Fluid dynamics feels natural once you start with quantum mechanics

This is the first part in a series about Computational Fluid Dynamics where we build a Fluid Simulator from scratch.
We highlight the Microscopic Perspective on Quantum Mechanics, Molecular Dynamics, and the Kinetic Theory of Gases that underlies and justifies Fluid Simulation Formulations in the first place.
The Microscopic Perspective provides the ground for the next part where we focus on the Macroscopic Perspective with concepts such as Pressure, Viscosity, Temperature, and Flow Velocity as well as its evolution with time.
Timetable:
-----------------
00:00 - What We Build
02:06 - Guiding Principle - Information Reduction
04:03 - Measurement of Small Things
07:09 - Quantum Mechanics and Wave Functions
13:45 - Model Order Reduction
16:48 - Molecular Dynamics and Classical Mechanics
26:50 - Kinetic Theory of Gases
30:23 - Recap
Selected Papers and Learning Resources:
-------------------------------------------------------------------
05:03 Experiment:
Paper: "Stodolna, Aneta S., et al. Hydrogen atoms under magnification: direct observation of the nodal structure of stark states. Physical review letters 110.21 (2013): 213001."
06:49 Atomic- and Molecular Orbitals Tomography:
Paper: "Vozzi, Caterina, et al. Generalized molecular orbital tomography. Nature Physics 7.10 (2011): 822-826."
Paper: "Itatani, Jiro, et al. Tomographic imaging of molecular orbitals. Nature 432.7019 (2004): 867-871."
07:24 Matter Waves, Double Slit Experiment:
Paper: "Jönsson, Claus. Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten. Zeitschrift für Physik 161.4 (1961): 454-474."
Paper: "Jönsson, Claus. Electron diffraction at multiple slits. American Journal of Physics 42.1 (1974): 4-11."
07:57 Quantum Mechanics Overview, Wave packets, Standing Waves, Eigenstates:
E-Book: "Mathur, Samir D. www.asc.ohio-state.edu/mathur..."
E-Book: "van Dommelen, Leon. Quantum mechanics for engineers. web1.eng.famu.fsu.edu/~dommel... (2004)"
16:01 Model Order Reduction, Modes:
Lecture Notes: from "Farhat, Charbel. Model Reduction. web.stanford.edu/group/frg/co..." to "CA-CME345-Ch9"
17:17 Classical Mechanics, Phase Space:
Lecture Notes: "Cerfon, Antoine. Mechanics (Classical and Quantum). www.math.nyu.edu/~cerfon/mech..."
18:15 Molecular Dynamics, Born-Oppenheimer Approximation, Potential Energy Surface, and Non-Quantized Approximation of Energy Levels:
Lecture Notes: "Allen, Michael P. Introduction to molecular dynamics simulation. Computational soft matter: from synthetic polymers to proteins 23.1 (2004): 1-28."
Paper: "Parker, J. G. Rotational and vibrational relaxation in diatomic gases. The Physics of Fluids 2.4 (1959): 449-462."
Paper: "Valentini, Paolo, et al. Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface. Physics of Fluids 27.8 (2015): 086102."
E-Book Chapter: "van Dommelen, Leon. Quantum mechanics for engineers. 9.2 The Born-Oppenheimer Approximation. web1.eng.famu.fsu.edu/~dommel... (2004)"
20:11 One-Dimensional Hydrogen Atom Approximation for the Coulomb Potential as opposed to the "true" One-Dimensional Coulomb Potential:
"Loudon, Rodney. One-dimensional hydrogen atom. American journal of physics 27.9 (1959): 649-655."
"Loudon, Rodney. One-dimensional hydrogen atom. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472.2185 (2016): 20150534."
27:06 Kinetic Theory of Gases, (Variable) Hard Sphere Approximation of Molecules:
Lecture Notes: from "volkov.eng.ua.edu/ME591_491_NE..." to "NEGD-06"
Disclaimer:
------------------
This series focuses specifically on the aspect of information reduction in dynamical systems. For the sake of clarity, I had to omit many interesting aspects of the topics addressed in the video. So, the video itself is a reduction. :-)
I hope you enjoyed this little braintruffle!
If you like this series, let the KZbin algorithm know by subscribing to the channel and ringing the bell icon.
Thank you for watching and see you next time!

