Refraction and reflection of a shock wave - Source in the lower speed medium @NilsBerglund

Nils Berglund | Refraction and reflection of a shock wave - Source in the lower speed medium @NilsBerglund | Uploaded September 2024 | Updated October 2024, 1 hour ago.
This variant of the simulation youtu.be/fQV6vgF9vSI shows again shock waves created by a source traveling faster than the wave speed in a medium, near an interface to a medium with different wave speed. However, here the wave speeds have been reversed.
The lower medium has relative refractive index 0.667 (the wave speed is 1.5 times faster in the lower part). As a result, part of the shock wave is refracted, changing its angle in the second medium, while part of it is reflected. The relative intensity of the reflected and refracted parts depends on the angle between shock wave and interface.
This video has six parts, showing the evolution with three different speeds of the source, and two different color gradients for each speed:
Speed 1, wave height: 0:00
Speed 1, averaged wave energy: 0:44
Speed 2, wave height: 1:36
Speed 2, averaged wave energy: 2:19
Speed 3, wave height: 3:12
Speed 3, averaged wave energy: 3:56
In parts 1, 3 and 5, the color hue depends on the height of the wave. In the other parts, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used on videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.

Render time: Part 1 - 17 minutes 5 seconds
Part 2 - 15 minutes 58 seconds
Part 3 - 16 minutes 2 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap

Music: "Stardrive" by Jeremy Blake@RedMeansRecording

See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ 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 hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #shock_wave #sonic_boom

$Refraction and reflection of a shock wave - Source in the lower speed medium$

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