,B) Gauss limitedLinear 1;". For me this limiter looks very similar to the minmod limiter instead of the factor 2: minmod: return max(min(r,1),0); The Sweby limiter reads max(0,max(min(beta*r,1),min(beta,r))). I wondering why this modified limiter is used because due to the factor 2 it lies on the opposite limit (lower left) compared to the minmod in the Sweby diagram. 
Hello everyone.
As a newcom
Hello everyone.
As a newcomer I have two concrete questions concerning two divschemes:  Gauss limitedLinearV 1 and  Gauss interfaceCompression. I suppose that the interfaceCompression scheme does some blending between UD and CD, based on the blending factor (limiter) calculated according to either quartic or quadratic formula. Is this true? Or where is the limiter for this scheme used? In limitedLinearV, I suppose that it is a kind of limited CD, but how is the scheme limited? Where is the limiter for this scheme used? Is there any written text about these two schemes, or can anyone shortly explain me how they work? Many thanks in advance, best regards. 

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I'm working with limitedLinear and I'm also trying to understand the limiter. Have you found any informations about it? Thank you. 
Hi to all,
I'm working with this limiter too and I would know if anybody found some information about it. Thank to all 
I think the twoByk_ term is just a calibrated term (i.e. a construct) that best suits what the limitedLinear scheme in OF is attempting to accomplish. I think it's to help place even more weight on higherorder differencing (in this case, central differencing vs upwind).
If you were to go through Jasak's thesis (pp. 9899) and go back to theory, one could see that this method is actually pretty effective in enforcing either central differencing or upwinding based on the userinput (k). One could actually show that, for a given ratio of successive gradients ("r"), inputting a low value of k (i.e. 0.1) would give more weight to central differencing, whereas a larger value (i.e. 0.8) places more emphasis on upwinding. I've also tried with beta values (1 < beta < 2) and the behavior is actually quite different. As such, I will have to conduct further studies. Also, just hypothetically speaking, I don't think there would be any difference between: Code:
max(min(twoByk_*r, 1), 0) Code:
max(0,min(twoByk_*r,1), min(r,twoByk_)) 
Are You Sure about this?

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Hello All,
I have some doubts with the representation of the following schemes in OpenFOAM. I asked this question here because it seems many of you are working on these. (1) Code:
default limitedLinear 1.0 phi; (2) Code:
default limitedVanLeer 2.0 3.0; :confused: 
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Thanks for any help :) 
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It is TVD for any of the value ranging from 0 to 1. But, the order of accuracy decrease as the k value decrease (i.e., less than 1). For k =1, it is most accurate. I hope it cleared your doubt.  Best Luck! 
Tushar,
Looking at Versteeg p. 168: Sweby (1984) has given necessary and sufficient conditions for a scheme to be TVD in terms of the r − ψ relationship: • If 0<r<1 the upper limit is ψ(r)=2r, so for TVD schemes ψ®≤2r • If r≥1 the upper limit is ψ(r)=2, so for TVD schemes ψ(r)≤2 but twor is greater 2 which wouldn't satisfy the first criteria. Can you give some reference for you're statement? Thanks Marvin Quote:

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Marvin,
Did you read it thoroughly before commenting? Anyways, If you reread the same page no. 168169 of the mentioned ebook it will clear your doubt. I have attached a file of the same book with marked lines of page no. 168, which clears explains the TVD region. Please find attached note with this comment.  Best Regards! 
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(compare http://www.openfoam.org/docs/user/fvSchemes.php) > For k = 1 it is most stable. For k = 0 it is most accurate. Sorry I didn't put that right earlier. Further do I still not see why limitedLinear is TVD. sourcecode: return max(min(twoByk_*r,1),0); (1) If I draw that function (1) for k = 0.5 that is definitely not in the shaded region marked in verteeg for k <1. It demands that twoByk_ < 2. https://www.dropbox.com/s/yvn97vvoak..._0383.JPG?dl=0 
Hi Marvin,
I might be wrong here, but I think that the way the limiter has been implemented allows the scheme to behave as a TVD. In fact, with k=1, your limiter will be ψ(r) = 2*r. (as long as 2*r < 1). Conversely, with k = 0 (which means == SMALL), your ψ(r) becomes somethingBIG*r. This is most likely >> 1 and 'the switch' will choose ψ(r) = 1 as limiter. When such thing occurs, you are using pure CD to interpolate phi values on the internal faces. Since I believe that the value r = (Phi_C  Phi_U)/(Phi_D  Phi_C) changes during the run, I expect the limiter ψ(r) to do the same. By choosing k = 1, one just increases the possibility to include in the interpolation process some UD diffusivity, I think. 
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