Stable Fluids using the FFT in Julia | Fluid Simulation in Julia

The Stable Fluids Algorithm by Jos Stam can be sped up with the help of the Fast Fourier Transformation. Let's implement this in the Julia Programming Language. Here is the code: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/simulation_scripts/stable_fluids_fft.jl The Julia language provides a binding to the FFTW package, the "Fastest Fourier Transform in the West". And indeed, it is fast! Using the FFT together with periodic Boundary Condition (which you then need to have) greatly simplifies many steps in the Stable Fluids algorithm. In particular, you do no longer have to solve linear systems of equations for the implicit diffusion and the incompressibility projection. On top of that, you do not have to handle Boundary Conditions. ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-learning-and-simulation 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff: https://www.linkedin.com/in/felix-koehler and https://twitter.com/felix_m_koehler 💸 : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim ------- Introduction 00:00 Introduction 00:56 Scenario 01:48 Algorithm Overview 05:22 Package Imports 05:58 Constants 06:21 Some Boilerplate 06:31 Defining the 2D Mesh 08:14 Defining the wave numbers 10:18 Precomputing diffusion decay 10:09 Computing normalized wave numbers 12:20 Defining the force 14:19 Pre-Allocating the Arrays 16:15 Setting up time loop 16:39 (1) Apply Forces 18:00 (2) Self-Advection by streamline backtracing 23:45 (3.1) Transform to Fourier Domain 24:16 (3.2) Diffusion in Fourier Domain 24:50 (3.3) Compute Pressure in Fourier Domain 25:43 (3.4) Project to Incompressibility 27:40 Advance in time 27:54 Visualize 31:15 Bug Fixing 33:14 Discussion 34:00 Outro