# Why are hex meshes better than tet?

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 May 14, 2009, 09:54 Why are hex meshes better than tet? #1 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 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

 May 15, 2009, 05:26 #2 Senior Member   Wolfgang Heydlauff Join Date: Mar 2009 Location: Germany Posts: 136 Rep Power: 8 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.

 May 15, 2009, 05:47 #3 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 Wolfgang, Thanks very much for enlightening me. So in general, hex are more accurate and take less time. Best Regards, Philip

 May 15, 2009, 14:24 #4 Senior Member   Gijsbert Wierink Join Date: Mar 2009 Posts: 383 Rep Power: 9 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).

 May 18, 2009, 09:01 #5 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 Gijsbert, Thanks for the reply.

 May 18, 2009, 11:19 #6 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 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

 May 18, 2009, 14:03 #7 Senior Member     Sebastian Gatzka Join Date: Mar 2009 Location: Frankfurt, Germany Posts: 729 Rep Power: 11 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. __________________ Schrödingers wife: "What did you do to the cat? It's half dead!"

 May 18, 2009, 14:13 #8 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 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?

 May 18, 2009, 14:30 #9 Senior Member     Sebastian Gatzka Join Date: Mar 2009 Location: Frankfurt, Germany Posts: 729 Rep Power: 11 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. __________________ Schrödingers wife: "What did you do to the cat? It's half dead!"

 May 19, 2009, 05:45 #10 Senior Member     Philip Cardiff Join Date: Mar 2009 Location: Dublin,Ireland Posts: 568 Rep Power: 19 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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