But How DO Fluid Simulations Work?
ฝัง
- เผยแพร่เมื่อ 25 มิ.ย. 2024
- Fluid simulations. How on is it possible that a computer can recreate the crashing waves, the rolling clouds and the swirling smoke that we see in our daily lives, phenomena which seem characterized by randomness and chaos? This video will attempt to explain exactly how the mathematics behind fluid simulations work.
Timestamps:
00:00 Intro
00:42 Navier-Stokes Equations
02:38 Representation
04:52 Diffusion
07:53 Gauss-Seidel Method
09:36 Advection
11:31 Clearing Divergence
14:33 Outro
Paper referenced: Jos Stam - Real Time Fluid Dynamics for Games (2003)
www.autodesk.com/research/pub...
Music: Soft Piano Music by Relax Music Meditation
• Video - วิทยาศาสตร์และเทคโนโลยี
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I like your funny words magic man
man
😂😂😂 your comment cracked me up
Dumb cant
Says any competent programmer could do it..instantly loses me in math...been coding for 30 years..not the imposter I swear
@@forbiddenera relatable
Nice video. Reminds me of my talks in the early 2000s. I also wrote a book about this. The Art of Fluid Animation. We also implemented this into the Maya software and has been used in blockbuster movies. We got a tech Academy Award for this in 2008.
it advanced a lot since then
@@podemosllegara840anti-tikt7 and?
Maya in the 00's was the MVP, I remember booting the silicon graphics stations and play with it for hours.
Amazing!!!
Nice to see you here, Jos!!
When I finished the video I expected it to have at least 100k views with how well made this is. You deserve many, many subs
50 views away from 100k as im typing this
@@t4ky0n hello fellow anarcho-troll-ist
@@David-zy1lr YOOOOOO
There is 100k views now
check braintruffle bro
Hey, I found this video via a Reddit post. This is really well-made, thank you!
What sub?
@Caleb Landry Wow you used a bot account to market some scam and reply to it using another bot account to make it seem reputable?? that's disgusting
Careful viewers! I might be wrong, but the equations shown for diffusion in the video are incorrect. If you look at the paper by Jos Stam, the simple, unstable equation for the next density is dn = dc + k(sc-4dc) (where sc means the sum of the densities in surrounding cells), which is not the same as the equation shown in the video, dn = dc + k(sc-vc), where sc is the average of densities in the surrounding cells. I saw that when implementing the method seen in the video, density was lost after diffusion even though it should just spread out.
Thank you! :D
TH-cam just recommended this video to me. Hope you get picked up by the algorithm!
Slight correction on the diffusion step, the equation according to original paper is x0[IX(i,j)] = x[IX(i,j)] - a*(x[IX(i-1,j)]+x[IX(i+1,j)]+x[IX(i,j-1)]+x[IX(i,j+1)] -4*x[IX(i,j)]), which would be d_n = d_c + k (s_c - 4 * d_c).
Without doing 4 * d_c, the amount donated to the 4 surrounding cells would only be subtracted once from the original, resulting in a net increase in density/velocity from nowhere and breaking conservation of mass.
Additionally, I believe the equation d_n = d_c + k (s_c - 4 * d_c) explains why its necessary to diffuse density reverse in time, because it blows up under certain scenarios, resulting in negative values. An example is if you have a really high value cell (say 100) surrounded by really small value cells (say 1). Let K=1. On the next iteration, the high value cell will have -396. While having negative velocity possible, having "negative density" is not and will cause the simulation to blow up.
Under a minute in and ive never been this excited to watch a video by someone ive never heard of before
The craziest thing: this seems to be this guy's first video from what I can find
Wow! Awesome video, I always hated how science videos never went deep into how equations actually worked and how to implement/use them, but you did both! Thank you! Awesome video, subscribed and I hope to receive new notifications from you :)
This channel is amazing! The quality of production this video has is incredible, keep up the great work!
This is extremely high quality, well made and really drives my interest in modeling and simulations. Thank you
Too bad I found about this video after I did the same thing. It took me over a year to understand the theory and algorithms behind Stam's papers, but you explained it in 15 minutes! Great video anyway!
If it took you a year, I'm sure you won't forget it anytime soon! :)
@@Gonkee I still have no clue how to program that. Have to watch the video 5 more times :D
@@pinkyrng7104 just start one step at a time, try and get the basic system working so that you only need to learn one new concept at a time to eventually get it all working
Same for me. But it's not an easy subject though and contains many different algorithms and approaches. I also skipped the lerp part, because on the GPU you are able interpolate between pixels by default, with the filtering step.
