# Visualizing Fluid Flow With Clebsch Maps | Two Minute Papers #170 ## Метаданные - **Канал:** Two Minute Papers - **YouTube:** https://www.youtube.com/watch?v=HUFh8cEDeII - **Дата:** 12.07.2017 - **Длительность:** 3:33 - **Просмотры:** 18,305 ## Описание The paper "Inside Fluids: Clebsch Maps for Visualization and Processing" and its source code are available here: http://multires.caltech.edu/pubs/Clebsch.pdf http://multires.caltech.edu/pubs/ClebschCodes.zip Recommended for you: Schrödinger's Smoke - https://www.youtube.com/watch?v=heY2gfXSHBo Two Minute Papers Merch: US: http://twominutepapers.com/ EU/Worldwide: https://shop.spreadshirt.net/TwoMinutePapers/ WE WOULD LIKE TO THANK OUR GENEROUS PATREON SUPPORTERS WHO MAKE TWO MINUTE PAPERS POSSIBLE: Andrew Melnychuk, Christian Lawson, Dave Rushton-Smith, Dennis Abts, e, Esa Turkulainen, Kaben Gabriel Nanlohy, Michael Albrecht, Michael Orenstein, Sunil Kim, Torsten Reil, VR Wizard. https://www.patreon.com/TwoMinutePapers Music: Antarctica by Audionautix is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/) Artist: http://audionautix.com/ Thumbnail background image credit: https://pixabay.com/photo-2427263/ Splash screen/thumbnail design: Felícia Fehér - http://felicia.hu Károly Zsolnai-Fehér's links: Facebook → https://www.facebook.com/TwoMinutePapers/ Twitter → https://twitter.com/karoly_zsolnai Web → https://cg.tuwien.ac.at/~zsolnai/ ## Содержание ### [0:00](https://www.youtube.com/watch?v=HUFh8cEDeII) Segment 1 (00:00 - 03:00) Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér. 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're going to run wind tunnel tests on hummingbirds. Typically, when a new engine, airplane, or even a new phone is being designed, we're interested in knowing how the heat flow and dissipation will look like, preferably before we're designing an object. To do so, we often run some virtual wind tunnel tests and optimize our design until we're happy with the results. Then, we can proceed to build these new contraptions. Simulating the pressure distribution and 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're 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 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 air flow 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 Chern, who was also the first author of this and the Schrödinger's Smoke paper just a year ago that we reported on. He is 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, for both this and the previous works, make sure to have a look. There is 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. --- *Источник: https://ekstraktznaniy.ru/video/14627*