To Bee or Not to Bee – That is the Meshing

CD-adapco loves them some polyhedral meshes. Not only do images of poly meshes have a special visual appeal but the meshes do appear to have benefits for CFD computations.

image from CD-adapco

image from CD-adapco

In a recent blog article (Nature’s Answer to Meshing), CD-adapco draws a parallel between poly meshing and a bee’s honeycomb in terms of their efficient space-filling properties. (I love the caption they put on the photo shown at the right – “Bees are better meshers than many engineers.”)

Back in the 19th century, Lord Kelvin’s 14-sided tetrakaidecahedron (aka tetradecahedron) was determined to be the shape that minimized surface area in the 3D packing of soap bubbles. The tie-in with bees is that bees need to minimize the surface area (i.e. the wax) because it’s a big deal for bees to make wax. In the 1990s, two physicists (Weaire and Phelan) figured out how to be a percent more efficient than Kelvin with a mix of 12- and 14-sided polyhedra. Serendipitously, you’ll find that CD-adapco’s poly meshes typically are a mix of 12- and 14-sided cells.

This is all great. But back to the bees. Why are bees so much better at meshing than the rest of us? Stated more scientifically, how can bees possibly create such a highly efficient packing?

As it turns out, bees are no better at meshing than the rest of us. Just as nature abhors a vacuum it also abhors discretizations (OMG, everyone hates meashing). Scientists have now shown that a bee’s honeycomb actually starts out as a circle. This makes sense – no one would be surprised to find circles in nature plus the shape matches the bee’s body shape. As the wax is heated and then dries, its material and fluid properties (like surface tension) take over and the cells morph into polygons.

Scientists have shown that honeycombs start out as circles and dry into the familiar honeycomb shape. Image from Live Science.

Scientists have shown that honeycombs start out as circles and dry into the familiar honeycomb shape. Image from Live Science.

What can we conclude?

  1. Just like a poly mesh, bee hives start out in one form (circle) and morph into a final form (poly). No one generates poly meshes directly – they’re a result of combining the cells of another mesh*.
  2. There’s irony in this tale where the use of poly meshes for fluid computations is shown to be analogous to nature’s poly meshes. But in actuality,  nature’s poly meshes are really the result of a fluids process. In other words, fluids in real life make a poly mesh which demonstrates how we can use poly meshes computationally to simulate fluids.
  3. Analogies are just that – a means of clarifying one subject by comparing it to another subject. Analogies aren’t intended to be iron-clad justifications. Or as I like to say, never debate the analogy. But that does not prevent me from having fun with it.

Also, it’s only coincidence that our friends over at FYFD wrote an article about the fluid dynamics aspect of this beehive circle to poly transition just a few days ago. Honestly, I didn’t see that post until after I had started drafting this one.

Certainly, CD-adapco’s polyhedral meshes are a beneficial technology and this brief article is in no way intended to denigrate their work. You can learn more about their capabilities on this page of their website.

Polyhedral mesh and CFD solution from CD-adapco.

Polyhedral mesh and CFD solution from CD-adapco.

But had I been able to figure out how to introduce birds into this wordplay  I would have.

*In this article, when I say poly mesh I mean the type of meshes typified by the image above. Of course you can make a polyhedral cell by including hanging edges on the face of a hex, for example where one quad face is actually comprised of two smaller quads. While it still looks like a hex, the cell would actually have 7 faces. Those can be generated directly. But that’s not what I’m talking about here.
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6 Responses to To Bee or Not to Bee – That is the Meshing

  1. Tim Tautges says:

    Awesome as usual. Count on a meshing guy (almost by necessity a polymath) pointing out these connections.

  2. Who said meshing wasn’t sexy?! Very interesting perspective of breaking down the barriers between complex meshing and things as tangible as honeycombs.

  3. John Chawner says:

    Derrek, it only would have been sexy had I been able to add birds to the bees. Thanks for reading.

  4. borofergie says:

    I love this John, and I agree with all of your conclusions. I think what the Bees are doing here qualifies as “engineering”, in that they are manipulating the forces of nature to build something clever. Following a set of simple rules to build a complex structure is exactly what most Engineering Meshers do. Most of us don’t understand the algorithms that underlie the meshing process, but we know what we have to do to make it work.

    As you say, it’s easy to push analogies too far.

    I agree that you need to work on the bird thing. There aren’t that many opportunities to work Cole Porter lyrics into engineering blog posts, and it seems a waste not to exploit the chance.

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