# All Hail The Adaptive Staggered Grid! 🌐🤯 ## Метаданные - **Канал:** Two Minute Papers - **YouTube:** https://www.youtube.com/watch?v=4etSuEQOzDw - **Дата:** 16.03.2021 - **Длительность:** 5:44 - **Просмотры:** 94,106 ## Описание ❤️ Check out Lambda here and sign up for their GPU Cloud: https://lambdalabs.com/papers 📝 The paper "An adaptive staggered-tilted grid for incompressible flow simulation" is available here: https://cs.nyu.edu/~sw4429/files/sa20-fluid.pdf https://dl.acm.org/doi/abs/10.1145/3414685.3417837 ❤️ Watch these videos in early access on our Patreon page or join us here on YouTube: - https://www.patreon.com/TwoMinutePapers - https://www.youtube.com/channel/UCbfYPyITQ-7l4upoX8nvctg/join 🙏 We would like to thank our generous Patreon supporters who make Two Minute Papers possible: Aleksandr Mashrabov, Alex Haro, Alex Serban, Alex Paden, Andrew Melnychuk, Angelos Evripiotis, Benji Rabhan, Bruno Mikuš, Bryan Learn, Christian Ahlin, Eric Haddad, Eric Martel, Gordon Child, Haris Husic, Ivo Galic, Jace O'Brien, Javier Bustamante, John Le, Jonas, Joshua Goller, Kenneth Davis, Lorin Atzberger, Lukas Biewald, Matthew Allen Fisher, Mark Oates, Michael Albrecht, Nikhil Velpanur, Owen Campbell-Moore, Owen Skarpness, Ramsey Elbasheer, Robin Graham, Steef, Taras Bobrovytsky, Thomas Krcmar, Torsten Reil, Tybie Fitzhugh. If you wish to appear here or pick up other perks, click here: https://www.patreon.com/TwoMinutePapers Károly Zsolnai-Fehér's links: Instagram: https://www.instagram.com/twominutepapers/ Twitter: https://twitter.com/twominutepapers Web: https://cg.tuwien.ac.at/~zsolnai/ ## Содержание ### [0:00](https://www.youtube.com/watch?v=4etSuEQOzDw) Intro Dear Fellow Scholars, this is Two Minute  Papers with Dr. Károly Zsolnai-Fehér. Today we are going to concoct some absolutely  insane fluid and smoke simulations. A common   property of these simulation programs is that  they subdivide the simulation domain into a grid,   and they compute important quantities like  velocity and pressure in these gridpoints. Normally, a regular grid looks something  like this, but this crazy new technique   throws away the idea of using this as a grid, and  uses this instead. This is called the Adaptive   Staggered-Tilted grid, an AST grid in  short. So what does that really mean? The tilted part means that cells can be rotated  by 45 degrees like this. And interestingly,   they typically appear only where needed, I’ll  show you in a moment. The adaptive part means   that the size of the grid cells is  not fixed, and can be all over the   place. And even better, this concept can  be easily generalized to 3D grids as well.    Now, when I first read this paper, two things  came to my mind, one, that is an insane idea,   I kinda like it, and two, it cannot possibly  work! It turns out, only one of these is true. ### [1:23](https://www.youtube.com/watch?v=4etSuEQOzDw&t=83s) Experiment 1 Carson Vortex And I was also wondering, why? Why do all this?   And the answer is because this way, we get   better fluid and smoke simulations. Oh yeah! Let’s  demonstrate it through four beautiful experiments! Experiment number one. Kármán vortex  streets. We noted that the tilted grid points   appear only where they are needed, and these are  places where there is great deal of vorticity.    Let’s test that. This phenomenon showcases  repeated vortex patterns and the algorithm is hard   at work here. How do we know? Well, of course, we  don’t know that…yet! So let’s look under the hood   together and see what is going on! Oh wow, look at  that! The algorithm knows where the vorticity is,   and as a result, these tilted cells are  flowing through the simulation beautifully. ### [2:23](https://www.youtube.com/watch?v=4etSuEQOzDw&t=143s) Experiment 2 Smoke plumes and porous nets Experiment number two. Smoke plumes and  porous nets. This technique refines the   grids with these tilted cells in the areas  where there is a great deal of turbulence,   and, wait a second. What is this? The net is  also covered with tilted cells. Why is that?    The reason for this is that the tilted cells not  only cover turbulent regions, but other regions   of interest as well. In this case, it enables us  to capture this narrow flow around the obstacle.    Without this new AST grid, some of these  smoke plumes wouldn’t make it through the net. Experiment number three. The boat ride. Note that  the surface of the pool is completely covered with ### [3:04](https://www.youtube.com/watch?v=4etSuEQOzDw&t=184s) Experiment 3 The boat ride the new tilted cells, making sure that the wake  of the boat is as detailed as it can possibly   be. But in the meantime, the algorithm is not  wasteful, look, the volume itself is free of them. And now, hold on to your papers  for experiment number four.    Thin water sheets. You can see the final  simulation here, and if we look under the hood, ### [3:41](https://www.youtube.com/watch?v=4etSuEQOzDw&t=221s) Conclusion my goodness, just look at how much work this  algorithm is doing. And what is even better,   it only does so where it is really needed it  doesn’t do any extra work in these regions. I am so far, very impressed with this technique.   We saw that it does a ton of work for us,   and increases the detail in our simulations, and  helps things flow through where they should really   flow through. Now, with that said, there is only  one question left. What does this cost us? How   much more expensive is this kind of AST grid  simulation than a regular grid? +100 percent   computation time? +50 percent? How much is it  worth to you? Please stop the video and leave a   comment with your guess. I’ll wait. Thank you! The  answer is none of those. It costs almost nothing, ### [4:31](https://www.youtube.com/watch?v=4etSuEQOzDw&t=271s) Outro and adds typically an additional 1% of computation  time. And in return for that almost nothing,   we get all of these beautiful fluid and  smoke simulations. What a time to be alive! Thanks for watching and for your generous  support, and I'll see you next time! --- *Источник: https://ekstraktznaniy.ru/video/13959*