That was one of the best explanations for advection I've seen online! Especially the pushing bubbles out of a phone screen protector analogy.

I understood none of this yet I was glued to it all the way through

videos like these are what internet was made for

Hugh, the standard first book on PDE is Walter Strauss's book. If you want to try questions on me I'm happy to help out.

love the experimental feel to how you moved forward itteration by itteration,

very good video. i'm glad you showed or mentioned what approaches didn't work

loved the video! feels like discovering sebastian lagues yt channel all over again :)

Great work, I can't wait to see your next simulations!

This is so cool, and you did a great job with the video editing! I hope you make more videos like this!

Can't believe I watched entire video about coding and didn't get bored

Really well produced, nice work

I wish the very best on KZfaq, I am so glad I discovered your channel. Keep up the good work !

I love this, thank you for makin my day on yt much better!

I loved this video! Really inspiring, and I'm sort of amazed that this was running on a macbook air too - great job :D Thanks so much for sharing.

Great and inspiring video, thanks a lot!

educational and entertaining! loved it, thank you

This is super cool, keep it up!

Thanks for the beautiful video.

Beautiful!

Subbing cause I wanna see you simulate the inside of Earth. Great content

first thing I thought about when I clicked on this video is about The Powder Toy which is a pixel based particle simulator game which actually has that exact same type of fluid simulation for simulating air in the game

In a way, this is functionally simulating Quantum Mechanics and illustrating the principle of "Particle/Wave duality". The entire fluid motion can be represented as a vector. But the vector, *itself,* must behave as a particle, moving in response to the overall "equation" of the fluid flow. And that flow, in turn, changes in response to how those velocities keep changing within it. The more "interactions" there are, the more you'd have to "zoom in" and re-calculate based on the rapidly changing velocities. But the fewer the interactions, whether that be due to smooth flow, "low temperatures" (less movement), etc., the more you can just look at the overall average equation for how the vectors evolve. So, in keeping with this notion that this is very much like Quantum Mechanics, using the principles of QM would probably help improve the quality of the simulation. *1)* Non-Zero Baseline: In QM, particularly Quantum Field Theory, one of the major notions is that everything isn't sitting at a baseline _zero_ state. Rather, there's a certain minimum baseline energy already present, and it's the net _difference_ over *or under* that baseline which is considered. To put it in context of a fluid, since we're discussing fluid dynamics, it's like there's a big ocean of energy already sitting there. How deep that ocean is is a question scientists argue over endlessly, but it's what happens at the surface that is actually important and what they more or less agree on. *2)* Constant Activity: There are constant "little ripples" going all over the place. The surface of the ocean isn't still; it's always churning and bubbling and mixing; and as those little micro-waves this motion generates interact with one another, the peaks of the waves amplify one another, the dips amplify one another, but where peak and dip meet they cancel out. And when it churns enough, it gets big enough to be called a true "wave" (a particle like an electron or a quark). You can't really say that an ocean wave has one specific location; it's a "part" of the ocean as a whole. But you could also point at a part of the ocean at any given time and ask, "Is this currently part of a wave?" Maybe yes, maybe no. The bigger and stronger the wave, the more likely you'll be to "catch" it. *3)* Quantized: This means that a wave can't be an arbitrary "height" in this ocean (where "height" here is a stand-in term for the "energy" of a particle). It would be as if waves can only be increments of 10 meters in height. Anything between 10 meters below the surface and 10 meters above the surface would effectively register as if it were right at the surface. Functionally, what this is is "statistical rounding". If there were a wave (particle) that could potentially be 17 meters tall according to the vector math, the particle math has no clue what that means. Particle math only deals in increments of 10 meters. So it has to round 17 meters; but it doesn't use formal rounding. Instead, it uses statistical, trigonometric rounding. 17 meters is 0.7 of the way from 10 to 20. I forget the exact formula, but it's 50/50 if it were X.5, but more than a mere 70% chance at X.7 to round up to the higher value (it follows trigonometric values around a unit circle). So these aspects could possibly be implemented in the following ways. First, have some non-zero "baseline" flow value. Never have "zero flow". Not zero *actual* flow, anyway. But simulate the actual pertinent _movement_ not based on this "real baseline" but, rather, relative value compared to that baseline. So, for example, if baseline flow has a vector weight of, lets say, 100, your actual fluid movement model *treats* 100 as if it were zero (staying still), and then movement of 105 is going 5 _faster_ than that. Next, have micro-purturbation in the model by allowing that baseline value to "jitter". While baseline flow that's considered "stillness" would still be considered 100, any specific "cell" of fluid would randomly, iteration to iteration, have a value between 98-102. And it can change its value by up to 2 either positive or negative. These will still factor into calculations, so these changes won't "come from nowhere"; if micro-flow is generated, it will pull from surrounding cells. Lastly, when it comes to evaluating how the vectors, themselves move, you can "fudge" the value a bit. Round it based on the statistical rounding I described to let it "zoom out" and use lower resolution, and then do more of a "random step" pattern instead of a complete vector calculation to determine how a vector moves. This way, vectors don't have to consider, "how am I moving based on everything around me" 100 times, they just have to decide, "how likely is it for me to move up, down, left, or right based on forces around me" 100 times.

Awesome 👍

Thank you for this video

Great video

Got recommended.....now in love

Thanks for the explanations and the sources! please add the links to the description though :D

This guy's gonna love learning about the weak fem form for the constitutive eularian fluid equations

You could have used MultiGrid for the solver since it land it self to parallelism better

No way Euler got named for a fluid dynamics problem. We're supposed to name the problem after the *second* person to solve it!

i bet this would run much better on a gpu with a cooling system and more than 10 cores (or whatever your model of macbook has)

Cool

Would it be possible to create a more complex velocity map by uploading an image, and only looking at hue and brightness, ignoring saturation? Obviously colors approaching white could be a problem, but you could remedy this by thresholding saturation and then treating anything below the threshold as a non-fluid/wall if the brightness is high enough that it would otherwise have a velocity

imagine putting a few ai's in there, make them evolve, adapt to the environment and make them learn how to utilise it to its advantage

Nice

no links to the code?

me: 50 frames per second that’s pretty bad performance RL: *”on my MacBook Air”* thats CRAZY

regarding the parallel part: would it be feasible to work the opposite way? Instead of writing to 4 cells, each cell would instead read from 4 neighbors and update itself.

So persistent zero velocity is like a solid object? I wish it were easier to see it against an unmoving background .

thanks so much all the other videos about water simulation is either way too complicated or just a blender tutorial

Imagine the kind of simulation you could do with a 4090 over the mac book.

Now I have to find someone to explain how to do that in Godot

do you think this could be used for electromagetics?

this thumbnail is better

11:11 that looks like the lines of a magnet.

This is really cool. Do you have a github repo available for this?

Could write conflicts also be avoided by just writing to a separate buffer fhan the one you are reading from?

this is so cool, is it possible to upload the source code to a public repo?

Very nice video. Now get a beefy graphics card and run at very high resolutions lol.

wait you need a macbook pro to do pro stuff?? (looks sexy)

How do you run these shader ? Can it use under sdl2?

Love this but if that’s how you say Euler I’ve been saying it wrong all this time 💀💀

Which method is cheaper to run?

"shaders are fun" consider me an opp

rather than updating a bunch of nonadjacent cells why don't you store two buffers, and instead of changing a cell's neighbors, instead calculate how a cell is affected by its neighbors, and write that into the second buffer.

I am trying to simulate aerodynamics of stl files in 3D space. But I haven't made it yet. Who can do such a thing?