Bragg diffraction

Описание: Bragg diffraction is another item that has been suggested several times in comments, and was on my to do list. So here is my first take on it, thanks to a recent comment that reminded me.
Bragg diffraction (see for instance https://en.wikipedia.org/wiki/Bragg%2... ) occurs when a wave encounters a regular lattice, for instance a crystalline solid. Depending on the wave length, the angle of incidence of the wave, and the geometry of the lattice, interference of the reflected waves can create various patterns, that allow to deduce properties of the lattice.
In this simulation, the lattice consists in 40 columns of 8 perfectly reflecting scatterers. One can note that the wave is reflected more in specific directions, and that the direction of propagation inside the lattice is different from that of the incoming wave. Note that the picture may look different a larger distance away from the lattice.
The video has two parts, showing the same simulation with two different color schemes:
Wave height: 0:00
Average energy (log scale): 1:53
In the first part, the color hue shows the wave height. In the second part, it shows the energy, averaged from the beginning of the simulation, on a logarithmic scale. There are oscillating boundary conditions on the left side of the simulation, and absorbing boundary conditions on the other sides.

Render time: 31 minutes 38 second
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music: "Sixteen Twenty Five" by Text Me Records‪@socialxwork‬

See also https://images.math.cnrs.fr/Des-ondes... 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...
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave_equation #waves #diffraction #Bragg_diffraction