The simplest flow physics that still makes sense
Вставка
- Опубліковано 19 чер 2024
- A vivid introduction to fluid simulation.
Topics covered: rarefied gas dynamics, continuum gas dynamics, fluid motion descriptions & coordinates (spatially fixed (Eulerian), material-fixed (Lagrangian), arbitrary), reducibility aspects, motivation on modeling unresolved flow structures, ensemble averages of microscopically and macroscopically varying data, usefulness of the modeling hierarchy, simplifying and decoupling the evolution equations, Navier-Stokes equations, compressible flow and the incompressible flow assumptions, and buoyancy-driven flow (Boussinesq approximation).
Special thanks to my supporters:
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AxisAngles
Yuxuan Zhang
Houston Lucas
Patrick Gibson
... and all my patrons!
If you like what you see and want to support my work, join my Patreon feed. I really appreciate it!
/ braintruffle
Timetable:
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00:00 - What's going on
02:15 - Recap on continuous fluid fields
05:06 - Continuous evolution and local similarity
06:52 - Motion description and evolution equations
20:41 - Ensemble averages of macroscopic data
23:52 - Usefulness of the modeling hierarchy
25:13 - Playing with the equations
27:50 - Compressible and incompressible flow
32:39 - Buoyancy-driven flow
37:22 - Decoupling of the equations
39:30 - Thanks to my supporters and recap
Selected Learning Resources:
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02:15 - Continuous flow fields from rarefied gas dynamics and continuum gas dynamics: [1,2,3,4,5,6]
04:10 - Continuous perspective on the microscale; continuum micromechanics (to be discussed): [7]
06:52 - Fluid motion description and coordinates (spatially fixed (Eulerian), material-fixed (Lagrangian), arbitrary); evolution equations; material derivative; discretization aspects: [8,9,10]
22:05 - Ensemble averages of microscopic and macroscopic data; modeling unresolved flow structures; Kolmogorov microscales (to be discussed); turbulence modelling (to be discussed); 2d vs 3d turbulence (to be discussed): [1,11,12]
27:50 - Compressible flow; incompressible flow assumptions: [2]
32:39 - Buoyancy-driven flow (Boussinesq approximation); treating slight density variations: [13]
37:22 - Decoupling the equations: [2]
References:
[1] - Lecture Notes: from "volkov.eng.ua.edu/ME591_491_NE..." to "NEGD-06"
[2] - Book: White, Frank M. "Fluid mechanics." Tata McGraw-Hill Education, 2010.
[3] - Book: Anderson, John D. "Governing equations of fluid dynamics. Computational fluid dynamics." Springer, Berlin, Heidelberg, 1992. 15-51.
[4] - Paper: Macrossan, M. N. "Scaling parameters for hypersonic flow: correlation of sphere drag data.", 2007.
[5] - Lecture Notes: Cerfon, Antoine. "Mechanics (Classical and Quantum)." "www.math.nyu.edu/~cerfon/mech..."
[6] - Lecture Notes: Kenkre, V. M.. "Statistical Mechanics." "www.unm.edu/~aierides/505/" specifically ".../bbgky2.pdf" & ".../bbgky3.pdf"
[7] - Paper: Zaoui, André. "Continuum micromechanics: survey." Journal of Engineering Mechanics-ASCE 128.8 (2002): 808-816.
[8] - Essay: Price, James F. "Lagrangian and eulerian representations of fluid flow: Kinematics and the equations of motion." MIT OpenCourseWare, 2006.
[9] - Book: Donea, J., Huerta, A., Ponthot, J.-Ph. and Rodríguez-Ferran, A., "Arbitrary Lagrangian-Eulerian methods,
The Encyclopedia of Computational Mechanics", Wiley, Vol. 1, Chapter 14, pp. 413-437, 2004
[10] - Book: Bennett, Andrew. "Lagrangian fluid dynamics." Cambridge University Press, 2006.
[11] - Lecture Notes: Lermusiaux, P. "Numerical Fluid Mechanics." "ocw.mit.edu/courses/2-29-nume..."
