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Error when calculating the second derivative using the derivative function d2dy2

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Old   July 8, 2018, 14:11
Question Error when calculating the second derivative using the derivative function d2dy2
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mona Li
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Hello everyone,

Recently, I have used tecplot 360 EX 2017 R2 ( Tecplot 360 EX 2017 R2, Version 2017.2.0.79771 (Apr 25 2017) OS X 64-bit) to post process my incompressible flow CFX simulation result which was exported as .cgns file. However, when I used the intrinsic derivative function d2dy2 to calculate the second derivative of VelocityX, I found that the results were seriously unreasonable and incorrect, and there were significant differences between the results under different settings.

The simulation domain of the processed case is shown as the figure above, which was divided by full hexahedron unstructured mesh. For the mesh has only one layer in the spanwise direction, the simulation result is quasi-2D. Now, I want to get the second partial derivative of Velocity X (i.e, streamwise velocity) with respect to coordinate Y (i.e, wall normal coordinate). To solve this, the first method I have tried is :
[1]change the frame to 2D Cartesian and show only the symmetry1 boundary (i.e, the boundary normal to the Z-axis ,with a contour on it in the figure above );
[2]then go to the alter-specify equations to enter the equation: {d2udy2}=d2dy2({VelocityX}) and computed it among all the existing zones;
[3]then extract a wall normal line which sits in the boundary layer at x=0.3 precisely and checked the calculated d2udy2 on it, but the result was seriously unreasonable! Like the figure1 shows below,

the green line is the first partial derivative of Velocity X, i.e. dudy, and the blue line is the d2udy2. It is obvious that as y grows, the decreasing of dudy must mean the negative value of d2udy2. But the results shown above does not satisfy the truth!
[4]for further check, I have also calculated the second partial derivative of Velocity X using another method, which is:
{dudy}=ddy({VelocityX}) then {d2u_dy2}=ddy({dudy})
The results of this method are also shown in the above figure 1 by the black line, which, in contrast, seems reasonable and satisfies the above truth!

Although the two method will correspond to different numerical scheme, I think they would be close to each other for they are both the numerical approximation of the second partial derivative of Velocity X. So I cannot understand the difference here and the error in using d2dy2 to calculate!

Further more, I also check this function under different settings, which are:
[1]the same case as above, maintain frame as 3D Cartesian, and calculate the {d2udy2}=d2dy2({VelocityX}), which results are shown in the figure2 below,

We can see the result is also wrong. But what more surprised me is that the result here is totally different with the results shown in figure1, which can be found in the probed information which is from the same point x=0.3 y=0.01!!!
[2]then I also test the setting that with the same case, 2D Cartesian frame, but with the line x=0.3 mentioned above be extracted into a new zone before calculating the {d2udy2}=d2dy2({VelocityX}), the results shown in the figure3 below shows that in this setting:

<1>the {d2udy2} one the line is equal to the {d2u_dy2}=ddy({dudy})!
<2>the {d2udy2} in the symmetry1 surface is still wrong and same as the first setting whose results are shown in the figure1!

To sum up, the above results seems to show that while the result calculated by ddy seems independent with these different settings, the result calculated by the intrinsic derivative function d2dy2 can be totally different under 2D or 3D Cartisian frame and also zones of different dimension (line or surface). But in my opinion, they would at least be close to each other in theory.

I don't know if there is something wrong with my comprehension and setting for the function d2dy2 here in tecplot, or some other reasons?

Can anyone please offer some help?

Thanks
mona
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cfx cgns file, frame dimension, second derivative, tecplot360, unstructed mesh

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