A SIGGRAPH paper uses Clebsch maps to visualize vorticity in fluid simulations by mapping regions on a sphere into vortex tubes. The technique works on hummingbird wing airflow and NASA aircraft data, with source code available from first author Albert Cherng.
Dear fellow scholars, this is two Minute papers with. Everyone who watches this series knows that among many other scientific topics, I am.
Severely addicted to fluid simulations.
And today it's time to relapse.
And this time we are going to.
Run wind tunnel tests on hummingbirds. Typically when a new engine, airplane or even a new phone is being designed, we are interested in knowing how the heat flow and dissipation will look like priority. Preferably before we are designing an object. To do so, we often run some virtual wind tunnel tests and optimize our design until we are happy with the results. Then we can proceed to build these new contraptions. Simulating the pressure distribution and the aerodynamic.
Forces is a large topic.
However, visualizing these results is at least as well studied and difficult as writing a simulator. What is it exactly that we are interested in? Even if we have an intuitive particle based simulation, millions and millions of particles, it is clearly impossible to show the.
Path for every one of them.
Grid based simulations are often even more challenging to visualize. Well, so how do we choose what to visualize and what not to show on the screen? And in this paper we can witness a new way of visualizing velocity and vorticity fields.
And this visualization happens through Clebsch maps.
This is a mathematical transformation where we create a sphere and a set of points on this sphere correspond to vortex.
Lines and their evolution over time.
However, if instead of only points, we pick an entire region on this sphere.
As you can see the north and.
South pole regions here, we obtain vortex tubes. These vortex tubes provide an accurate representation of the vorticity information within the simulation. And this is one of the rare cases where where the validity of such.
A solution can also be shown.
Such a crazy idea.
Loving it.
And with this we can get a better understanding of the airflow around the wings of a hummingbird. But we can also learn more from pre existing NASA aircraft datasets.
Have a look at these incredible results.
Publishing a paper at the Siggraph conference is an incredible feat that typically takes a few brilliant guys and several years of unbelievably hard work. Well, apparently this is not such a.
Challenge for Albert Cherng, who was also.
The first author of this and the Schrodinger Smoke paper just a year ago.
That we reported on.
He's doing incredible work at taking a piece of mathematical theory and showing remarkable applications of it in new areas where we would think it doesn't belong at all. The link is available in the video description. Both for this and the previous works.
Make make sure to have a look.
There's lots of beautifully written mathematics to be read there that seems to be from another world. It's a truly unique experience. The paper reports that the source code.
Is also available, but I was unable.
To find it yet.
If you have found a public implementation, please let me know and I'll update.
The video description with your link.
Thanks for watching and for your generous.
Support, and I'll see you next time.
Sam.