[@JoeTaber]

I love the general approach you took, starting at the very bottom of our known reality -- quantum mechanics -- and explaining it's inherent complexity, then acknowledging possible simplifying assumptions and how they sacrifice accuracy in exchange for computational feasibility. And then moving up from there. This "motivated stack of assumptions" explainer style is beautiful. Thank you!

[@braintruffle]

I'm so happy to reach people who feel the same way about this approach. It helps me a lot to step back, realize what is true and build up from there. Thank you!

[@amirpasagic162]

@@braintruffle you are not alone, when I seen this title I put it immediately on my "watch later list" and was excited the whole day about coming home and watching this. Especially as I am currently trying to teach myself computational fluid mechanics for professional reasons, while reading about quantum physics in free time as a hobby. Knowing high level things but going down to fundaments and trying to reach back to the top is the best approach. Especially to question some dogmas you are not even aware you adopted with years .

[@s1l3nttt]

I saw the views and my jaw dropped, this is actually insane, the quality is Soo good, continue on brother!! I will be following with my own simulation

[@braintruffle]

Thank you! :-)

[@furyzenblade3558]

@@braintruffle yeah this is insane

[@sbepic1235]

Agreed

[@otakudesu568]

Well you will obviously grow I bet

[@thatguyalex2835]

@@braintruffle Hello bro. Does this simulation work on Jupyter Notebook (Anaconda 3 -> Python notebook software)? This simulation looks pretty neat by the way

[@LimitedWard]

This is truly masterful. I can't even imagine how long this took to make. Between the beautiful animations, the clear and cohesive script, and the massive amount of research required (as evidenced by the bibliography in the description). If I were a professor grading this for a project, I would quit my job knowing I could never achieve such clarity.

[@baldichuck353]

I'm too stupid for this video

[@Jack98745]

Same

[@Ascyt]

You're not, the video just assumes a lot of knowledge.

[@AlexandroPantano]

Do you think

[@mech-tech6680]

Please don't think about yourself that way

[@powerguido3141]

I anderstantood it very well. It's easy

[@wlockuz4467]

This video is like finding a treasure in the jungle. Its not only well made but it ties together all branches of knowledge that is Mathematics, Physics, Quantum Mechanics and Computer Science so seamlessly that you're left with wanting more. Truly marvelous stuff!

[@avtomatk6506]

I am a researcher in mathematics and I have very little knowledge in physics, but the video is so well explained that I could even understand the ideas behind your explanation, excellent work.

[@quarry1030]

"How did the monkey fall off the bed?" Well, once upon a time, an electron flipped from a down to an up spin.....

[@ididnotgetanyuniquename]

Did you stop working on it??? How did I find it so late? 🥺 One of the best video I've found so far. The depth of the topic with visual animations is truly remarkable. Please never stop doing what you are doing, and I would like to contribute if possible.

[@Yobs2K]

I don't know if you've seen it already but he made a new video so I guess he didn't stop :)

[@AlnisSmidchens]

This is the best video I have seen on KZbin, bar none! I am currently starting my second year of studying physics at university, and this video is so _so_ *_so_* helpful for getting an intuitive sense of how different scales connect and interact. The visual demonstrations and interactive style cannot be matched by any textbook. Thank you so much for the wonderful video!

[@braintruffle]

I really appreciate your comment and I'm happy that this video can help a little bit. Best of luck with you studies and thank you very much!

[@Schwuuuuup]

If the author of this video would write a recipe for a cake, he would start with "firstly you'll need a big bang" - I love it!

[@Topodic]

One of the best recommendations I've ever received from KZbin. Cheers for the excellent work and phenomenal presentation, content like this deserves to reach the widest audience it can.

