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Tim June 25, 1999 03:41

Why hex better than tet ?
Hello all,

in the last time I often hear that a grid consisting of tet-volumes is less accurate than a grid of hex-volumes.

Could anyone explain, what's the background.

What's the difference if I sum the fluxes of 6 cellfaces in hex grids or 4 cellfaces in tet grids.



Fabien Coppens June 25, 1999 04:54

Re: Why hex better than tet ?

I, too, would be interested in getting a better view of the numerical justification of hex meshes versus tets. What is the impact of hex/tet in laminar or turbulent simulations ? Numerical error added, problems with wall functions, etc... ? I am more interested in the nitty-gritty numerical issues of this subject rather than discussions regarding extra RAM or CPU requirements. Any experts out there ? Thanks !

John C. Chien June 25, 1999 09:36

Re: Why hex better than tet ?
(1). I think it is based on what people are doing and publishing in using the unstructured mesh. I mean, it is based on their experience. (2). If you look at the mesh they used for flow over an airfoil, a car, you would notice that near the wall the hex mesh (brick type) is used. (3). You could in principle, grow the hex mesh into the flow field to cover the whole computational domain. But, in reality, for complex geometry, it is easier to replace it by tet mesh(a four sided pyramid). (4). So, I would look at the issue from this point of view. That is, based on one's intuition, the tet mesh was used because of the need to cover the complex geometry. Near the regular surface or boundary, the ideal choice of mesh would be the body aligned hex mesh. One could also replace it by the tet mesh in this regular region, but in reality, people are not using it ( I think, you can give it a general name, such as accuracy. But it is really a combination of many things.). (5). It is easier to find the answer to this question by just performing two calculations, one with regular hex mesh, and the other with a tet mesh. (6). In theory, the absolute accuracy is limited by the approximate scheme used. In practice, the comparison of accuracy is usually performed under certain constraints. It is hard to make comparison without mentioning the schemes used and the constraints applied. (7). In a tight space, it is not easy to pack a lot of tet cells for needed resolution. In most cases, there will be only one cell across the tight space. On the other hand, it is much easier to squeez in many thin hex cells into a tight space. (8). So, 3-D geometry and mesh generation is still art work. It is not a math problem.

Md. Ziaul Islam June 26, 1999 13:27

Re: Why hex better than tet ?
Yes John, I agree with you in this matter.

Peter Dittrich July 3, 1999 15:41

Re: Why hex better than tet ?
Hi guys, hex are better that tets for several reasons. Numerical codes for the NS equations are mostly written for an orthogonal coordinate system. Nondistorded HEX grids satisfies the orthogonality while tets never do. If you use a code based on finite difference or finite volume approximations the numerical error increases dramatically for non-orthogonal grids. TETS can never do the job there. With TETS however you can do an easier grid generation for complex geometries. So one is tempted to use TETS or a mix of TET and HEX elements for a fast grid generation. Another great disadvantage of TET elements is the difficult application of wall boundary conditions. Laminar and Turbulent boundary layers need a high degree of accuracy because they affect the whole flow solution considerably. With TET elements close to the wall one cannot use body fitted grids. If you still like to use TET elements than one should consider an higher order Finite Element solver. There the inaccuracy of the irregular grid may be overcome through the higher order approximation of the space derivatives.

Maybe you have heard of the fact that upwind differencing schemes are needed in CFD problems. Try to locate the upstream direction of a special flow problem yourselve and see how this is reflected on an irregular TET grid. ---- Peter

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