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June 30, 2005, 15:02 
triangular grid or quadrilateral grid

#1 
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for viscous computations triangular grids are better or quadrilateral grids. under what circumstances triangular grids works well.
Thank you. 

June 30, 2005, 18:37 
Re: triangular grid or quadrilateral grid

#2 
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Hex are aways better than tet for boundary layer capture. Only use tets when you really can't mesh with hex. You can always use fewer hex than tet to give the same accuracy. Automatic tet meshing has taken the hard work out of CFD but sadly the results obtained using tet meshs never match up those obtained using a good hex mesh. However, it might take weeks and quite a bit of skill to build a hex mesh...rather than seconds and no skill to generate a tet mesh! This is a good topic to start a discussion, although it has been talked about quite a few times on this forum. It might be worth having a look at some of the previous posts.


July 1, 2005, 03:10 
Re: triangular grid or quadrilateral grid

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Stay as far away from tets as possible...for your own good What CFDuser says is absolutely true.
Your optimal mesh is a hex mesh that is aligned with the flow...not always possible. But hex is better than tets. Luckily the ease of mesh generation with tets has now been captured with polyhedral meshes, which will eventually replace all tet and hex meshing for CFD using FVM. Take a look at StarCD web page for more details on this remarkable technology that will revolutionize the way that CFD is done!! Happy modeling! 

July 1, 2005, 06:43 
Re: polyheds, triangular grid or quad grid

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Talking about polyhedral meshes, has anyone done any practical work with polyheds? I am asking 'cos I was quite impressed by a recent demonstration but unfortunately they only compared polyheds against tetraheds (not quads). There, a 65,000cell poly mesh was compared against a 394,000 cell tetramesh. Apparently, the computing time for the polymesh was less than a tenth of the computing time for the tet mesh and the solution was "more accurate" (i.e. converged quicker). I suggest we don't talk about 'accurate' CFD solutions here but one point remains: Why doesn't everybody use them?
I wonder what the number would look like if they had compared the poly mesh against the quad mesh. 

July 1, 2005, 07:49 
Re: triangular grid or quadrilateral grid

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Does anyone know about some references that compare these discretization schemes? I'm working with unstructured grids too (quad meshes, luckily), but I can't find a paper with comparisons between them in CFD.


July 1, 2005, 10:28 
Re: polyheds, triangular grid or quad grid

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I did some test beween hex, tet any polys.
The hex meshes created with GridPro are about 20 times faster than tet meshes and also more robust during the calculation. The polys were about 4 times slower than hex and about 5 times faster than the tets. The polys are also much more robust than the tets. I converted a tet mesh which always caused convergency problems into polys and it run without any problems. All the test were done with StarCD and StarCCM+. I should also note that also OpenFOAM is able to work with the poly meshes and can import the files from StarCCM+. 

July 1, 2005, 11:22 
Re: triangular grid or quadrilateral grid

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accuracy of analysis goes: hexa > poly > tet ease of creation goes : tet and poly > hexa
its not really that simplistic but you get the idea hexas are nice and accurate but take a lot more effort to mesh, tets are not very accurate but take no time to mesh and poly meshes are fairly accurate (a lot more than tets but still less that hexas) and take a little more time to mesh than tets (but not much more) 

July 1, 2005, 11:43 
Re: polyheds, triangular grid or quad grid

#8 
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I did some test beween hex, tet any polys.
The hex meshes created with GridPro are about 20 times faster than tet meshes and also more robust during the calculation. The polys were about 4 times slower than hex and about 5 times faster than the tets. The polys are also much more robust than the tets. I converted a tet mesh which always caused convergency problems into polys and it run without any problems. All the test were done with StarCD and StarCCM+. I should also note that also OpenFOAM is able to work with the poly meshes and can import the files from StarCCM+. 

July 1, 2005, 14:24 
Re: triangular grid or quadrilateral grid

#9 
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Does it mean that in 2D quads are better than triangles in terms of analysis and actual numerical results? And can anyone pt out why?


July 1, 2005, 14:40 
Re: triangular grid or quadrilateral grid

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">accuracy of analysis goes: hexa > poly > tet ease of creation goes : tet and poly > hexa" !! Is this observation good for FEM solvers too? Can anyone comment?