[12] - Paper: Boffetta, Guido, and Robert E. Ecke. "Two-dimensional turbulence." Annual review of fluid mechanics 44.1 (2012): 427-451.
[13] - Paper: Mayeli, Peyman, and Gregory J. Sheard. "Buoyancy-driven flows beyond the Boussinesq approximation: A brief review." International Communications in Heat and Mass Transfer 125 (2021): 105316.
Please note:
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This series focuses specifically on the aspect of information reduction in dynamical systems. For clarity, I had to omit many exciting facets of the topics addressed in the video. So, the video itself is a reduction. :-)
I hope you enjoyed this little braintruffle!
Do you like what you see and want more of it in the future? Then, you may consider supporting my work on Patreon. It would help me a lot in producing more such videos for you. I really appreciate it! www.patreon.com/braintruffle
Any chance you’re looking for people to help grow the channel/help you with the workload? I’d be interested if so!
Yes! I need more similar videos
already have a video that proves this dc 0 point to ac Flux
@@jeremiecorkery9421 easy ua-cam.com/video/nPVvlo2Hpjk/v-deo.html
I have the dream of creating a game engine that could support a perfect (statistical) simulation of reality. Really love your approach to fluid dynamics!
Fantastic video once again, I'm always stunned by the visuals, can't wait for the next one!
Thank you for taking the time to check out my latest video! I'm happy you like it and for your support!
This video, and the previous ones, are masterpieces! Definitely in the running for the single best scientific/mathematical video series ever put on youtube! These videos leave graduate level courses in college in the dust (I know, I've taken them). My question is, how did you come to this level of understanding!? Was it just reading textbooks, working through the problems, etc.??
Thank you so much for your kind words! I'm really happy my work is seen as enjoyable and helpful. Throughout my studies, I often played with the problems at hand, trying to solve things on my own - intentionally postponing the thorough literature study to a later learning stage. This pushed me to think outside the box. One of the most valuable insights for me was realizing how similar lots of problems and solution approaches are once observed through the 'right' lens and, therefore, to keep looking for these lenses! That's what these videos are meant to promote: daring to change the perspective on things. There is so much fun stuff to explore along the journey, and with time the patterns will unveil.
@@braintruffle Thank you for your reply! I appreciate your perspective on problem solving lenses. I'm currently tackling some very complex thermal/heat transfer problems that are requiring me to search for these lenses. These videos definitely inspire me keep looking!
I wish I could describe how amazing these comments are, but it would take me so long to do it justice. Just please keep doing what you are doing - you are making the world a better place.
I don't know how I've only just seen this video.. it's an absolute masterpiece!
Came here looking for an explanation of lift (from aerodynamics) from first principles. Ended up watching the whole series so far :) Not sure how many would appreciate, but simulations comparing airfoils would tie nicely all concepts explained so far. Your content is amazing!
The visuals in this video are unparalleled in effect. actually goated. wow
The Material Coordinates method you outlined is just fascinating to me, how similar the idea is to one used in *video compression* of all things, the way one uses optical motion vectors to move regions of pixels around on the screen. And once that comes to mind, there's so many other things that video codecs do that then make total sense to backport to the original fluid simulation: resetting the material coordinate grid at regular intervals (similar to what I-Frames do for video); using a quadtree acceleration structure just like the macroblock structures used for P/B-frames.
Heck, there might even be a way to leverage some of the video encode/decode acceleration features present on so many platforms these days to do part of the work, and get a _really_ performant simulation.
Hands down the best produced mathematical content, by miles. The effort put into the animations are truly head and shoulders above anything else. Not to say there aren't plenty of amazing math channels already out there, but every time I watch one of your videos I am just stunned at the clarity and practicality of the explanations/animations.
This topic feels far above what I should be able to understand mathematically, but the conjunct animations make it so that I can just manage to keep up. Can't wait for the next episode of this series!
Bro this is series is so fucking good! Please dont stop!
The quallity of the animations for the video is absolutely amazing! Thank you, that is so much better than anything in this area.
