But How DO Fluid Simulations Work? 

I like your funny words magic man

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.

Hey, I found this video via a Reddit post. This is really well-made, thank you!

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

RU-vid just recommended this video to me. Hope you get picked up by the algorithm!

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!

Under a minute in and ive never been this excited to watch a video by someone ive never heard of before

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.

Man, I'm a Unity dev and RU-vidr. 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!

This channel is amazing! The quality of production this video has is incredible, keep up the great work!

woah I just realised how less subs and views this guy has. This video deserves way more views with such good animation and narration.

This is extremely high quality, well made and really drives my interest in modeling and simulations. Thank you

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

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 channel is gonna blow past 1M subs if videos like these keep getting posted

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 :)

Great editing and informative video, you deserve a lot more acknowledgement for the quality you put out!

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.

I can’t believe people can actually understand this stuff. Great job man, this is amazing stuff. I just subscribed

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 :)

Very nice video! I randomly came across your channel via my recommended lol I like the pacing and the animations a lot. Keep going!

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.

Wow! Can not believe you have this little subs. Fantastic video and you have inspired me to give fluid simulation a try.

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

Cool video! (U got that Jos Stam reply, epicccc.)

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.

Very happy to find a kind of beautiful genuine, well understand concept channel.

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.

This is such a great video, I probably won't be making fluid simulations, but I really enjoyed that

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.

Your explanations for these very complex are amazing

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.

This is an amazing video with great information which I will promptly use in about 20 years.

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.

video got reccomended to me! it was really good. I hope you hit algorithm gold with this one.

Great video! That was really insightful

Awesome stuff, I came from reddit and i really like the quality of your video keep it up.

This is awesome. Thank you for making this.

great video! Can't wait for the next

Amazing! Amazing source for research!

This was extremely helpful and well made video.

Super informative video, really aided my understanding - thanks very much!!

Great video, looking forward to more.

Duuude! 11:59 is something I've been trying to wrap my head around for ages. Thanks!

Very good video! Exactly what I was searching for 👍👍👍

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.

This is really easy. Thanks for the good explanation and the paper.

Keep it going man, your content is really great. I believe your channel will grow really well. +1 subscriber

Exactly what I was looking for! Thanks man!

I read the same paper before I watched this video and I must say this video is amazing

very very well made and informative video. thank you!

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!!

Thank you, this demystified it a lot!

Awesome video! Thank you!

Jus what I was looking for! thanks

Thank you for this video, it really helped me :)

Really great explanation, thank you!

Hella underrated channel

Very cool explanation, thanks!

I just found this channel today. Quite underrated :)

Great explanation, nice job ^^

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! Well made.. Nailed it👌

You explain Jos Stam's code and theory extremely well

beautiful, amazing. thank you

quality content! good job, very helpful

Phenomenal. Amazing video.

Great explanation for this topic.. simply intellegence Thank you!

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!

Wow ! Really well made and educational 👏🏻👏🏻 subscribed to your channel 👍🏼 However, I can't help but wonder using what softwares was this made 🤔🤓

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 like how you explained such complicated thing in quite simple words. The video is very well made. Keep it up.

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

You are amazing, I don't remember ever clikcing the bell button, but today I did.

Probably the best explanation I have seen on the topic. Please can you do another one on the advanced topics

this is a hidden gem of a channel

well done - good presentation

Attempting to make my own fluid sim right now and this is extremely helpful!

Great stuff, thank you

Awesome explanation! Thanks

this channel deserve a lot more subs!!

I don't know why youtube has been recommending me some really interesting videos lately but I like it

i will need to rewatch this a couple times but it's extremely interesting

Dude, thank you so much!

This work is underrated!

Great video, thank you

Thanks for this, I was able to make my own using it. I'd looked at other explanations but this was the best, especially for the part about clearing divergence

Wow! This is an incredible video.

Incredible video! Needs more views! I feel like with a few more years of learning math (I'm in Algebra 2) I could program my own fluid sim!

So I've just recently started on a computational fluid dynamics journey myself, so I was Stokes-d (sorry) to see your video! I love this video, and am really looking forward to your next ones! I often struggle with the disconnect between math on the page, and code on the screen, and learn best by having examples to pick apart. So, will you be planning to have some comprehension implementation / code videos?

This is so beautiful!

this was best explained, I saw many but I was not able to understand the simulation, thx for tutorial

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?

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!

I thought you had 800k subs until I looked at the comments. This is next level, well done

Great video, earned yourself another subscriber

Really well made Video and you manage to get to the point of the subject. Can you do something like structural simulation next?

It's a amazing video to me. Thanks a lot.