Navier–Stokes equation (2D incompressible), solved live numerically on a discrete grid ρ (∂u/∂t + u·∇u) = −∇p + μ Δu + f, ∇·u = 0 The ink (the white stuff on the left) is added so you can see the motion of the fluid.

Nice live visualization of the equations! Here’s a real-world laminar → turbulent transition in the Isar Canal (single frame vs. average from a 4K video).

Built something similar a while ago for reaction-diffusion patterns!

I enjoyed this.

I’ve watched this over and over, and it never gets boring

The contest/prize is rigged though because nature and reality is not smooth. Any thoughts on that?

Where is cascade to larger scales? 2D turbulence is very different from 3D turbulence. The movie says nothing about the correctness of the simulation

PhDad. Appendix A, Project 2 Navier Stokes Solution

What does this conjecture try to prove/disprove...sry, im lost

Awesome 👏

nice!

Now do 3D

Thats interesting as i dont see the way you designed said grid. I happen to know the only determanistic grid that can do this because i built it....the question then becomes why...

That looks very fractaly.

How about air over an airfoil, Reynolds number ~10^6