I don’t have enough comprehension of language to describe how awe inspiring your videos are. It shows the front-edge of what is possible at the intersection of mathematics, engineering, and story telling - that even us simple humans can begin to understand. Wow. Wow. Please never stop showing us what is on your mind. I, for one, am curious.
Haven't watched it yet but liked anyway cuz I know it's gonna be amazing!
Your videos are masterpieces ! You can explain such difficult topics with clarity and wonderful simulations.
You deserve a lot bigger audience : your work is fantastic 😁
By far the most in depth videos I’ve ever seen on, well, anything. This series is simply incredible!
This is insane! I don't understand it but it's so fascinating. I just started my first class on differential equations and never found the modelling part of it interesting until now
I'm just speechless how clear and with such a deep insight this topic gets explained. And on top of all of this those beautiful animations. Chapeau!
This is the most amazing video series I'm much too dumb to understand.
I've been looking forward to your next video!
Awesome quality! Worth the wait
Man this is way underrated than it should be!!!🤯🤯
I appreciate you for putting this up on UA-cam.
This grid-bending effect at 0:00 reminded me of how, according to GR, spacetime is deformed due to gravity
I don't think that's a coincidence. Notice how, as you climb the ladder, waves become fields, which become vectors, which generate particles, which make waves, and so on. This sounds a lot like real life systems. I wonder if entropy is just an inevitable data compression scheme; as the scale of a system goes up, it alternately behaves as particle, then wave, then field, then a particle again, all of which recursively affect each other in all dimensions simultaneously, and the line of time which we experience is simply the least energetically expensive way for that system to evolve. Imagine the stock market. It has particles (trade actions), waves (a big disruption propagates), and fields (prices). It can be analyzed fractally at any resolution, but The Uncertainty Principle still applies, to an extent.
What an educational masterpiece! Thank you very much! Hope you will improve more
Great man !! actually i just became a postgraduate student and hella interested in such type of simulations and complex fluids dynamics , i guess your work just ignited a spark within me to explore it further, THANK YOU very much !! keep doing the good work
I really loved and appreciated this video. The explanations of Material derviatives where very insightful. And I'm about half way through the video!!! Excelent job!!
My favorite series on youtube. Thank you.
One small addition to your wonderful description of spatially-fixed and material-fixed coordinate systems (one I only know of because my grad school officemate studied it while working on his dissertation): The "unified" coordinate system. Here, the computation nodes move in the direction of flow but at a different (slower) speed than the flow. The speed of the nodes is something you choose yourself, and can be different at different points in space or time -- so you can try to encourage, e.g., the preservation of grid angles while still letting the grid deform into tight spaces or around corners.
Incredible video and great explanation!
I love how you disect everything perfectly so that we can understand complex things easier!
I subscribed a few months ago and it's great that you're continuing to make this S-tier content
baltarfajinkankonk satan 🤣 hahahaha
ua-cam.com/video/nPVvlo2Hpjk/v-deo.html
infinit potential but hole
This channel present fascinating content but with rate of 17.55 second /day
This series sets a new bar of how to teach STEAM. I look forward to a world where all education has content this clear and well thought out. Amazing work!
Absolutely stunning. Bravo! 🎉
This video is so awesome I can even start to visually understand how black holes work. In fact, it basically explains a lot of things about the universe.
Your videos are sooooooo Good. Can't wait for the Discretization video
This is super high quality series.
funny that the part with the box of swirls is the most replayed, it's very pretty. I'd love to play around with that myself, just watching the swirls and chaotic flow.
Thank you for another amazing and informative video :)
Awesome video! Thank you!
I could fall asleep to this.
That's not criticism. It's a compliment.
Beautiful
the levels of approximation and regimes of validity dsicussed at the end were helpfu in understanding some of my own simulation work
Simply lovely work
Brilliant visuals...! As a graduate student, studying fluid mechanics and using CFD, I am really curious what kind of tools you use for simulation and visualizations.. It is literally beautiful.
Just discovered your channel and I am hooked! This is so pleasant to watch :) Do you mind sharing what software tools you are using for the animations? I love the style, it really stands out.
