# 4th order central scheme

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 July 30, 2010, 10:39 4th order central scheme #1 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Hi, I was wondering if there are any fourth order centeral differencng schemes in OpenFOAM. Sincerely, Maani

 July 31, 2010, 07:24 4th order central scheme #2 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 8 Hi Mani How are you? I think there is not. Good luck Best regards Ata

 July 31, 2010, 07:41 #3 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Hi dear Ata, Thanks for the reply. I appreciate your time. If there are not, then what about the "Cubic" Scheme? In page U-112 it says "Fourth order, unbounded". Also I wanted to know if linear is second order or 1st order. Again at U-112. I am running LES simulations and I need higher order central-differencing schemes (upwind/TVD/NVD are too dissipative) for div, grad and laplacian terms. Bests Maani

 August 1, 2010, 01:41 #4 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 I have a serious problem! Does anybody know what are the best high-order discretization schemes for LES? I know that QUICK is too dissipative! Sincerely, Mani Mahdinia

 August 1, 2010, 02:37 4th order central scheme #5 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 8 Hi Mani Are you sure in U-112? There is fourth order scheme for surface normal gradient, are you mean it? Best regards Ata

 August 1, 2010, 03:27 U-pages #6 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Hi, Yes. But I meant: OF 1.5 User guide p 112 which is equal to: OF 1.6 User guide p 116 which is equal to: OF 1.7 User guide p 116. Here it says: linear = second order, unbounded cubicCorrected=fourth order unbounded Sincerely, Maani

 August 1, 2010, 08:11 I have 1.6 #7 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 8 Hi Excuse me I have 1.6 Best regards Ata

 August 1, 2010, 08:53 My mistake #8 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Hi ata, I know it was my mistake. Sorry. Do you think they are 2nd and 4th order for all the terms like grad/div/lap? Sincerely, Maani

 August 1, 2010, 09:10 4th order central scheme #9 Senior Member     ata kamyabi Join Date: Aug 2009 Location: Kerman Posts: 322 Rep Power: 8 Hi Mani Your welcome, no problem. It seems replying via forum is not fast and very easy for me. Are you at Sharif University of Technology in Department of Mechanical Engineering? If it is true or you are at Tehran we can have easier conversation. You can send an Email to me and I'll send you my phone number. However I think that it is fourth order only for normal gradient at faces. Best regards Good luck Ata

 August 1, 2010, 13:50 #10 Senior Member   Alberto Passalacqua Join Date: Mar 2009 Location: Ames, Iowa, United States Posts: 1,894 Rep Power: 26 Hello, cubic and cubicCorrected are fourth order central schemes. For gradients, there is the "fourth" scheme. Best, sh.d likes this. __________________ Alberto Passalacqua GeekoCFD - A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as live DVD/USB, hard drive image and virtual image. OpenQBMM - An open-source implementation of quadrature-based moment methods

 August 1, 2010, 14:12 #11 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Thanks alberto, I have a question. Is it odd that I get better results with the QUICK scheme (which as you know, is too dissipative) than the cubic Scheme in LES? I have to mention that my grid is relatively, coarse. Sincerely, Maani

August 1, 2010, 14:43
#12
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Alberto Passalacqua
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Quote:
 Originally Posted by mmahdinia Thanks alberto, I have a question. Is it odd that I get better results with the QUICK scheme (which as you know, is too dissipative) than the cubic Scheme in LES? I have to mention that my grid is relatively, coarse.
Two questions:

- What do you mean with "better results"? Your results compare better with experiments, or there are unphysical results with cubic?

- Is your grid satisfying the stability criterion for central schemes?

A suggestion:

A finite volume scheme is second order whatever you do, so I would suggest you to use "linear" for convection, and leastSquares for gradients. They usually work fine.

Best,
__________________
Alberto Passalacqua

GeekoCFD - A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as live DVD/USB, hard drive image and virtual image.
OpenQBMM - An open-source implementation of quadrature-based moment methods

 August 1, 2010, 15:02 The problem #13 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Dear Alberto, Regarding your first inquiry: I am simulating a release of a higher density fluid (salt-water mixture) underneath a lower density ambient fluid (water). I am also solving the concentration equation along with NS. I use the dynamic Smagorinsky method is used for the simulation. The runs are in 3D. Here are two animations: http://mech.sharif.edu/~mahdinia/A1.htm http://mech.sharif.edu/~mahdinia/A2.htm I tried these: 1) Linear schemes for div/grad/lap/interpolation: The 3D instabilities at the interface of the two fluids are not created as they are supposed to. 2) Cubic schemes for div/grad/lap/interpolation: The 3D instabilities at the interface of the two fluids are created along with unphysical waves. 3) QUICK schemes for div/lap and Cubic for grad/interpolation: The 3D instabilities are created as they should be created physically, in the horizontal and span-wise directions. I can put some 3D pictures if required. I am not sure why the QUICK scheme gives the best results. Regarding your second inquiry: I don't know about the stability criterion for central schemes. But the the location of interest is in the middle of the domain and the grid there is nearly fine enough. Is the QUICK scheme always not appropriate for LES or it may be used for some of the flows in nature? Sincerely, Maani

August 1, 2010, 15:53
#14
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Alberto Passalacqua
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Quote:
 Originally Posted by mmahdinia I don't know about the stability criterion for central schemes. But the the location of interest is in the middle of the domain and the grid there is nearly fine enough.
The stability criterion for the linear scheme is that the cell Peclet (Reynolds, defined as DeltaX*|U|/nu; in 3D deltaX = cubeRoot(cellVolume) gives an indication) number is less than 2.

