Waves colliding with a hexagonal grid
Channel: Nils Berglund
Date: 05/07/2021

This variant of the video https://youtu.be/yt3T4ZaAJas shows a wave interacting with a hexagonal lattice of circular obstacles, as opposed to a square lattice. Here the color scheme represents the wave height instead of the energy density. I realize this makes comparison difficult, but I plan to make a few side by side comparisons that will show any differences more clearly. This simulation gives a good indication of how the lattice of scatterers is able to store the energy for some time, thereby spreading the waves' impact over a longer time period. 

Music: "A Trip Around the Moon", by Unicorn Heads@UnicornHeads

See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on  a few previous simulations of wave equations. 

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf 

Reflections on the boundaries of the rectangle are minimized by adding Neumann-type boundary conditions on the time-derivative of the wave.
C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html 
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!