Wave protection comparison13: Triangle pointing right vs gradually rotated triangles
Channel: Nils Berglund
Date: 2022-01-02

This new comparison of wave protection arrangements based on triangles implements a suggestion from the comments, which is to turn the triangles slightly from one column to the next.The top panel shows triangles placed on a triangular grid, and pointing to the right. We have seen in the previous comparison https://youtu.be/jkA7UokqZWk that the triangular grid is more effective than the square grid, which in turn performs better than a square grid of triangles pointing left, see https://youtu.be/C-bDmzeO12k . In the bottom panel, the triangles in each column are rotated a constant angle compared to the previous column, in such a way that the triangles in the last column point to the left. The size of the triangles has been slightly decreased compared to previous simulations in this series, to let more energy pass. 
While this arrangement is not as efficient as the random one seen in the simulation https://youtu.be/XZvUMExbTz0 , it does perform slightly better than the regular arrangement at the top. 
The colors indicate the wave's energy, according to the color bar on the right. The numbers at the top, bottom and corners indicate, for each panel, the total energy in the area filled with obstacles, at its left and at its right. There are periodic (wrap-around) boundary conditions between the top and bottom of each panel, and (imperfect) absorbing boundary conditions on the left and right boundaries. 

Render time: 46 minutes
Color scheme: Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music:  Local Forecast by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1300010
Artist: http://incompetech.com/

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 
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!