# Problem with very high gradients

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November 27, 2012, 14:12
Problem with very high gradients
#1
Member

Join Date: Nov 2012
Posts: 57
Rep Power: 4
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
 microchannel2.jpg (41.2 KB, 25 views) microchannel.jpg (42.6 KB, 22 views)

 November 28, 2012, 17:23 #2 Senior Member     Ehsan Join Date: Oct 2012 Location: Iran Posts: 2,205 Rep Power: 17 hello Where did you write these codes?

 November 29, 2012, 18:05 #3 Member   Join Date: Nov 2012 Posts: 57 Rep Power: 4 the code is in the rhoPimpleFoam.C after the pimple loop or what do you mean exactly?

 February 13, 2013, 16:22 #4 Senior Member   Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 129 Rep Power: 8 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 ZMM

 February 15, 2013, 18:27 #5 Member   Join Date: Nov 2012 Posts: 57 Rep Power: 4 sadly not. for what do you need it?

 February 15, 2013, 18:40 #6 Senior Member   Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 129 Rep Power: 8 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 ? Best ZMM

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