[@fritt_wastaken]

I'm speechless, this is so incredibly well made, and the idea for step by step disclosure of the topic is brilliant! One of a kind educational content, keep it up!

[@zotur5884]

3Blue1Brown vibes with the detailed explanation of TwoMinutePapers. I love this

[@SuperMariocapo]

KZbin just recommended me this video and it's simply wonderful. The way it's animating, the voice, the background music, it's so soothing. Keep on this! It's stunning

[@Skystrike70]

Excellent visualizations! The good microphone sound quality is also appreciable!

[@braintruffle]

Thank you so much! Hearing myself was super weird in the beginning, though; I really had to get used to it. :-)

[@jsheav]

This is really great. I am finishing up my PhD specializing in MD simulations, and your QM discussion is the best I have seen to date

[@ryanaiden]

When you said: “looking actually means, interacting” I knew we were in for an enjoyable ride. What a truly amazing video 🙌

[@SergioHidalgoAero]

Hey Mate, this is soo good quality, here an aerospace engineering that really appreciates your work, I´ll recommend this channel to my followers and as me, they´ll love it

[@ManishKumarMishra6016]

Hey, this is so wonderfully done. Love your explanation, clean visualization, and the general direction of it. Really looking forward to this series :) Thank you for doing this and wish you luck!

[@braintruffle]

Thank you very much for your kind words! I'm happy you like it.

[@Snort70]

Looks like your video has started to hit the YT algorithm... Godspeed, I hope this content reaches as many as possible.

[@thatguyalex2835]

Same here. I am a huge science guy. I love science and physics, and hope that this video wins over and crushes all those cruddy Tik Tok videos. :) By the way, these fluid sims could be used in the future as a way to make more efficient technologies such as aircraft (already happening), and potentially be used in molecular assemblers (far future).

[@kevinbissinger]

It sure did

[@johanneszwilling]

😳 I’m getting 3blue1brown-vibes!

[@MrOvipare]

Well that's an easy A+ for the structure, animations, clarity and overall wisdom present in this video. As a physics engineer, fluid mechanics is the only big field of physics we never really covered at university. Thank you!

[@fenixluciferum]

Being a student of Biomedical Engineering, having studied Biofluid Dynamics, I'm in absolute awe to this series. We didn't study the subject as far as going to these depths, but I'm really enjoying it!

[@danielcockerspaniel]

I highly recommend a book “life in moving fluids” the fluid dynamics of biological flows.

[@1.2.3.4..5]

So hyped for this series

[@veloxsouth]

Absolutely beautiful, well written, thorough, and relevant to my interests. Really can't wait for the next part.

[@CampingAvocado]

Starting a quantum mechanics and a fluiddynamics lecture next semester, revisiting this series to warm up, thanks again!

[@agaluszka]

The way you give information out makes you one of the best teachers I've ever listened to... With such gift you could sell the Eifle Tower to enybody!

[@imagiro1]

What a great presentation! Not just the knowledge, but also the way how you present it. Amazing!

[@xenontesla122]

This video is incredibly well crafted! You started with the most intuitive explanation of quantum mechanics I’ve seen, and ended with a great framework for how abstraction is used in the sciences!

[@erv993]

This is an absolute masterpiece! Beautiful visuals and clean storytelling!

[@nightraven1958]

I'm in awe of this video. Incredible animation and explanations. So many more people need to see this

[@lumanaughty1025]

This was the best explanation of how “a quantum particle is in all possible locations until it is observed”. I don’t think I really understood what “observe” it ment. Amazing video!!!

[@felipeolivares6277]

Yeap,just like"faith". The observer, / the "witness" INFLUENCES the out come of the "endeavour"./ Experiment.". No big deal.

[@urekah37]

My mind has been thinking about fluid flows for the last 9 months it is so nice to find such well put together information.

[@Dream4rc]

i never really understood the principles behind fluid mechanics. Now i have a framework. This is a great video.XD

[@lambda_calc]

The clarity of your visualizations and explanations is outstanding. Very well done, you earned my subscription!

