Polyhedral Meshes

[AeroGT3]

Hey all,

I just wanted to check on how frequent the use of polyhedral meshes are on here. I just came across them in Fluent 6.3, and wow, they are pretty amazing. I'm able to get the same level of accuracy with 5, 6, 7 times fewer cells! I love these things!

Question for those who've used them frequently: how are they along walls? Tets were obviously rubbish compared to prism or hex elements along walls. Is this the case with polyhedra, or are they adequate for near wall cells as well?

Many thanks,

[kilcoo316]

I'm using CFX, so have had no exposure to them yet - but 2 of the other guys in here use 6.3, and Mark was harping on about them a while back.

I'll ask and see if he has anything on comparing them in the BL.

(But its monday morning, and neither of them are in yet )

[checkered]

Not an expert,

but thought it'd be OK to post links to a couple of articles. These don't go as far as being anything like mathematical treatises, but do discuss the issue in some depth ... Still, based on what was explained on the theory of polyhedral meshing there, I'm pretty much sold on the idea. Given enough free time, I might even familiarize myself with the geometry on a theoretical level. In fact, to be absolutely convinced I would have to do so, since obviously any such polyhedral mass as put forward here can be broken down into tetrahedra. Thus the relative computational efficiency must have more to do with the mathematical methods in defining the mesh and subsequent flow equations than the shape itself. Both meshing methods, as far as I can understand, can indeed create identical volumes.

The first article is a bit on the dry side, but gets to the point:
The advantage of polyhedral meshes

http://www.cd-adapco.com/press_room/dyn ... spoly.html

This one I enjoyed more, the writer has a "renaissance type" approach:
Polyhedra: Nature’s Answer to Meshing

http://www.deskeng.com/index.php?option ... ew&id=1383

Finally, an image of an F1 polymesh from Fluent, just for inspiration:

[kilcoo316]

Aero, unfortunately no-one has actually used the things yet in here, I thought they had, they were just talking about the advantages over it [probably to wind me 'cos fluent has it and CFX, which Im using, doesn't ].

Anyway, we've industrial contacts, and one of the fellas was saying his main industrial supervisor is evauating this topology, he'll be having the weekly meeting on wednesday, anything comes out of it re the meshes, I'll let ye know.

[miqi23]

Well I have used it a bit but not on a daily basis. Yes, they are good but to be honest I am not comfortable with it at all! I would rather prefer the good old method I have been using so far.

[AeroGT3]

So no one's really familiar with them yet?

Maybe I'll have to run a few comparison cases and prove them, because they're my new best friend.

I solved flow over a wheel (http://www.fluent.com/solutions/automot ... _wheel.pdf), and I was able to match their results (exceed them actually, I caught the peaks and troughs better) using k-w and 43,000 tet cells (symmetry plane).

BUT, I converted to a poly mesh, (keeping the boundary layer) and reduced cell count to 12,000. I received almost identical results, with Cp being dead on with the solution from the tet mesh, and only the wake being different. I didn't capture the wake because the poly cells replaced 4 tets, so the mesh off of the surface was much coarser. Obviously the poly case ran faster, but it also converged in fewer iterations and was less erratic.

I'll have to run a case of 12,000 tet cells as a comparison along with a comparison on more complicated geometry (a "numerical experiment" if you will) to really prove it to myself, but right now I am very close to sold on them. Miqi, since you seem to be the only one to have used both, why do you prefer the standard method?

[miqi23]

Aero, I would suggest you try and compare drag and lift values of a single element wing using both the meshes. Grab something where you can easily find standard wind tunnel data for comparison purposes.

Yes, you are correct that Polyhedral meshes converge quicker compared to pure tets, however I believe this is due to the quality of the volume mesh being generated. I think Polyhedral meshes produce a higher quality mesh hence allowing robust convergence. Try comparing Poly with pure hexahedral grids and see what you get! I am sure Hexahedral will converge even quicker. Moreover, how are you producing your tetrahedral mesh? Are you using the Delaunay mesher or the Advancing Front method?

By standard method I mean Hybrid grids and the reason I prefer them is that it has so far produced accurate results and I am not sure if Polyhedral meshes can do that at the moment. It also depends on the turbulence model being used. the K-Omega is so sensitive in free stream, however very good close to the walls. Try using the RnG-kEpsilon and see if you get the same result...

I think I had a simple 2D wing lying somwhere in my laptop, if you need it PM and I will email it to you. I think its the case file for the actual thing, but you can use the coordinates from there. I will try to find the windtunnel data for it as well...

[AeroGT3]

Aero, I would suggest you try and compare drag and lift values of a single element wing using both the meshes. Grab something where you can easily find standard wind tunnel data for comparison purposes.

I've yet to do a 2-D wing; only a wheel. I will try a wing, especially if you can send me those files.

Yes, you are correct that Polyhedral meshes converge quicker compared to pure tets, however I believe this is due to the quality of the volume mesh being generated. I think Polyhedral meshes produce a higher quality mesh hence allowing robust convergence. Try comparing Poly with pure hexahedral grids and see what you get!

I haven't done this either, because I usually can't get hex meshes over complex shapes (Gambit . . .) I don't doubt hex's being superior to polyhedral, I just can rarely get the pure hex grid you're describing. We're getting better meshing tools though, which should solve that problem (hopefully.)

I am sure Hexahedral will converge even quicker. Moreover, how are you producing your tetrahedral mesh? Are you using the Delaunay mesher or the Advancing Front method?

Delaunay I believe.

The K-Omega is so sensitive in free stream, however very good close to the walls. Try using the RnG-kEpsilon and see if you get the same result...

What do you mean by "sensitive in free stream?"

By standard method I mean Hybrid grids and the reason I prefer them is that it has so far produced accurate results and I am not sure if Polyhedral meshes can do that at the moment.

StarCD claims polyhedral are more accurate than tetrahedral, but they say nothing about polyhedral compared to hybrid grids. In fact, I can't find anything really comparing the two in detail, and Gambit is quite poor at hybrid grids. I will compare pure hex to polyhedral, but it seems there is no real way to compare hybrid to poly?

Sorry for all the questions! Just trying to learn from someone with more experience!

[kilcoo316]

The classical K-W turbulence model of... Wilcox I think it was, was very sensitive to freestream turbulence levels (actually through W values in the freestream).


But that has been modified several times - Menter developed 2 variations, the first used the K-W model close to the wall, then blended to the K-E model in the freestream.

Then 2nd variation is the SST model, which builds on his first modification by changing the way of calculating eddy viscosity slightly.


I don't know if any current solver would still be using the original Wilcox model without the modifications to be honest.

[syguy]

Just wanted to clarify that CFX does and has always effectively solved on polyhedral. CFX is a node-based solver as opposed to Fluent and STAR-CD which are cell-based solvers. That means that dependent flow variables are stored at nodes in a node-based solver and stored at cell centers in a cell-based solver.

Effectively a node-based solver computes gradients etc. based on the surrounding cells at each node - a polyhedra. In special cases it can be considered equivalent to an edge-based finite element method. The large stencil around each node tends to lead to the same benefits quoted for polyhedral meshes in a cell-based solver.

The advantage of a node-based solver is that there is no need to process a standard mesh into a polyhedral mesh, thus it is relatively easy to incorporate mesh movement and adaptation techniques.

Maybe someone could comment on how node-based solvers (like CFX) compare with cell-based solvers (like Fluent) in terms of accuracy and performance?