17 - How to write an Eulerian fluid simulator with 200 lines of code.

In this tutorial I explain the basics of Eulerian, grid-based fluid simulation and show how to write a simulation engine based on these discussed concepts.

[Pjx]

As a fluid dynamic engineer, I’m very aware of the complexity of CFD. It’s absolutely stunning not just that you wrote a basic cfd code in 200 lines, but that it even runs on a browser and, most of all, that you could explain it in 10 minutes. Astonishing

[TenMinutePhysics]

Hi all, thanks so much for all your positive feedback! A great motivation to do more videos!

[CosineKitty]

This is exactly what I have wanted to understand for years now. I have long thought it would be so cool to simulate a lava lamp, or the waves on the surface of a swimming pool. Every time I try to read about fluid mechanics, it's page after page of differential equations. You have made this so clear and intuitive. Thank you so much!

[notapplicable]

These videos are such a nice breath of fresh air after reading simulation papers

[joepeters]

I know that you have little views, but the content you makes me delightet! It is very hard to find University level tutorials or explanations for fluids and softbodies, so your well made videos are a treasure!
Especially for me as a Games Engineer it is very funny to know the math and algorythms.

[rstknives]

Everything is easy when you are both a programmer and a physicist

[kathmanducity]

I have been looking for this eloquent lecture for the last 15 years.

[texloch]

I'm a programmer and aerospace engineer. Love this video and it's simplicity. For clarification though, the full code is 700+ lines, although I give credit to the fact that only 200+ are needed for the fluid flow mathematics. Thanks for sharing and please keep making content.

[snsacharya]

A great video for aspiring numerical analysts. Amazing to see how you covered incompressibility to the Gauss-Seidel method within 10 minutes and a code that demonstrates all that 👏

[alansmithee]

Something I've noticed in my physics course is that simulations of complex systems can be incredibly simple.

The difficult bit is determining what is the best way to program something, so that it is both accurate and has reasonable computation costs. The programming itself will almost invariably result in a very short program.

From what I can tell the huge thousands-of-lines projects that people spend years developing are tools which have many different methods of doing many different things for many different purposes. Each thing is short, the collation of them all into one widely useable toolkit so that no one ever has to code any of it again is not.

[pixel_physics]

Ohh my, i never thought i will see a tutorial from THE Matthias Müller. Im such a fan of your works and papers! You are probably the most cited person in my bachelor and masters thesis - both about fluids. And damn i like your research. So awesome!
Keep up your work! Youre freakn awesome in what youre doing!

[lamienkassienou]

I didn't ask for more. What can I say except a very big thank you. Tank you really.

[erang]

Love your videos, Matthias! Such a great initiative to create this video series, and to use web-based tech so that it's easy to play around with your interactive demos. Keep up the great work. ~ Eran.

[georgen]

Fluid pressure in a tank demo
Advection
Pressure distribution
Guass seidel method
Water tunnel
Wind tunnel

Divergence = 0
Pixels
Pixels of television
Depends on the resolution of the television

Great sir thank you

[jds]

I just stumbled on your channel. It is great how much good explanations you pack into a dozen minutes. I will recap all the videos in your series and try out the code.

[halihammer]

Thank you so much for this information! This is such valuable content for people who are interested but don't have the opportunity or time to acquire this knowledge at a university or by reading specialist literature!

[AlienXtream]

THANKYOU! SO many talks about fluid simulations (and fluid/water in general) mistakingly claim (orimply) that water *is* incompressable. this is the first time i've seen someone correctly assert its "functionally incompressable" XD

[abonham]

Quite appreciate the way you articulate variables. “Boldface V”, “italic u and v”. Great work

[joxterjones]

Great video, thanks for posting this. I first wrote a MAC-type simulation for incompressible viscous flow back in the early 1980's. Seeing what you have done in 200 lines of code is amazing - we have come a long way! Your explanations are excellent and are a first rate introduction to a complex topic.

[veitheld]

Awesome! That is the little programm that I always wanted to write myself to simulate the flow around airfoils or sails, but I never managed to get this done. I got a s far as translating the equations to discrete cells, but then I always ended up with very large scarce equation systems, which needed an engine like Matlab to solve. Your choice of the staggered grid and all the other tricks are so elegant and make the solution so lean and efficient. Too bad that you did not post this video years ago, it would have saved me a lot of time. Great job!! Now I am looking forward to your solution of the full Navier-Stokes equations. OK, I'll give you a budget of 300 lines of code for that...😀