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Navier-Stokes fluid simulation explained with Godot game engine

89 points by myzek 4 days ago | 20 comments

If you haven't tried Animal Well, give it a shot. The whole game and its custom engine are like 35MB and it's filled with really cool visuals and physics powered by fluid equations.

https://store.steampowered.com/app/813230/ANIMAL_WELL/

markstock 13 minutes ago

Before you go adding vorticity confinement, consider performing a higher-order backward advection scheme (Runge-Kutta 2nd or similar), and using a higher-order interpolation method (triangle-shaped cloud instead of bilinear).

In my implementations I use 4th order for both and vortices stick around a lot longer.

genxy 2 hours ago

The unlinked Jos Stam paper is available from his website https://www.dgp.toronto.edu/public_user/stam/reality/Researc...

amarant 34 minutes ago

This is great! When I have some leftover time I want to try copying this implementation for 3D. I reckon I could get away with minimal modifications to support the third axis...I think...

That'll perform even worse though, hopefully my CPU can handle it or I'm gonna need a lot of leftover time to make a shader

markstock 16 minutes ago

You are correct: Stable Fluids extends to 3d relatively easily.

myzek 4 days ago

So once upon a time I stumbled upon simulating fluids in gamedev and I really wanted to learn how it works. Fast forward 2 months and I decided to write down everything I learned to hopefully make it easier for others in the future!

magicalhippo 4 days ago

Fluid sims are just so darn fun! Nice writeup, very accessible.

Couple of notes, I think you forgot to apply timestep when adding rocket exhaust velocity, pretty sure it should be

  u[idx] += backward.x * flame_velocity_amount * falloff * delta
  v[idx] += backward.y * flame_velocity_amount * falloff * delta

You need to compensate by scaling up flame_velocity_amount, I used 85, seemed about the same.

myzek 4 days ago

Yeah it seems I missed that, adding the rocket at the end was a cherry on the top and I was so exhausted already I'm surprised it even works lol

magicalhippo 3 days ago

It made it very fun to play with though :D

brandonpelfrey 2 hours ago

Great job. I have spent a lot of time working on fluid simulations (I still am). Glad to see more people still mesmerized. If you’re interested, this rabbit hole goes very deep.

nick__m 3 hours ago

excellent article, great vulgarisation and human written !

Thank you

Stevvo 3 hours ago

For anyone wanting to dive further, Fluid Simulation for Computer Graphics by Robert Bridson is the definitive textbook.

amelius 3 hours ago

Did they test if it satisfies the relevant conservation laws?

brandonpelfrey 2 hours ago

It won’t satisfy those laws. It’s also not a goal though of this post.

amelius 2 hours ago

I mean if you're writing a ray tracer and the reflected light has more intensity than the light sources, then that's not desired. You can have the same sort of thing going on with a fluid simulation.

markstock 17 minutes ago

One of the nice aspects of Stable Fluids is that you don't need to iterate the pressure correction terms to convergence. Just run a fixed number of Jacobi or Gauss-Seidel sweeps and keep performance consistent. The only drawback of this is some mass loss in areas, which for the present purposes is acceptable.

frankdlc222 4 days ago

This is really cool. I love how much detail you went into explaining the setup and walking through each piece of the simulation. Definitely bookmarking this to play around with later!

analog8374 3 hours ago

Oh don't let us pinch zoom. That would be a disaster.

zamadatix 2 hours ago

Assuming you mean the site - pinch zoom & pan works for me on Windows and iOS?

analog8374 2 hours ago

well android chrome doesn't

nryoo 3 hours ago

[flagged]