Overall very detailed and well made video! It helps a lot of curious people.
@@pinkyrng7104 You're making it sounds complicated more than it is. You just look at the N solver equation and implement an N loop for it. I did it in 1 time watching the video and just rewinding it to where the equations are.
Great editing and informative video, you deserve a lot more acknowledgement for the quality you put out!
This channel is gonna blow past 1M subs if videos like these keep getting posted
woah I just realised how less subs and views this guy has. This video deserves way more views with such good animation and narration.
Man, I'm a Unity dev and TH-camr. I came here from reddit, when I saw the video I thought you had somewhat around 100k subs bro. Keep griding you'll easily reach there :) Good Luck!
Gdrinding*
@@AkariInsko *grainding
@@makra2077 *grdinaining
Are "subs" so important to you? Who cares how many subs. The world is not only about money. Good is minority, stupidity is majority.
@@user-cw3nb8rc9e 110k now hehe
Great job with all the videos. The level is very good and the explanations are great. Most of all the topic/topics are a good niche - they're not some sort of basic tutorial, but they're not at an advanced academic level either discussing the details of the respective topics they cover. They're very much the type of stuff I'd love to see if I just want to get an actual technical introduction to something I've never thought about before.
Wow! Can not believe you have this little subs. Fantastic video and you have inspired me to give fluid simulation a try.
Finally, I’ve been looking all over for information on health physics simulations in general work but literally every single one just tells you to get a library and doesn’t actually go over the math. Thank you for making this video
This video doesnt even come close to what really happens.
Btw the book that has complete navier stokes solver as used in industry is by milovan peric. Google cfd and peric.
thanks for this video man. with the help of this video, jos stams paper, a paper by nvidea and weeks of my life spent understanding everything i was able to implement jos stams fluid simulation, while understanding all the processes involved in it. your visualizations we're really valuable in the way they helped me visually grasp everything.
Cool video! (U got that Jos Stam reply, epicccc.)
Very nice video! I randomly came across your channel via my recommended lol
I like the pacing and the animations a lot. Keep going!
Your video is really well made ! The animations, the pace, the narration, the music, everything looks like a professionnal channel with many thousands of followers. Keep up the great work ! I can't wait to see more videos from you
if not the best than one of the best ever youtube explanaion here of CFD.... Did't knew it was so easy to understand the CFD.... Appriciated mate
great video! Can't wait for the next
Excellent presentation dude. Insta-subscribed. A couple of weeks ago I simulated a boat by voxelizing it and using buoyancy and drag laws, then I wanted to simulate a fluid next... and found your channel. This is pure gold.
This is such a great video, I probably won't be making fluid simulations, but I really enjoyed that
I can’t believe people can actually understand this stuff. Great job man, this is amazing stuff. I just subscribed
It wasn't that hard to follow. The hardest part was actually the lerp for density redistributions. The rest was purely vector calculus and was nothing new.
This is awesome. Thank you for making this.
Honestly, the best content. I dont understand why youtube didn't put this high up on the search results when I was searching for something similar a week back - all I got was shitty lectures and some other crap. Keep going @Inspecto.
Very happy to find a kind of beautiful genuine, well understand concept channel.
Great video, looking forward to more.
Really nice video, despite having read several papers about fluidsim recently, I still feel like I walked away with a clearer understanding of the fundamental implementation details.
video got reccomended to me! it was really good. I hope you hit algorithm gold with this one.
Great video! That was really insightful
Came across your video from YT algorithm. It's really well-made! Subbed
This kind of stuff if the stuff I want to make more of but don't know how. You just earned a sub :) keep up the good work and make more!! Things like this are hard to learn on your own but things like this make it possible. Thanks.
Amazing! Amazing source for research!
Duuude! 11:59 is something I've been trying to wrap my head around for ages. Thanks!
Awesome stuff, I came from reddit and i really like the quality of your video keep it up.
Hey, I recently changed from engineering at Uni to computer science/math, I’ve been feeling a little Gino because I miss physics concepts and understanding things, but this video reminded me that with math and computer science I can recreate all the sciences that lie between using mathematical models and programming skills. Thanks :)
if you ever touch bits of game dev, its full of math/physics (a lot more than people realize), would totally recommend trying it out, the math is very interesting and visual.