[@mghemke]

Awesome explanations - Love the holistic way you just tied together like 10 of my college classes ranging across campus from chemistry and physics to engineering and math to computing and numerical methods. Fantastic content!

[@verified_tinker1818]

This looks incredible. Unfortunately, it's _too_ incredible for a brain of my smoothness. Maybe I'll understand more in the future.

[@PaulanerStudios]

I have waited for a video like this for years... unfortunatly so long that I had to figure out most of what goes into coding fluid sims on my own... This is still probably my favourite youtube video. Thank you very much!

[@braintruffle]

Learning this on your own certainly helped you a lot, so this is actually a good thing :) During my studies I spend a lot of time just playing with equations and simulations and that had the biggest impact I would say. Thank you so much!

[@Mjallux]

Wow man, just the thing i was looking for!

[@VascovanZeller]

This is one of the best recommendations youtube has ever given me. Thank you for tickling my brain, what a wonderful presentation you have here! I wish you a very long career in science communication!!

[@UnofficialFoneE]

Your effort and work has not gone unnoticed. Great video!

[@outside8312]

Your voice feels like a brain hug

[@MachineLearningSimulation]

That is amazing work! The detail, the love, the editing. This video will be of immense benefit for everyone learning about CFD. Thanks for also contributing to open education

[@ZubairKhan-sp8vb]

I am sold in just first 40 seconds of this video. Good work!

[@user-sj5lc3uw2i]

fluid dynamics stuff is complicated but i think its so fascinating since i get to see it all the time in so many different circumstances

[@AdhamElarabawy]

This is genuinely amazing. Thank you so much for this beautiful series. I'm beyond impressed!

[@VerifyTheTruth]

This Is The Most Honest, Concise, And Descriptive Explanation Of Computational Fluid Mechanics And Dynamics That I Have Ever Seen. Well Done.

[@VerifyTheTruth]

Pinball/Pingpong/Pool/Chess At Play.

[@andresyesidmorenovilla7888]

Dude, you're gonna blow up! I trully believe so. Talent like this won't go unnoticed for long. Keep up the great work!!!

[@braintruffle]

Thank you a lot! I am often very self-critical and hearing motivating words helps a lot! :)

[@thomasengels7817]

He actually put more work into the video description alone than I did into my bachelor's thesis.

[@sese1713]

Thank you for this amazing video! Cant wait to see the next one, this is gold.

[@braintruffle]

I am happy to hear that. Thank you very much!

[@juanalvarez1789]

10 seconds into the video, I immediatly subscribed. I can't wait to see what comes next! Hell yeah!!!!!!!!!!

[@TimTeatro]

In a pervious life, I was a theoretical physicist and did computaional quantum mechanics (ab initio molecular dynamics). This was a nice reminder. Your pedigogical approach is superb and-of course-you viasuals are just stunning. For example, your choice to use a 1D slice of the 2D single slit problem (at 9:55) was brilliant. Thanks. I really hope to see more.

[@braintruffle]

Thank you so much for your feedback! You can't imagine how worried I was when I built all this. Since you clearly have the theoretical background, you can see how many more interesting topics I left out, and I was so worried that it would be perceived as too oversimplified. There are so many non-content constraints involved; to hear that this small, stripped down contribution is still perceived as valuable is really motivating. Thank you! :)

[@floontsybloonts9609]

Ive been watching this channel for 5 minutes and I already love it. Clear and consice explanation with fun animation. Awesome job

[@ethanpratt747]

I don't usually comment but I have to in this case. The amount of effort and talent evident in this video is honestly outstanding. You've managed to compact many topics considered highly unapproachable into a format that explains them better and more thoroughly in 30 minutes than I have seen any attempt do in 5+ years of learning about them. The fact that you don't have a subscriber count in the millions is a tragedy, one that I hope is remedied soon. My university professors and textbooks should take notes from you. Thank you for your work. Wow.

