Hello people,

My task is to compare tet and hex grid with each other. Could you give me some suggestion how it could be quantitively compared?

The aim of the comparison: Usually I am working with CFX 5.6 and using hex grid for my simulations. I would like to validate the simulation time and the simulation quality for tet grid in comparison to the hex.

Problem: How tets and hexs can be compared? For getting approximately equal calculation time, should the number of faces be equal? For getting the same resolution (or quality), should then the number of cells be equal? What about the equal number of nodes? Are there also another comparison criteria?

Another matter is also about the mesh adaption possibilities with hex and tets. Is there a reasonable tet mesh adaption possible?

Thank you very much for any ideas and hints. Of course, I am going to provide you with the results of my investigation if you will be interested. Have nice simulations and happy days

Thanx olaf

Very interesting, You might get some inspiration on the CFX community pages, I remember a paper about comparing time, memory etc. with different grids, for laminar flow though. Title: "Comparison of accuracy for various element types: laminar flow" Looking forward to see your results Jan

I don't believe that you can get an equal quality answer from a tet and a hex mesh both having equal numbers of cells. For valid comparison, I believe you have to establish a physical criteria for the solution. For example, is the drag and lift the same or is the pressure drop from point a to point b the same for any 2 meshes, and then keep increasing the number of tets until the solution matches the hex solution. The correlation will vary depending upon what criteria you decide on, so it should be what is of interest to you. You also have to decide what to do at the wall. That's typically where tets have the greatest problems. Many times people throw in a layer of prisms at the wall to better deal with the boundary/turbulence models. Generally the trade-offs are that tet meshes are more easily and quickly generated, but the solution time and memory goes up because you need more for a given quality.

A coworker performed some sort of comparison and concluded he needed 8X the number of tets for the same accuracy as hexes. Seems about right based on my impressions so far.

based on number of cells or nodes?

I am a bit surprised that the ratio is 8X, I do not believe that it is a general number. It depends very much on the flow, heat transfer or not, and if walls have an impact on the flow etc…

Try to read the very interesting report on the CFX community pages where different meshes has been compared for a laminar 3d driven cavity with heat transfer. I quote

"For the uniform meshes, four times as many elements are required when the element type is tethrahedal as when it is hexahedral..." (uniform grid was used, meaning same element length.

A funny observation was made when comparing hybrid meshes and hexahedral "The hybrid meshes require the smallest number of elements to get the 1% accuracy in heat transfer", so for this specific point was the ratio less than 1, but for hybrid meshes. (But who would not use a hybrid mesh when there are walls)

A very good point is also given in the report "Whilst these results give some interesting statitisics aboyt the relative effectiveness of elements …. In pratice the actual number of elements required is of less importance than how much CPU time or memory is required to get a given level of accuracy…"

Yes Jan,

very good advice to everyone is to get a copy of the report from your CFX service contact or the community site.

The ideas and approach in the report can then be applied to a problem that is similar to your real applications. The conclusions from this specific report probably will not (ok I can safely say will not) generalize to all CFD problems. However, a logical approach of setting something up and trying it, comparing to something else, etc will always lead to better application of CFD to your real problems.

Yes the choice of pure tets for a wall bounded flow, particularly a heat transfer prediction....is clearly a bad choice for this problem and one should know this apriori. However, it does nicely demonstrate what doing something really silly will lead to in terms of results.

There are lots of validation reports, papers, etc out there done by very experienced people. A beginner might be lead to believe that anybody can do CFD and get results that are the same order of accuracy without even thinking about the problem.....believe me I have seen things that really make one wonder.

Has anybody ever seen a beginner try to do a tet mesh for a free-shear layer flow or a free-surface interface capturing problem?? Then they wonder why the results are off by a factor of 2 or so?

Anyhow that is my 10 cents worth.

Regards,

Bak_Flow