Looking forward to follow your journey and future videos :)
The whole series has been AMAZING. The narrative, visuals and quality of production is top notch, thank you for gifting us this work
best youtube channel ever
Fantastic simulations. What rendering software do use for plotting the dynamics data? Blender?
How can I pay to support your content? We need more content like this, this is pure quality, thank you for bringing this wonderful content for free
It’s an excellent video. It’s good to use computers with it. It seems like Mandelbrot and Julia sets and predicted dependable weather. Thankyou
Really amazing visuals. You could probably do a whole series teaching people data viz!
sehr gut gemacht!
well done~ mind blown!
Making a note to come back and watch later ;)
Really superb video!
Amazing video! BTW, i think about the part of infinitely fast compression waves could be better illustrated using a zoomed in visual which scrolls with the wave, that let's you see the flow speed equivalence more effectively.
please consider making a video on how you're making these videos. i'm particularly interested in how you're animating formulae and what software you're using for combining formulae and video clips with simulaiton.
If u post stuff like that even once per 2 months , i ll never unsub
I really like the visuals used in this video. May I ask what software you used to create these animations?
Thanks ! Have a nice day !
gdamn man your visualisations are beautiful
The visuals are absolutely stunning, you talk about it very casually yet I am in awe. How can I learn to do this on my own? I have a background in physics but no fluid dynamics yet...
ua-cam.com/video/nPVvlo2Hpjk/v-deo.html right here
Amazing!
Can you simulate electrical currents as long-range-interacting pressure waves travelling through the conductor?
What software do you use for the 3-D rendering and/or simulations?
I have most definitely forgotten some important details but I think it might be possible to limit the small scale detail by making the continuous thing into discreet units like pixels or something? But then also treating it like a continuous thing in other ways? Like a field I guess
right in the intro and later on when you have a wing profile flow, even though it looks pretty, it's actually behaving like a really bad wing surface due to flow separation and turbulence. in reality you never want turbulence to form around your wing, you want the flow to be as laminar as possible until it reaches the tip of the wing.
What does the “e” variable represent at 25:57 ?
An admiring and inspiring video. Music, tone of voice of the narrator, Everything's perfect. The only problem is the accent of narrator. It is very hard to follow for me. Thank you.
i love conciseness
Excelente!!!
at 29:47. what do you mean by artificially scalling up the slower simulation velocites and the "playback speed" to "match" the flow speeds "visually" ?
Damn this channel is so cool!
this too ua-cam.com/video/nPVvlo2Hpjk/v-deo.html
awesome.
Hi, I am not so familiar with differential equations. Why do you use sometimes "D" and sometimes the turned 6 (I think it's a lowercase delta?) and what is the difference between these expressions?
normal d is used in normal differential equations. Delta is used in partial differential equations. Big D is the material derivative and is dependent on how you look at things. In the Eulerian view in fluids its usually the expression he explains in 11:00
@@schadenfreude7812 Thanks for the explaination ^^
Brilliant
Hi, sorry for asking a question before watching the video in its entirety, but I've got a question about the "Trajectory Perspective" and "Spatially Fixed Perspective". I've studied some fluid dynamics in the past and encountered some different terminology. Are these perspectives also known as "Lagrangian" and "Eulerian", respectively? Thanks!
I am looking to learn CFD from scratch, I have done some basic projects like simulation of air through airfoil but want to have in-depth knowledge on the topic. Can anyone suggest me place to start?
I see in this a formal definition of magic.
To find a perturbation or introductory states which are irreversible using the general laws derived by fluid mechanics - introductory states or perturbations that yield dramatically improbable results.
These clearly exist, but are generally averaged out. But what if we can repeatably induce them by determining the math of them?
nice!
Which software do you use sir ? Blender ?
I think he is using Unity. I could be wrong. He doesn't mention anywhere from I can tell.
thank you 👍👍👍
So why do we add the temperature stuff afterwards, instead of making the assumption that our density is 100% determined by the temperature? Wouldn't that also remove one equation?
right here ua-cam.com/video/nPVvlo2Hpjk/v-deo.html
perfect
So far I managed to grasp every aspeckt in the videos, but on this one I got lost
what is the program language ??