I would suggest an experiment to understand what is going on there, since you tried different combination of schemes.
1. Check if the grid satisfies the stability criterion.
2. Use leastSquares for gradients, and linear for all the rest, with a grid where the stability criterion is satisfied.
3. Use backward time scheme.
With this setup we obtained good results with LES in confined flows.

About QUICK, it has been quite widely used in the literature for LES (they essentially use a bounded version called B-QUICK). I would try to avoid upwinded schemes in LES, especially if you are interested in capturing details.

Best,
__________________
Alberto Passalacqua

GeekoCFD - A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as live DVD/USB, hard drive image and virtual image.
OpenQBMM - An open-source implementation of quadrature-based moment methods

 August 1, 2010, 16:38 Thanks #15 Member   Join Date: Mar 2009 Posts: 46 Rep Power: 8 Thanks, I'll do the above and see if the things get right. Sincerely, Maani

 August 1, 2010, 22:48 #16 Senior Member     Daniel WEI (老魏) Join Date: Mar 2009 Location: South Bend, IN, USA Posts: 688 Blog Entries: 9 Rep Power: 12 @Maani: I am afraid that in many occasions, the comparison conclusion based on coarse grid simulations would be quite misleading. I find a hard time to see how higher order (I mean higher than second) works for finite volume method. Since FV need estimation of a variety of items, so I think it would be pretty hard to get a order higher than 2nd. I am thinking is it possible to build finite difference scheme in openfoam framework, any ideas? __________________ ~ Daniel WEI ------------- NatHaz Modeling Laboratory Department of Civil & Environmental Engineering & Earth Sciences University of Notre Dame, USA Email || My Personal CFD Blog

August 1, 2010, 22:56
#17
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Alberto Passalacqua
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Quote:
 Originally Posted by lakeat I find a hard time to see how higher order (I mean higher than second) works for finite volume method. Since FV need estimation of a variety of items, so I think it would be pretty hard to get a order higher than 2nd.
You are correct. The formal accuracy is always second order, at best. However it is known that increasing the accuracy on some term can limit some side effect.

Quote:
 I am thinking is it possible to build finite difference scheme in openfoam framework, any ideas?
Why finite differences? Or better, why not discontinuous Galerkin methods or internal penalty methods, which are actually innovative and allow accuracy to be increased without losing the good properties gained with finite volumes? (I'm not saying it would be easy to do in OF )

Best,
__________________
Alberto Passalacqua

GeekoCFD - A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as live DVD/USB, hard drive image and virtual image.
OpenQBMM - An open-source implementation of quadrature-based moment methods

 August 1, 2010, 23:07 #18 Senior Member     Daniel WEI (老魏) Join Date: Mar 2009 Location: South Bend, IN, USA Posts: 688 Blog Entries: 9 Rep Power: 12 Hey, what! I feel I left behind in life. Any Good papers on that? Could you share some links? And why you think it's not easy to implement them? You know it would be great that openfoam could continue serving as not just for FV but for a many CFD C++ class Basis. For example: For finite volume, we build dir ./src/finiteVolume For finite area, we build dir ./src/finiteArea (as in extend fork) For discontinuous Galerkin methods, we build dir ./src/discontinuousGalerin .... __________________ ~ Daniel WEI ------------- NatHaz Modeling Laboratory Department of Civil & Environmental Engineering & Earth Sciences University of Notre Dame, USA Email || My Personal CFD Blog

 August 1, 2010, 23:11 #19 Senior Member     Daniel WEI (老魏) Join Date: Mar 2009 Location: South Bend, IN, USA Posts: 688 Blog Entries: 9 Rep Power: 12 ***************** __________________ ~ Daniel WEI ------------- NatHaz Modeling Laboratory Department of Civil & Environmental Engineering & Earth Sciences University of Notre Dame, USA Email || My Personal CFD Blog Last edited by lakeat; August 2, 2010 at 14:04.

August 1, 2010, 23:23
#20
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Daniel WEI (老魏)
Join Date: Mar 2009
Location: South Bend, IN, USA
Posts: 688
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Rep Power: 12
Quote:
 Originally Posted by alberto The stability criterion for the linear scheme is that the cell Peclet (Reynolds, defined as DeltaX*|U|/nu; in 3D deltaX = cubeRoot(cellVolume) gives an indication) number is less than 2. I would suggest an experiment to understand what is going on there, since you tried different combination of schemes. Check if the grid satisfies the stability criterion. Use leastSquares for gradients, and linear for all the rest, with a grid where the stability criterion is satisfied. Use backward time scheme. With this setup we obtained good results with LES in confined flows. About QUICK, it has been quite widely used in the literature for LES (they essentially use a bounded version called B-QUICK). I would try to avoid upwinded schemes in LES, especially if you are interested in capturing details. Best,

Concerning the Schemes, I am also very interested. I guess the openfoam team must have done a lot of works on testing the different schemes.

So,
1. You mean
Code:
```gradSchemes
{
default        leastSquares;
grad(p)         leastSquares;
grad(U)        leastSquares;
}```
but what about "extendedLeastSquaresGrad" (see in the dir), would it better than LeastSquares?

2. Will "boundedBackward" be better than backward ddt?

I know there is not formal documentation on these schemes items for openfoam, but do you any information on where we can find papers showing the foam-techniques progress in detail other than (http://powerlab.fsb.hr/ped/kturbo/OpenFOAM/)?

Thanks and good night!
__________________
~
Daniel WEI
-------------
NatHaz Modeling Laboratory
Department of Civil & Environmental Engineering & Earth Sciences
University of Notre Dame, USA
Email || My Personal CFD Blog

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