Extending the Stable Fluids Algorithm with the FFT in Julia to 3D

Описание: 3D Stable Fluids is a way to perform "unconditionally stable" fluid simulation. If we have periodic boundary conditions, it can be vastly simplified by the Fast Fourier Transformation (=FFT). Let's extend the Julia code to 3D and visualize with Paraview. Here is the code: https://github.com/Ceyron/machine-lea...

The Stable Fluids with the FFT is a way to solve the Navier Stokes Equations, which are Partial Differential Equations that define fluid mechanics. In a previous video (   • Stable Fluids using the FFT in Julia | Flu...   ) we coded a two-dimensional version in which we used the Plots.jl package to visualize the 2D curl while simulation. Now, we want to write out vtk files for our three-dimensional extension to then load them into Paraview, a proven software for three-dimensional transient scientific visualization.

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📝 : 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-lea...

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Timestamps:
00:00 Introductions
01:07 What changes in 3D?
02:01 Import changes
02:41 Constants
00:47 Recap on the 2D
03:23 Auxiliary Functions
03:55 Mesh
04:46 Wavenumbers
05:48 Forcing
08:49 Pre-Allocations
09:26 Trajectory Containers
10:06 (1) Force Application
10:22 (2) Semi-Lagrangian Advection
11:16 (3) Diffusion & Incompressibility
12:08 VTK Write-Out instead of interactive visualization
13:14 WriteVTK (Paraview Collection with time steps)
16:15 Executing the new file
16:50 Exploring the created files
17:14 Paraview: Loading the saved dataset
17:44 Paraview: Velocity Magnitude Volume Rendering
19:07 Paraview: Playing with Transfer Function
20:43 Paraview: Computing Vorticity (=Curl)
21:38 Paraview: Vorticity Magnitude Volume Rendering
22:43 Paraview: Changing the Color map
23:23 Outro