As a fellow cs student, a degree in cs is just tools that need to be applied to some other field, and physics is a fun and interactive one to program
This is an amazing video with great information which I will promptly use in about 20 years.
Great video! The part about subtracting the divergence was especially fascinating.
Having never implemented any actual fluid dynamics, I sort of assumed you'd rely on the density to pull and push to even it out, close your eyes, and hope you don't have any rounding errors.
Exactly what I was looking for! Thanks man!
I just found this channel today. Quite underrated :)
Your explanations for these very complex are amazing
You explain Jos Stam's code and theory extremely well
Thank you, this demystified it a lot!
Awesome video! Thank you!
This was extremely helpful and well made video.
Phenomenal. Amazing video.
Jus what I was looking for! thanks
I'm a CS student and I have a critical paper review to write on Stam's Real Time Fluid Dynamics for Games paper, your video really explained fluid simulations well! Also realised I'm already subbed to your channel from your sound synthesis video I used to understand the concept for a personal project implementing a sound synth in C++ from last year. Cheers!
I read the same paper before I watched this video and I must say this video is amazing
Very cool explanation, thanks!
this is a hidden gem of a channel
I loved on how this video was crafted, and your other videos too, like legit, you somehow exploit most of human senses to really impart a rather complex idea to someone brain in a really engaging way. It would be highly appreciated if you can make a video or any other form of guidance detailing on how this video is produced, like how you do your research, what tools, to do the research, the video editing software or even the content brainstorming management. I'm so sorry if this is too much to ask for but you would really help me or maybe others in communicating our own ideas or any other complex ideas to the layman. Again, your videos are already on the top notch category and you'll definitely reach a bigger audience and prospects in no time!!
Very good video! Exactly what I was searching for 👍👍👍
This is really easy. Thanks for the good explanation and the paper.
Great explanation, nice job ^^
beautiful, amazing. thank you
Super informative video, really aided my understanding - thanks very much!!
You are the 3B1B of computers. You are going to get reeealy big eventualy. And i will love to say that i was here while you only had 4 videos and not even 10k subs.
Thanks for the absolutely top notch content
Thank you for this video, it really helped me :)
Really great explanation, thank you!
Keep it going man, your content is really great.
I believe your channel will grow really well.
+1 subscriber
You are amazing, I don't remember ever clikcing the bell button, but today I did.
very very well made and informative video. thank you!
Hella underrated channel
quality content! good job, very helpful
LieAr
I don't know why youtube has been recommending me some really interesting videos lately but I like it
Algorithm brought me here and you got me super interested in Fluid Simulations, extremely well-made video and I'm also leaving this comment to help the algorithm pick up your video for engagement!
this channel deserve a lot more subs!!
This work is underrated!
Wow ! Really well made and educational 👏🏻👏🏻 subscribed to your channel 👍🏼
However, I can't help but wonder using what softwares was this made 🤔🤓
Attempting to make my own fluid sim right now and this is extremely helpful!
Probably the best explanation I have seen on the topic. Please can you do another one on the advanced topics
I thought you had 800k subs until I looked at the comments. This is next level, well done
Great stuff, thank you
This is pure gold
This is so beautiful!
Dude, thank you so much!
Great explanation for this topic.. simply intellegence Thank you!
Assuming that the divergence is 0 is indeed valid in most cases. This is based on the assumption that the fluid is incompressible. However with compressible flows one should use the continuity equation which allows you to solve it. But great video!
Wow! This is an incredible video.
WOW! Well made.. Nailed it👌
Awesome explanation! Thanks
well done - good presentation
Great video, earned yourself another subscriber
Seriously fantastic content, thank you for answering the very question I have been asking the past few weeks - just how on earth do computers simulate the chaotic motion of fluids ?? Subscribed
Great video, thank you
I'm already a fan!
i will need to rewatch this a couple times but it's extremely interesting
So that's where the advance mathematics and CFD equations come to play in real life! Also I thought I'd never be seeing those iterative equation solving methods. You've no idea what this video is to an enthusiastic mechanical engineer! Thanks alot!
Excellent!
Great video!
ive always been mystified by navier stokes so super looking forward to watching this series
Whoa man, awesome job your channel is going big soon enough just keep doing quality content like this! How do you recommend me start implementing this for my very first fluid simulation? My main issue is just where to start for making the graphics and data structures for the grid and display of vectors. Which programming paradigm is best for this kind of endeavour?
Outstanding Space Cowboy!
This channel is severely underrated