[Paraview] Calculation of Lambda2 using ParaView...

[Stefan Melber]

Hi Andy,

unfortunately my comparison values (correct lambda2) does not have an 
results in between to compare with. Regarding the gradients i am sure 
they are ok. For this dataset i calculated other stuff based on the 
gradients and thats ok. Maybe the error is in the syntax or the usage of 
the eigenvalues-function - will check there ...

     Stefan
> Hi,
>
> Maybe compute each portion manually and check that against the correct 
> values. Also, verifying the gradient calculation is correct is another 
> thing to look at. If the grid isn't specified properly then the 
> gradient operation will likely be wrong.
>
> On Fri, Jun 9, 2017 at 8:46 AM, Stefan Melber <Stefan.Melber at dlr.de 
> <mailto:Stefan.Melber at dlr.de>> wrote:
>
>     Hi,
>
>
>     for vortex-detection i (tried) to calculate the lambda2-criterion
>     (see e.g. https://en.wikipedia.org/wiki/Lambda2_method
>     <https://en.wikipedia.org/wiki/Lambda2_method>) with ParaView. The
>     way of calculation is based on this link
>     http://www.iesensor.com/blog/2016/01/24/using-paraview-to-visualise-vorticity-lambda2-vorticity-q-criterion/
>     <http://www.iesensor.com/blog/2016/01/24/using-paraview-to-visualise-vorticity-lambda2-vorticity-q-criterion/>.
>
>     However - the results are a kind of "wrong" - see attached
>     pictures: l2_solver.png shows what the flow solver writes out for
>     lambda2, l2_paraview.png shows what calculated with the algorithm
>     below.
>
>     Calculation of lambda2:
>
>     D = Gradients = [d_ij]
>     S = strain(Vel)
>
>     S     = (D + D^T)/2
>     Omega = (D - D^T)/2
>
>     lambda = EigenValue_of(S^2 + Omega^2)
>            = EigenValue_of(S^2 + (D - S)^2)
>            = EigenValue_of(S^2 + (Gradients - strain(vel))^2)
>
>     lambda2 = lambda_Y
>
>     and in ParaView this mean
>
>     o Vector of velocity with "Calculator".................: Vel =
>     iHat*x_velocity+jHat*y_velocity+kHat*z_velocity
>     o Gradients of Vel with "GradientOfUnstructuredDataSet": switch on
>     "compute gradient" and name it "Gradients"
>     o Calculate lambda with "PythonCalculator".............: lambda =
>     eigenvalue(strain(Vel)**2+(Gradients - strain(Vel))**2)
>     o Caluclate lambda2 with Calculator....................: lambda2 =
>     lambda_Y
>
>
>
>     Does anyone see the error why the calculation of lambda2 with
>     ParaView does not work?
>
>     Remark: i contacted the author of the blog above already - seems
>     he never tested his calculation and has no idea what is "wrong".
>
>         Stefan
>
>
>
>     ================================================================
>
>                          _/ *Dr. Stefan Melber-Wilkending*
>                        _/_/
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>
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