[davibarreira]

There is Dr Jasak's thesis, which is a must for people using OpenFOAM (just google it and you will find right away). And also Versteeg and Malalasekera book on CFD.

[janGaertner]

Hey,


I have seen in many posts, that limitedLinear uses the Sweby limiter function. This is not correct.



If you look at the code of the limitedLinear.H file you see:

     

scalar limiter
      (
         const scalar cdWeight,
         const scalar faceFlux,
         const typename LimiterFunc::phiType& phiP,
         const typename LimiterFunc::phiType& phiN,
         const typename LimiterFunc::gradPhiType& gradcP,
         const typename LimiterFunc::gradPhiType& gradcN,
         const vector& d
     ) const
     {
         scalar r = LimiterFunc::r
         (

             faceFlux, phiP, phiN, gradcP, gradcN, d
         );
         return max(min(twoByk_*r, 1), 0);
     }

I have plotted this function in the r-psi(r) plane, limitedLinear.png

[s.v]

Response to post #11 in this thread:

I am guessing the reason why "linear" and "limitedLinear 0" do not give identical results is because "limitedLinear 0" becomes upwind outside the Convection Boundedness Criterion (CBC) region on the NVD diagram -- see for example the discussion and figures around page 35 in my PhD thesis (https://drum.lib.umd.edu/handle/1903/21883).

Cheers ....

[bany]

Originally Posted by jurich

limitedLinear is used in fvSchemes as Gauss limitedLinear k

The value k you specify when activating the scheme is not the same as , as used in Jasak's thesis.

What you get from limitedLinear is , with r as defined in Jasak's thesis, and limited between 0 and 1.

See the discussion: http://www.cfd-online.com/Forums/ope...ar-scheme.html, and lines 76 and 95 of limitedLinear.H

So if you use k = 0, will be fixed at 1.0, and you get the higher order scheme everywhere, in this case central differencing.

If you use k = 1, you get a limiter of applied. This limiter is the edge of Sweby's TVD region; it is TVD conforming.

That's why the documentation describes it that way.

Thanks for this explanation for , where defined in Dr. Jasak's thesis. Now i have two questions :

(1) If phiD-phiC=0, r equals? Just like the case:in a initial field, the value of phi (a scalar field) is uniform.

(2) As we know, r is related to the successive grad of phi. And C, D and U are at the upwind, downwind and far-upwind cells. While for the cells whose faces are at boundary, how does the definition of U and how does (phiC-phiU) calculate?


Any reply is grateful!

[Tobi]

How do you examine the far-upwind cell in an unstructured FV mesh?

[bany]

Originally Posted by Tobi

How do you examine the far-upwind cell in an unstructured FV mesh?

We only consider the simple condition: a 1-D structured FV mesh.

[s.v]

Originally Posted by Tobi

How do you examine the far-upwind cell in an unstructured FV mesh?

Tobi -- Jasak et al. discuss this point in their gamma scheme paper (https://citeseerx.ist.psu.edu/viewdo...=rep1&type=pdf) -- see for example the text below equation 10 in the paper -- they work with gradients ....

This link might also be useful -- https://www.openfoam.com/documentati...e-nvd-tvd.html

[bany]

Originally Posted by s.v

Tobi -- Jasak et al. discuss this point in their gamma scheme paper (https://citeseerx.ist.psu.edu/viewdo...=rep1&type=pdf) -- see for example the text below equation 10 in the paper -- they work with gradients ....

This link might also be useful -- https://www.openfoam.com/documentati...e-nvd-tvd.html

Thanks for your reply. And when phiC=phiD, how to calculate r?

In my work: a 1D structured FV mesh, and the scalarField phi is uniform at the beginning. Thus phiC=phiD for initial time in every mesh.

When i output the matrix of convection term for the first timestep, i found the upper() and lower() of the matrix for convection term when using limitedLinear scheme is like that when using linear scheme. That means that when phiC=phiD, r=k/2. However, i failed to find the relative code in openfoam -- https://github.com/OpenFOAM/OpenFOAM...cheme/NVDTVD.H

[s.v]

Originally Posted by bany

Thanks for this explanation for , where defined in Dr. Jasak's thesis. Now i have two questions :

(1) If phiD-phiC=0, r equals? Just like the case:in a initial field, the value of phi (a scalar field) is uniform.

(2) As we know, r is related to the successive grad of phi. And C, D and U are at the upwind, downwind and far-upwind cells. While for the cells whose faces are at boundary, how does the definition of U and how does (phiC-phiU) calculate?


Any reply is grateful!

Bany it has been a while since I looked at OpenFOAM ....

But I think the answer to your first question is in this file most likely -- https://www.openfoam.com/documentati...8H_source.html

It looks like if phiD-phiC=0 (I think in the file above they call phiD as phiN and phiC as phiP) the following lines in the above file will come into play:

if (mag(gradcf) >= 1000*mag(gradf))
{
return 2*1000*sign(gradcf)*sign(gradf) - 1;
}

which means r will either become 1999 or -2001 if phiD-phiC=0 or phiN-phiP=0 depending upon the signs of the gradients ....

