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Problem with very high gradients

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Old   November 27, 2012, 14:12
Default Problem with very high gradients
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Hi Foamers,


i'm trying to implent a new boundary condition for which i need the second derivative of U in normal direction. (slip velocity)

In order to get a second order derivative (which isn't laplacian) i'll do:

Code:
    volScalarField Ux(U.component(0));
    dU=fvc::grad(Ux);//VolVectorField
    partial2UT=fvc::grad(dU);//VoltensorField
in partial2UT only components 0,4,8 are of interest i store these values in another tensorfield and repeat it for Uy and Uz so that i finally get.

| Ux,xx Uy,xx Uz,xx |
d2U=| Ux,yy Uy,yy Uz,yy |
| Ux,xx Uy,xx Uz,zz |

This works great but only to a certain dimension of the mesh. Attached to this post there are 2 cases and a modified rhoPimpleFoam solver.

the first case "microKanal2"(Kanal:channel in german) has a height of 1.68e-3 meters. The velocity field result in a parabola with an increasing maximum for higher x values. Therefore the first derivative dU shows in y direction a linear function. The tensor compoent(3) Ux,yy should be a a constant value for a cross section of the channel, but changing with the position of x (see picture).

the second case "microKanal" has a height of 1.68e-4 meters. For component 3 of the tensor there are following values (see attached picture)

The field isn't smooth at all it suddenly jumps to another value. A possible reason for that could be that double isn't accurate enough.

Does anyone know what the problem is and how it can be solved?

Best regards

Henning

http://dl.dropbox.com/u/9273087/microKanal2.tar.gz
http://dl.dropbox.com/u/9273087/microKanal.tar.gz
http://dl.dropbox.com/u/9273087/rhoPimpleFoam.tar.gz
Attached Images
File Type: jpg microchannel2.jpg (41.2 KB, 25 views)
File Type: jpg microchannel.jpg (42.6 KB, 22 views)
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Old   November 28, 2012, 17:23
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hello
Where did you write these codes?
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Old   November 29, 2012, 18:05
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the code is in the rhoPimpleFoam.C after the pimple loop

or what do you mean exactly?
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Old   February 13, 2013, 16:22
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Hello Henning
I am facing the same problem.
I need to calculate second derivative e.g for field F i need F_xx, F_yy.
I did it the same way as you.
gradF = fvc::grad(F) // vector of first derivatives
gradgradF = fvc::grad(gradF) // tensor of second derivatives

as far as gradF is fine/smooth, gradgradF is not anymore ...

Were you able to solve this problem ?

Best
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Old   February 15, 2013, 18:27
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sadly not.

for what do you need it?
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Old   February 15, 2013, 18:40
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Dear Henning,
please see my post located at:
how to calculate mixed derivative

where I am writing about other way of dealing with second order mixed derivative.
What do you think about that ?

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