[@braintruffle]

Wow, I really appreciate that you took the time to write such a lovely comment! Thank you! :)

[@martinsupitis]

Incredible amount of work you have put into each of these videos. I binged all of them in a single day and did not skip a second. Sublime

[@sabinsulzer7254]

This is hands down 3b1b level quality! Amazing stuff, keep up the great work!

[@JaredBrewerAerospace]

My thesis topic was a quantitative approach optimized to preserve qualities in reduced-order computational kinematic mechanisms for combustion in microelectromechanical devices used as reaction control systems on satellites. At these scales, the no-slip condition is no longer true which means fluids now have friction! To simulate a single molecule of gasoline combustion would require 119,000 reactions of 86 chemical species that occur in 2 billionths of a second. Approaching it from quantum mechanics or a macroscopic scale, it ultimately comes down to what is "good enough" @24:18 After 15 years in industry, this still remains true.

[@Crustyislooking]

This is way too good. Like, you went so far beyond expectations I’m shocked

[@ammyvl1]

funnily enough, 8:00 is probably the best description of quantum mechanics I've heard so far

[@MaxWeinhold]

Absolutely stunning visuals, and told in such an intutive way! A great explanation of building up fluids from the ground'up by investigating which simplying assumptions allow us to retain the overall behavior.

[@danielhader4063]

Instantly subscribed after watching! This is so beautifully done and easy to follow. Thank you!

[@scifactorial5802]

Fantastic content with a great presentation. It is incredible seeing how much effort is put in to making such high quality videos by people like you. Keep up the excellent work and I'm sure the algorithm will reward you. I'm looking forward to the next videos.

[@afvallejos]

Your visualizations are absolutely amazing!

[@fergarram]

Incredible level of detail and quality !!! Thank you for creating this :)

[@alanmahnekalin9145]

This video should be the example of the word "explanation" in future interactive dictionaries! Masterpiece!

[@johnevans9911]

this is amazing! I tried to model the behavior of particles in a ripple pool once and your video is lightyears more advanced than what I did. You're amazing thank you for producing this video

[@stepphun]

Insane graph simulations there! Very well done and explained.

[@MrCk0212]

Please keep going. The quality and information in this video are fascinating!

[@giuseppematteucci5174]

I've not even finished the video yet, but your animations on QM are awesome. The best I've seen

[@danamulter]

13:50 "ways to interact >> things that interact" is such a concise way of saying something so significant and translatable. There's a linguistic elegance to this phrase that surpasses even the subject matter in where it can both be applied and intuited with some thought.

[@coolsebz]

Wow this is so high quality! And the references in the description too! 👏

[@user-go6kw3ye3u]

this video is astonishing, so informative and well animated

[@xgozulx]

The quality! the explanations! the best recap of QM I've ever seen! the awesomeness!! Wow this video is great

[@Polaris_Babylon]

This channel is pure golden

[@doublemax77]

Just found this video by accident. Great work, incredible quality. Can't wait for more of the series.

[@wakka247]

This is a good overview and explanation of fluids and modelling them. Awaiting the next part of this incredible quality video.

[@braintruffle]

That’s very kind of you. Thank you.

[@bleblo13]

This just showed up on my front page, love it! Didn't expect quantum mechanics to show up this much for fluid simulation (even though it makes sense). It also seems like the video is gaining some traction with the influx of new comments, at least I hope it does. This wave of great new educational videos is amazing.

[@braintruffle]

I was very happy that the first part reached many people in the last few month and I was very happy with the feedback (a lot of positivity) and then youtube decided to show it to more all of a sudden. Many thanks :)

[@kartikanand5374]

Dude that's amazing

[@braintruffle]

Thank you! :-)

[@Rydn]

I just found a new fav. channel. I love this.

[@cristianrivas2870]

Amazing video with insane quality. Really really cool. Thank you!

[@iyxan2340]

This is absolutely well-made!

[@eren3527]

You, random man on internet, created one of the finest educational videos on internet. I appreciate you.

[@Damoon010]

Incredible work

[@das_it_mane]

These are some of the best visualizations I've ever seen! Would love if you explore more aspects of quantum mechanics!

