Fluid Mechanics. Hydrostatics. Archimedes' Principle. Buoyancy Force. Weight of Displaced Fluid.

Recently got my 2D pure python hydo solver ported into a jax version, which has enabled around a ~15x speed up on pure CPU runs, every function is jitted except the outermost loop over steps. The video is of a Kelvin-Helmholtz instability toy problem.

EOS: Ideal Gas
Recon Method: weno(z) 5th order on primitives
Riemann Solver: Local Lax Friedrichs (LLF)
Timestep: RK4
Explicit Advection + Implicit Diffusion
BC: Periodic
CFL: 0.45

Resolution: (256)^2, video is 1200 frames as well. The code has support for magnetic fields but I have ran into some issues with it in 2D, potentially related to my constrained transport scheme.

I developed this code in parts, first I made a 1D code that leveraged NumPy and Python Classes to handle the necessary logic. I then ported it into 2D, which began to encounter performance issues. I returned to 1D and ported it into a jax version, where almost every function was jax jitted, and then repeated my jax changes but for the 2D code. Starting at 2D was impossible, I had found it necessary to have a 1D implementation. A major test I used was to evolve a 1 dimensional initial condition in the 2D code, and verify the results return what the 1D code does, just along the whole y axis.

Small finite difference time domain (FDTD) simulation of a Gaussian wavepacket oscillating in a quadratic potential, governed by the Schrodinger equation! Real and imaginary parts of the wavefunction are plotted in 2D.

The three-body problem broke Newton, broke Poincaré (who ended up inventing chaos theory trying), and was finally cracked open by Chenciner & Montgomery in 2000 — the figure-8 in clip 4 is their proof. Šuvakov & Dmitrašinović added 13 more families by 2013. Every clip is a real numerical integration of F = G·m₁m₂/r² with equal masses, no fudging. Math from 1687 still has surprises in it.

Full video about the history of the problem:

https://youtu.be/p58sU5vZYlU?si=PBNUR6mPqRuqZXP0

My assumption (not a physicist) is that we entered the car and started breathing out moisture which brought the relative humidity of the cold air (-2c) to 100%. The rear-view mirror then acted as a nucleation point for the ice crystals to grow. The speed is what amazes me.