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July 8, 2010, 05:36 
fvc::reconstruct( ) algorithm

#1 
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Hi Foamers,
I am trying to figure out how the fvc::reconstruct( ) algorithm works. My first thought was: Sum up the facefluxes multiplied with the facenormal over a cell and divide it by the sum of the magnitude of the facevector components of every face of the cell. The algorithm in the "fvcReconstruct.C" file seems far more complex then my thought: inv(surfaceSum(sqr(mesh.Sf())/mesh.magSf())) & surfaceSum((mesh.Sf()/mesh.magSf())*ssf) The second line is what I expected, but the first line is a little mystery to me. Can anybody explain this to my, please? Rainer 

July 8, 2010, 10:31 

#2 
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David Gaden
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Just a guess... it looks like it might be nonorthogonal correction...?


July 9, 2010, 12:15 

#3 
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Kevin Maki
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Rainer, I agree with your description. The first line finds one over the square of the components of the area. The second line has the the components of the area in the numerator, so the result is just one over the area times the sum of what ever you are reconstructing. This is what you want for a faceareaweighted average.
There is another post by Henry which is relevant here: http://www.cfdonline.com/Forums/ope...integrate.html Kevin 

March 16, 2011, 13:27 

#4 
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SungEun Kim
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I am also puzzled by what fvc:reconstruct does. Has anyone here figured what it does? It seems it is not based on any mathematical identity (like Gauss theorem), but some sort of approximation.


January 16, 2012, 13:06 
fvc::reconstruct explaination

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Thibault Pringuey
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Hello,
I have had a look at the fvc::reconstruct method. Please find attached an attempt to explain it. Cheers, Thibault 

January 17, 2012, 05:00 

#6 
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Thibault, excellent! Thank you for you work! Currently I am working on improving my model introducing a reconstruction for them... So hope to find some advantage on using it, will post some general conclusions.
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August 27, 2014, 14:56 

#7 
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Charlie
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Hi makaveli_lcf,
Did you find any advantage using fvc::reconstruct ? In my experience, using fvc::reconstruct seems too dissipative? need to find out what cause the dissipation, maybe due to the faceweighted averaging ? Just curious, did you find anything similar? 

July 23, 2015, 00:41 

#8 
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Xavier Pivan
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Hi Cheng,
Did you figure out why renconstruct was too dissipative ? I'm trying to reproduce an experiment with settlingFOAM everything work except that my system dissipate too much and then the velocities are not strong enough. reconstruct might be a start. Thanks 

July 27, 2015, 00:11 

#9 
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Kyle Mooney
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There could be several sources of numerical dissipation. To start make sure you have achieved mesh convergence and using 2nd order discretization.


September 22, 2015, 06:37 

#10 
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Michael
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I think that fvc::reconstruct is dissipative because it is first order accurate.
It assumes Sum_f n_f ( S_f * u_p) = Sum_f n_f ( S_f * u_f) which is accurate up to irst order. I have another question: What is the difference between the method used to reconstruct the velocity at the cell center from the face center used in fvc::reconstruct and simply calculating it by Sum_f 1/S_f phi_f n_f ? 

October 27, 2015, 06:33 

#11 
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Michael
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I have to add that the fvc::reconstruct is second order accurate for orthogonal grids. It can be seen by a Taylorseries expansion of the face velocity, i.e., U_f = U_c + dU/dx_c delta x + ... and inserting it into the relation sum n_f (S_f * u_c) = sum n_f (S_f * u_f)


March 16, 2020, 05:39 

#12 
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Dongyue Li
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1. The fvc::reconstruct() function was used to smooth oscillation by combining usage of fvc::snGrad(). Typically you can write either 1) fvc::grad(p) or 2) fvc::reconstruct(fvc::snGrad(p)*mesh.magSf()). But the result is different. The first method uses a extended stencil whereas the second one employs a compact stencil. Thereafter the oscillation can be avoided by the second one (fvc::reconstruct method). Similar technique can be also found if you think why we discretize the laplacian term as fvc::laplacian() instead of div(grad()).
2. What it do is simply \sum U_p \cdot S_f = \sum phi, the reason you see there is because inv() function cannot handle velocity. 3. The order of it is influenced by the scheme of snGrad function. Therefore, orthogonal grids provide the best accuracy.
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March 30, 2020, 15:48 

#13 
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Tomislav Maric
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The fvc::reconstruct is only second order accurate, if the field that is reconstructed is regular enough to be approximated by Taylor series up to secondorder. For example, the velocity at the fluid interface is not regular enough, as it is only C^0 continuous at the fluid interface  it has a kink there  so Taylor series do not apply at the interface.
We checked fvc::reconstruct a bit in our latest paper on Level Set / Front Tracking, see section "3.4. Surface tension force reconstruction" in the linked PDF. The error estimate corresponds to the numerical error exactly for a smooth velocity field, and for the velocity field from the HadamardRybczynsky flow, which confirms the estimate. fvc::reconstruct is used in flows with variable density to reconstruct things like the force term resulting from the decomposition pressure into the dynamic and hydrostatic part, or the cellcentered surface tension force source term, cellcentered velocity at the end of the internal iteration, etc. All these fields are not C^2 continuous in multiphase flows. arXiv version of the paper is here OpenFOAM tests for generating convergence data are here. The data from the paper is here.
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April 3, 2020, 14:23 

#14 
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Santiago Marquez Damian
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Hello, we discuss the foundation of fvc::reconstruct and other reconstruction techniques here,
https://www.sciencedirect.com/scienc...21999118301931 please let me now if someone needs a copy. Regards!
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April 3, 2020, 14:29 

#15  
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Tomislav Maric
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Quote:
Thanks, I wasn't aware of this paper!
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April 3, 2020, 14:39 

#16 
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Santiago Marquez Damian
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You're welcome. Big fan of your papers and work.
State of the art concerning "spurious currents" in interFOAM Regards!
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April 3, 2020, 14:47 

#17 
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Tomislav Maric
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Thanks! Also thanks for the link! I've read your comments there. I agree, everything is interconnected: surface tension model, curvature calculation, pU coupling (reconstruction as a part of it), there is also the issue of hydrostatic/dynamic pressure decomposition for multiphase flows, as its flux has grad rho at the face center, that's bad for the reconstruction as well... in any case, it's not boring.
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April 17, 2021, 11:23 
fvc::reconstruct operation

#18 
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behnamCheraghi
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I think that the following link is very useful for understanding the fvc::reconstruct operation:
https://github.com/wyldckat/reconstr...tefields/wiki 

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