Stan's Stable Fluid Simulation

This is my from scratch implementation of Jos Stam's Stable Fluids method, based on the paper included in this repository

I was mainly doing this to understand how the method actually works rather than just following an existing implementation

Stuff I used

• Stable Fluids Paper - this implementation is based on this paper attached in the repo
• The Visual Room - Poisson equation for pressure - helped me understand the pressure and projection part
• LLM - used to explain things like gradients and laplacians because I had never really worked with them before

Most of the functions are in main.py and have comments explaining what they are doing and which equation from the paper they correspond to

The simulation

This is what is currently looks like:

fluid_simulation.mp4

It's not the prettiest fluid simulation ever made, but it works well enough for me to see what the Stable Fluids method is doing

Implementation

The main steps are:

• Advection -> trace backward through the velocity field and interpolate
• Diffustion -> solve for the new velocity field
• Projection -> make the velocity field divergence free
• Extras -> Added some dye and density to make the simulation look good

This whole thing is in main.py

Performance

It's a bit clanky.

The whole simulation is written in python with a bunch of regular loops over the grid, and I haven't done any NumPy vectorisation or other optimisation

I'm much more comfortable with C++ than NumPy, so if I get some time I'll probably rewrite this in C++ and see how faster it gets

Prbably will do the math of what was slow when I rewrite..

Running it

Simple -> after installing all the required modules (just matplotlib)

python main.py

That's pretty much it

The code is definitely not perfectly structred - I wrote it from scratch while working through the paper in roughly a day, so expect some questionable code choices.

But it works, and more importantly, I understand it.