Regarding your second question -- see my response to Tobi above -- they work with gradients -- they don't explicitly use the far-upwind cell ....

Again I have been away from OpenFOAM for a while -- but most likely what I have said above should be OK ....

Also remember that the gamma and limitedLinear schemes are very similar -- the only difference is how they switch between upwind and linear schemes -- if we use the factor "k" equal to 1 then gamma scheme switches more smoothly compared to limitedLinear scheme (see for example figure 2.9 in my thesis -- download link given above in one of my other posts) -- if we use a smaller value of the factor "k" like 0.2 then both schemes become pretty much the same (see figure 2.10 in my thesis) .... also note that the gamma scheme is generally bugged in OpenFOAM (this is also briefly discussed in my thesis) -- so I plot the dbGamma scheme in figures 2.9 and 2.10 -- dbGamma basically means debugged gamma scheme -- thats the best name I could come up with for my thesis ....

[s.v]

Originally Posted by bany

Thanks for your reply. And when phiC=phiD, how to calculate r?

In my work: a 1D structured FV mesh, and the scalarField phi is uniform at the beginning. Thus phiC=phiD for initial time in every mesh.

When i output the matrix of convection term for the first timestep, i found the upper() and lower() of the matrix for convection term when using limitedLinear scheme is like that when using linear scheme. That means that when phiC=phiD, r=k/2. However, i failed to find the relative code in openfoam -- https://github.com/OpenFOAM/OpenFOAM...cheme/NVDTVD.H

Bany -- for limitedLinear to behave like linear scheme r does not need to be exactly = k/2 ....

https://github.com/OpenFOAM/OpenFOAM...imitedLinear.H

At the end of the above file we see:
return max(min(twoByk_*r, 1), 0);

so if r = 1999 like I mentioned in my other post -- the above line will return 1 -- and for a value of 1 -- limitedLinear will behave like linear I think .... the above line is returning \psi(r) in the TVD framework I think .... sorry I do not know how to use math in these posts yet ....

[bany]

Originally Posted by s.v

Bany it has been a while since I looked at OpenFOAM ....

But I think the answer to your first question is in this file most likely -- https://www.openfoam.com/documentati...8H_source.html

It looks like if phiD-phiC=0 (I think in the file above they call phiD as phiN and phiC as phiP) the following lines in the above file will come into play:

if (mag(gradcf) >= 1000*mag(gradf))
{
return 2*1000*sign(gradcf)*sign(gradf) - 1;
}

which means r will either become 1999 or -2001 if phiD-phiC=0 or phiN-phiP=0 depending upon the signs of the gradients ....

Regarding your second question -- see my response to Tobi above -- they work with gradients -- they don't explicitly use the far-upwind cell ....

Again I have been away from OpenFOAM for a while -- but most likely what I have said above should be OK ....

Also remember that the gamma and limitedLinear schemes are very similar -- the only difference is how they switch between upwind and linear schemes -- if we use the factor "k" equal to 1 then gamma scheme switches more smoothly compared to limitedLinear scheme (see for example figure 2.9 in my thesis -- download link given above in one of my other posts) -- if we use a smaller value of the factor "k" like 0.2 then both schemes become pretty much the same (see figure 2.10 in my thesis) .... also note that the gamma scheme is generally bugged in OpenFOAM (this is also briefly discussed in my thesis) -- so I plot the dbGamma scheme in figures 2.9 and 2.10 -- dbGamma basically means debugged gamma scheme -- thats the best name I could come up with for my thesis ....

Oh, what you said helped me a lot and your thesis is so clearly. Thank you very much.

For the second question, the gradients are used. For the cell near the boundary just like the cell C in figure. The gradient of phi for the cell C is calculated by following: grad(phiC)=(phiC-phib)/(XC-Xb), where phib is the value of phi on the boundary.

If something is wrong, please note that.

[bany]

Originally Posted by s.v

Bany -- for limitedLinear to behave like linear scheme r does not need to be exactly = k/2 ....

https://github.com/OpenFOAM/OpenFOAM...imitedLinear.H

At the end of the above file we see:
return max(min(twoByk_*r, 1), 0);

so if r = 1999 like I mentioned in my other post -- the above line will return 1 -- and for a value of 1 -- limitedLinear will behave like linear I think .... the above line is returning \psi(r) in the TVD framework I think .... sorry I do not know how to use math in these posts yet ....

Yeah, you are right. If r >= k/2, limitedLinear will equal to linear. Thanks again.

For the math scheme, you can quote any posts included math scheme and you will see the original math code. Just like: "[ math]......[ /math]" (of course, there is no space in [].). And is "[math ]\psi[/math ]" in math scheme.