Simulation of a meteor impact in the Atlantic Ocean @NilsBerglund

Nils Berglund | Simulation of a meteor impact in the Atlantic Ocean @NilsBerglund | Updated October 2024, 3 hours ago.

$When waves crossing a square lattice have a larger phase than group velocity The simulation https://youtu.be/15fpsopRyn8 , that showed waves from two different sources having different frequencies cross a regular square grid of obstacles, revealed another interesting feature: After a while, the waves from the source with a lower frequency seemed to propagate through the lattice at a larger speed than the wave speed. This has to be an instance of the situation where the phase velocity (measuring how fast wave fronts move) is larger than the group velocity (measuring the speed of energy transfer). This video focuses on this phenomenon, by using only one source, having the lower frequency, and an additional plot of the signal in the x-direction. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:16 In the first part, the color hue depends on the height of the wave. In the second part, 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. There are absorbing boundary conditions on the borders of the simulated rectangle. The displays at the right and bottom show a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy). Render time: 30 minutes 28 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 https://github.com/BIDS/colormap Music: Future Girl by RKVC@rkvc 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 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 Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #diffraction #phase_velocity$

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$Classics revisited: A parabolic resonator This is a remake of the video https://youtu.be/AUPhTGrukHY of a parabolic resonator with four sides, in much higher resolution, and with a pulsing source. The resonator is made of four parts of parabolas, which share the central point as a common focus. Whenever a circular wave centered at the focus hits a parabola, it is transformed into a linear wave. When this linear wave hits another parabola, it is transformed back into a circular wave, converging at the focal point. This pattern repeats almost periodically, except that diffraction effects (and probably also some numerical dispersion) slowly degrade the pattern. This video has two parts, showing the same evolution with two different color gradients: Averaged wave energy: 0:00 Wave height: 1:40 In the first part, the color hue depends on the energy of the wave, averaged over a sliding time window. In the second part, it depends on the height of the wave. Render time: 21 minutes 9 seconds Compression: crf 23 Color scheme: Part 1 - Inferno by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Part 2 - Twilight by Bastian Bechtold https://github.com/bastibe/twilight Music: Twisted Bandits All Around Me by NotMBe@nombe See also https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations. The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf C code: https://github.com/nilsberglund-orleans/YouTube-simulations https://www.idpoisson.fr/berglund/software.html Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #resonator$ $Waves of two different frequencies crossing a regular square lattice In this simulation, we compare the effect of a regular square grid of scatterers on sources of different frequency. Not so surprisingly, the waves pass the lattice more easily than in the case of a random lattice, and one can observe some interesting resonance effects. The frequency of the lower source is three times the frequency of the upper one. The resulting wavelengths are such that the open intervals in the grating are roughly between both wavelengths. As a result, waves of the lower source pass the grating a bit more easily, as can be best seen on the energy plot. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:11 In the first part, the color hue depends on the height of the wave. In the second part, 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. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows a time-averaged version of the signal near the right boundary of the simulated rectangular area. More precisely, it shows the square root of an average of squares of the respective field value (wave height or energy). Render time: 28 minutes 38 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 https://github.com/BIDS/colormap Music: Ghost Cop by Dougie Wood 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 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 Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #diffraction #grating$

Transition from symmetric to asymmetric rock-paper-scissors-lizard-Spock equation on the sphere