fvc::reconstruct( ) algorithm
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 
Just a guess... it looks like it might be nonorthogonal correction...?

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 
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.

fvc::reconstruct explaination
1 Attachment(s)
Hello,
I have had a look at the fvc::reconstruct method. Please find attached an attempt to explain it. Cheers, Thibault 
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.

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? Quote:

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

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 ? 
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)

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