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Why are hex meshes better than tet?

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Old   May 14, 2009, 09:54
Default Why are hex meshes better than tet?
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Philip Cardiff
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Hi,


I have been looking around a bit for a while and I can't seem to find why hex meshes are better than tet meshes, in finite volumes.

I was able to find papers for finite element, but not finite volume.

Can anybody point me in the right direction to where I might read up on this, or even briefly explain why?


Best Regards,

Philip
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Old   May 15, 2009, 05:26
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Wolfgang Heydlauff
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hi bigphil,

hex mesh are usually structured, so the cell-koordinates can easily be transformed into the calculation matrx (i,j,....).
the tet-meshes usually are unstructured. that's why there is the need for a transformation matrx. while calculation the cpu has to read out the calculation matrx for each timestep.so calculation time is longer.

furthermore a tetraeder has sharper angles than an hexaeder. in FVM the flux is calculated scalar, so sharp angles should be avoided.
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Old   May 15, 2009, 05:47
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Philip Cardiff
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Wolfgang,

Thanks very much for enlightening me.

So in general, hex are more accurate and take less time.

Best Regards,
Philip
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Old   May 15, 2009, 14:24
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Gijsbert Wierink
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That's right. Also, a tet mesh can have very skewed cells, especially when your geometry contains different shapes (e.g. a cube in a relatively small cylinder).
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Old   May 18, 2009, 09:01
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Gijsbert,

Thanks for the reply.
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Old   May 18, 2009, 11:19
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Philip Cardiff
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I have one more question:

How does the cell shape affect convergence of the solution?

I have found that if I use quite skewed cells, then my case will not converge.
Is this a general rule or how does the cell shape affect convergence?

Thanks,
Philip
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Old   May 18, 2009, 14:03
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Sebastian Gatzka
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Skewed elements are sometimes "bad" because the fluxed over their boundaries are calculated wrong and have to be treated with "corrected" schemes.

I can give you some literature reference about that, but I have to look it up.
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Old   May 18, 2009, 14:13
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Philip Cardiff
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Hi Sega,

I would love if you could give me some literature reference, that would be great!

Thanks you.

Philip

Also, does all this apply equally to stress analysis as it does to fluid dynamics?
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Old   May 18, 2009, 14:30
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Sebastian Gatzka
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Hi.

Have a look at this picture


It may illustrate the basic problem when dealing with skewed elements (so called non-othogonal grids).
Basically when interpolating from the cell centers to the face the midpoint of the face is not matched with the connecting line between the two cell centers thus creating a erroneous flux.

You can deal with it by using corrected schemes (first of all for snGrad!).
The "strength" of the correction can by controlled by the entry behind nOrthogonalCorrectors. (There has been a discussion about this entry before.)

The above picture is from:
M. Schäfer. Computational Engineering. Springer 2008. (Chapter 4.5).
And there are some lines at
Ferziger. Computational Methods for Fluid Dynamics. Springer 2002 (Chapter 8.6.2 I think).

Hope this helps. Have a nice day.
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Old   May 19, 2009, 05:45
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Sega,

Thanks you very much, this really helps.

I will have a look through Schafer and Ferziger, and I will also have a look around the forum.

Kind Regards,
Philip
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