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Tom Brady January 10, 2007 23:01

all hexa grid for pyramid
How do we build all hexagonal mesh for a pyramid? Looks like it's an open problem. Somebody in this forum claimed he had it but the link has been broken.


O. January 11, 2007 03:52

Re: all hexa grid for pyramid
As far as I know a tetrahedron can be split into four hexas by adding nodes in the centres of each edge, side and the tetra itself.

A pyramid can be split into four tetras by adding one node in the centre of the rectangular base. Add an edge between this new node and the top of the pyramid and you end up with four tetras.

If I am not wrong here this should subdivide the pyramid into 16 hexas.

Was that what you were looking for?

pc January 11, 2007 08:03

Re: all hexa grid for pyramid
You can make it even simpler by splitting the pyramid into only 2 tetrahedra by adding a diagonal edge at the base, and then proceed with your hex splits. Then it would be just 8 hexes.

Tom Brady January 11, 2007 17:57

Re: all hexa grid for pyramid
Please draw your mesh and you will set it's not all hexa mesh (6-faces).


Renato. January 11, 2007 21:10

Re: all hexa grid for pyramid
The following article might be helpful to you



Tom Brady January 11, 2007 23:58

Re: all hexa grid for pyramid
Thanks. There are quite a few papers about hybrid grid like the one you recommended. Pyramid may be the simplest open problem but I've already seen tetrahedral mesh even in this thread even though I cleary said all hex.

Apart from which one is better (hex vs. tet), I like to approach it with a mathmatical point of view. I've been thinking this problem on and off for more than a year. Found nothing.

I believe CFD people are the smartest. Somebody in this forum will come up with good news.


O. January 12, 2007 03:55

Re: all hexa grid for pyramid
Ok, maybe you try to actually read and understand what people write, before you complain about people's replies.

For a second take the evil of the word tetrahedron and read on, please! Any tetrahedron can be subdivided into four hexas (see the following link).

A pyramid can be subdivided into tetras in several ways. Two have been suggested in this thread. Once you have split your pyramid into tetras, you split the tetras into hexas and there you are with your ALL HEXA GRID!!!

The quality of such a grid can be subject to discussion and a tetrahedral grid might be better in some cases, but it is topologically fairly simply to split a pyramid into hexahedral blocks. I think the ICEM-CFD people were experimenting with this in order to automatically create mesh topologies for multi-block structured grids.

Renato. January 12, 2007 08:42

Re: all hexa grid for pyramid
Sorry, my intention was not to supply your final solution but give some path instead. As O. said, you can always split pyramids and tetras into hexas and vice-versa. In the article that I suggested you may find clearly explained the subdivisions from everything into tetra. Ok, I know, you´re only interested in hexas but after reading some papers you could realize how you can do what you want.



Tom Brady January 12, 2007 12:03

Re: all hexa grid for pyramid
That's it. Sorry not for reading you message more carefully.



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