[@Orangaria]

This is one-of-a-kind type of work man, this is amazing content!

[@sachkofretef]

this is the best channel on youtube for science. you actually understand what you are talking about and it's complex and not just feel good stuff like veritaserum etc. keep it up !!

[@Sebastian-rp9np]

Srsly in my opinion the most underrated and insane Video i've seen so far on YT

[@GeorgeSladkovsky]

Absolutely stunning video. Great demonstration and explanation!

[@jackwilliams1468]

I study quantum information theory. I clicked on this being interested in fluid dynamics -- I didn't expect to get an incredibly intuitive description of quantum mechanics as well. Edit: the first 13 minutes are also a PERFECT motivation for why quantum computers are more powerful than classical computers.

[@MrRussianComrad]

This is one of the greatest educational videos I stumbled upon. The 30 min here were far more insightful than a collective 4 hours of lectures on introductory Molecular Dynamics I had last term

[@MarcusTinkersTooMuch]

That was great. Looking forward to more. Thank you.

[@TheRelain]

Really good video, looking forward to the next!

[@kerbodynamicx472]

Not often would I watch 3 minutes into the video and subscribe. This is brilliant! I'm a high school student and I just started using CFD to mess around, but to me, they are always this kind of wizardry that somehow works. I really appreciate how much research have gone into the making of this video, and how much I have learned. It's shameful to think some nonsensical videos could get millions of views, while this one only get less than 100k (as of the making of this comment)

[@Graywolf116]

Wanna say I really appreciate you illustrating *why* it's difficult to start from quantum mechanics, and how even for tiny scenarios it gets out of hand fast.

[@bhavyakabade]

I dont normally comment, but this was incredible. The ease with which complex topics are explained is unmatched. Will be looking to learn way more

[@oleit3]

Thank you!! This video's quality is amazing, loving the clarity explaining such a complex subject. Keep up

[@PiotrekPomorski]

Oh my holy moly. Sitting now with my Fluid Dynamics books, reading and solving problems during my masters... and you come with this marvel. Out-stan-ding work. Would love to know a bit about your process. Are you a team? Do you animate/code/research on your own? The quality of it is batshit splendid my friend! Cheers!

[@braintruffle]

Wow, thank you so much. I'm so glad you find it useful! I'm doing this on my own, I just love math and physics and learning while seeing things in action. I also like that creating this content involves so many different aspects. As I have a background in non-linear dynamics theory, I'm familiar with the math and physics related work, but building the visual aspects involves also very interesting things I was not exposed to so far. :)

[@PiotrekPomorski]

@@braintruffle That would be super fascinating to get a glimpse into your visual creative process, not gonna lie! Keep up the good work. Couple weeks into it and you'll have your hard work reflected in thousands of subscriptions. Cheers!

[@danielcockerspaniel]

Stick to your classical fluid dynamics textbook, and follow with traditional numerical methods. To a hammer everything is a nail. The author of this video is a physicist, not a fluid dynamics modeler. Eventually he’s going to get onboard the navier-stokes train like everyone else if he wants to actually model fluid flow.

[@PiotrekPomorski]

@@danielcockerspaniel no doubt about that. Textbooks are a groundwork, no way around it. Nevertheless having a possibility to extend and enrich the imagination with such visuals is a value in and of itself.

[@alejandrotenorio2327]

Can I ask which type of master are you doing to work on topics like this?

[@jcespinoza]

I'm amazed at the quality of this video! Outstanding job man!

[@TheBooker66]

Absolutely extraordinary video! The graphics are great, the naration is great (though it's also great that you wrote subtitles, for certain specific words), and the explanations are incredible. I saw this video a few days ago, at night, on my recommend section but thought "This looks interesting, but I really don't have the brainpower for this at night" and boy am I happy I got recommended it again, this time at a better time of day. I will for sure go on to watch the next of the series, and you've earned yourself a sub.

[@tfs711]

Oh Man!!! Your deserve to get not only viral but EXTREME VIRAL..!!! What a wonderful explanation! WOW!!!