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/

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.

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

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

  last Wednesday at 12:54 AM

  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

    last Wednesday at 8:39 AM

    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

      last Wednesday at 10:08 PM

      It made it very fun to play with though :D

• brandonpelfrey

  today at 3:49 PM

  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

  today at 2:32 PM

  excellent article, great vulgarisation and human written !

  Thank you

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

  today at 5:03 PM

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

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

Did they test if it satisfies the relevant conservation laws?

• brandonpelfrey

  today at 3:48 PM

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

  • amelius

    today at 4:09 PM

    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

      today at 5:02 PM

      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.

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!

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

• zamadatix

  today at 3:27 PM

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

  • analog8374

    today at 3:34 PM

    well android chrome doesn't

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