July 2, 2005, 03:20 
Re: triangular grid or quadrilateral grid

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Dear Friends,
Well, Quads and Triangles are both favourable elmements in FVM provided the problem at hand. Structured grids are easy to generate and hence for geometries that are not too complicated we can go for 2D quads. For more complex geometries, an unstructured mesh is a suitable option, though other techiniques employing structured data are also in place. For a viscous flow, it is a quad mesh near the body(possibly stretched) which is most desirable and possibly triangles outside it. Such a hybrid grid is usually a very good option to get good accuracy with little effort. Alternatively, if the geometry is complicated and you go for triangles, then adaptation seems the only possibility of geeting a better solution, which is also the case if your initial grid is coarse, no matter what the elements are. I would conclude that the element constituting the grid is dependent on the problem at hand and its choice is a compromise between the ease and accuracy at any level of grid. Hope this helps Regards, Ganesh 

July 4, 2005, 05:49 
Re: triangular grid or quadrilateral grid

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Little bit of a myth going on here regarding hexes always being the best...
When you run secondorder (which you should ALWAYS do for CFD) accuracy for hexes is only better than tets when the flow is alligned with the hex direction as there is less numerical diffusion. If the flow is not, as it wont be in most engineering problems, unless they are trivial, then hexes have more numerical diffusion than tets. If you combine tets with inflation layers for wall boundaries, then this is just as good as hexes for boundary layer predictions. 

July 5, 2005, 09:31 
Re: triangular grid or quadrilateral grid

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Well. For my case, I get convergence problem using tet mesh but not on hex mesh (with same geometry). If the solution doesn't converge, no matter how good the tet mesh can cope with the flow direction, it's useless. However, I must say it's problem dependent.... If you can get a good convergence using tet mesh, just go for it.... If not, try hex mesh then.... It's really really problem dependent.....no absolute answer to which mesh is better than which, I think...


July 6, 2005, 07:49 
Re: triangular grid or quadrilateral grid

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The observation is not any good for FEM solvers because FEM solvers can't handle polyhedra. Nobody has figured out how to write a shape function for general polyhedra.


July 6, 2005, 10:58 
Re: triangular grid or quadrilateral grid

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Regarding your comment "If the flow is not [aligned with the hexdirection], as it wont be in most engineering problems, unless they are trivial, then hexes have more numerical diffusion than tets."
WHAT? Please explain! First of all, take the example of say flow along a flat horizontal plate (trivial case). If you choose hex, all hex element will be orientated parallel to the plate so that the flux vector of the flow will be perfectly aligned with the face normals of each element. This will not change as you travel downstream so that the main flow direction coincides with the face normal. However, if you now choose tets, the orientation of the main flux vector with respect to the face normal changes every time a new tet element is faced by the flow (which happens every time a new element is face as you travel downstream). If you now convert this scenario onto a more complex (constant curvature!) geometry, the misalignment between flux vector and face normal for hexes is constant while that of tets could reduce or it could increase (depending on the characteristic cell size of the tets). The statement that in such complex geometries the numerical diffusion of tets is lower than that of hexes, depends only(!) on the way the orientation of the tets with respect to the upstream cells was controlled (is this practical?). 

July 10, 2005, 06:12 
Re: triangular grid or quadrilateral grid

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Shubidu: do you have any reference/paper for details about the scenario that you describe here? Jon's comments are what I learnt from some commercial codes so far. Thank you anyway.


July 10, 2005, 21:06 
Re: triangular grid or quadrilateral grid

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personally, if i were a control volume for a CFD solver,i would prefer to have all my faces with these two properties:
1. the angle between the normal of the face and the line joining my neighbour cell should be zero or as close to zero as possible. 2. the point where the line joining me with neoghbouring cell and the face crosses, should lie on face center or as close to it. as far as flow alignment is concerned, i can take care of it by flux splitting among my faces. so, what i want to say is that as a control volume i would be as happy to work as all equilateral triangles (2d) as i would be happy has been a quadrilateral with all equal sides. or in other words, the error heavily depends upon above mentioned two factors. the main advantage of being connected to more neighbours is convergence, which could be better if i had more neighbours. 

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