The probabilistic description of microscopic particles reminds me of the distinction between the ontic and epistemic models of the wave function. Some believe the wave function is real (ontic), and there are no hidden variables. Others believe the wave function is a description of our state of knowledge of the system (epistemic).
Does your intuition lean one way or the other?
Regarding Bell's theorem, a often neglected requirement of the theorem is statistical independence of measurements. With a deterministic universe, that assumption can be dropped, and local hidden variables are still allowed.
One approach to two-dimensional fluid dynamics uses vorticity in Brownian motion, as proposed by Alexandre Chorin. So we have a big system of differential equations and a random number generator. It is natural to ask what we can do for quantum mechanics. I have made a number of suggestions in various UA-cam videos on quantum theory.
Subscribe to the channel by going through the comment section itself. Yet to watch the video.
Heavy Duty ! 👍
I wanted to touch on your statement around 36:30. This is actually also the reason why in fields like astronomy there are so many different groups building different simulations. Depending on the theory you are trying to simulate you build the simulator with the contrains given by the theory in mind and then try to do model robustness tests. The only thing that bothers me with this approach is that it feels a lot like enabling confirmation bias. You are building a sim that shows the effect you want it to show because of the theory you want to prove. What are your thoughts on this?
I cant it is so beautifulllllllllllllllllll
21:07 so cute!!!!!!!
9 ways to solve the same problem!? Whoa
wow
You use a lot of precise and usefully technical terms, that describe exactly what you want to explain, but as a casual viewer who doesn't have familiarity with these terms or a background in engineering, it makes it hard to follow along. Watching 3Blue1Brown or Primer (who I assume share the software you use to make these videos) I also don't have a background or formal education in what they're talking about, yet they're able to put the theory into simple (or simpler) terms much more clearly.
I should also add that the earlier videos in this series were much closer to their style, and I was incredibly interested, very invested and only slightly confused throughout those videos. I guess it's just the continual reference to equations I am unfamiliar with that made me struggle so much with this episode
Not everything can (and should) be explained in simple terms. 3Blue1Brown is great for entertainment and/or getting a bird-eye view, but you hardly can solve any real problem after watching his videos. I'm glad too, that the video like this one that covers such advanced topics exists in such a supreme quality.
@@idoben-yair429 the concept is indeed complex, but the language of the narration was unnecessary overloaded with those "academic"-y long multilayered sentences, where you forget what the sentence started from when you reach the middle of it. It may be fine for scientific papers where it is easy to reread the sentence, but not for a video with its own pace where it is harder to re-watch the same sentence. Add the pretty monotonic voice -- and I almost fell asleep several times, despite the interesting subject and stunning animations.
In most cases the long sentences could be broken into simpler and more digestible pieces without losing any information. I liked the video very much, but I also agree with the Evelyn's critique.
I love his videos but you are correct. I feel that this is mainly because of the sources he has used so an art in itself would be to take the complexity and make it understandable for beginners or even a 5 year old. *Feynman entered the chat*
@@idoben-yair429 I definitely do not criticize the video and think it's absolute ace! Different lecturers offer different lecture styles so I think it's up to the audience to decide what they would like to consume. And I truly believe that there is a ton of academics out there enjoying the video series from braintruffle. :)
Здравствуйте. Благодарен за видео.
У Вселенной есть цикличность во времени, которые разделяются по комбинациям взаимодействий и делятся на периоды; 1. Вселенная собранная в одну квант струну. 2. Вселенная из коротко живущих фрактал с переходом в хаос. 3. Вселенная из хаоса с переходом в долго живущие фракталы. 4. Вселенная из долго живущих фрактал с переходом в одну квант струну.
При всех комбинациях, квант струна, может рваться но без отрыва при этом петлями складывается в мембраны образуя из них бутоны которые могут, от периода времени, сворачиваться ограничивая связи.
Awesome video series. But this video is a bit long. It requires dedication and time, and does not really work by watching it in multiple sessions. Yeah, so I recommend grabbing a snack for this.
what's your target audience?
I’m confused
huh?
I think i saw this posted on reddit?
a
who are you ?