Viewer request: Simulation of an asteroid impact off the coast of California @NilsBerglund

Nils Berglund | Viewer request: Simulation of an asteroid impact off the coast of California @NilsBerglund | Uploaded October 2024 | Updated October 2024, 4 minutes ago.
This simulation has been requested by a viewer, who wanted to see the effect of an asteroid impact "500 km off the coast of Santa Monica". They didn't say why, maybe it's because their mother in law lives there, but since I have the code ready, I am happy to oblige.
The simulation is based on a shallow water equation. The model includes lunar forcing accounting for tides, and allows for some flooding of land areas. The vertical scale of both mountains and waves has been exaggerated.
The main difference between the nonlinear equation and the linear wave equation is that the wave speed becomes larger when the water is shallower, which can lead to build-up of the waves in coastal and other shallow regions. This causes problems in the simulation, because land masses can lead to blow-up of the solution. This problem is circumvented here by replacing the continents by a repelling force field, plus a dissipative term. The initial state features velocities radiating outward from the impact point of the asteroid.
The shallow water equations are nonlinear equations, which give a better description of the motion of water than the linear wave equation. In particular, unlike the linear wave equation, they conserve the total volume of water. The linear equation gives an approximation of the solutions, when the wave height remains close to its average over space.
The equations used here include viscosity and dissipation, as described for instance in
en.wikipedia.org/wiki/Shallow_water_equations#Non-conservative_form , including the Coriolis force.
One difficulty is to model the wetting boundary, which separates regions that are under water and those which are not. This difficulty has been circumvented here by replacing the continents by a repulsive force field, directed downslope, instead of a sharp boundary.
The video has four parts, showing simulations at two different speeds and with two different visualizations:
Time lapse, 3D: 0:00
Time lapse, 2D: 0:14
Original speed, 3D: 0:29
Original speed, 2D: 1:26
The color hue and radial coordinate show the height of the water, on an exaggerated radial scale. The 2D parts use a projection in equirectangular coordinates. In the 3D parts, the point of view is slowly rotating around the Earth in a plane containing its center. In parts 1 and 2, the animation has been speeded up by a factor 4.
The velocity field is materialized by 2000 tracer particles that are advected by the flow. The tracers are randomly "respawned", by moving them to a random new location at random times. This is to avoid that particles concentrate in some areas, as has happened on some previous simulations.

Render time: 3D parts - 2 hours 2 minutes
2D parts - 1 hour 50 minutes
Color scheme: Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
github.com/BIDS/colormap

Music: "Frequency" by Silent Partner

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 2D shallow water equation by discretization (finite differences).

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!

#shallowwater #waves #Earth

An asteroid impact in the North Pacific Ocean, with tsunami-induced flooding

$Cherenkov radiation of an even faster particle In this third simulation of Cherenkov radiation, the speed of light in the medium has been reduced by a factor 1.5, compared to the one used in the video https://youtu.be/BpkKYLuwRlc . As a result, the shock wave created when the local speed of light becomes smaller than the speed of the particle occurs earlier. I dont have a good explanation for the envelope of the created wave, but I think it is due a combination of the space-dependent speed of light and interference of waves emitted at different times. If anyone has a more precise explanation, feel free to comment. Update: I finally found the origin of this singularity, which is, sadly, a mistake in the way I initialized the refractive index of the medium. Instead of decreasing linearly while remaining positive, the wave speed in the medium decreases linearly, then reaches zero, and then increases linearly again. The singularity happens where the wave speed vanishes. A corrected version will be released in a couple of days. Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum. In this simulation, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, reaches zero and increases linearly again. The ratio of the indices between the left to the right boundary of the simulation rectangle is 2.78. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:12 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. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, slightly below the path of the particle. Render time: 22 minutes 48 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: Meditation by Silent Partner 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 Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #Cherenkov #shock_wave$ $A slightly refracting magnetron-shaped resonator at higher wavelength$ $Cherenkov radiation Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum. In this simulation, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, reaches zero and increases linearly again. The ratio of the indices between the left to the right boundary of the simulation rectangle is 2.75. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation. Update: I finally found the origin of this singularity, which is, sadly, a mistake in the way I initialized the refractive index of the medium. Instead of decreasing linearly while remaining positive, the wave speed in the medium decreases linearly, then reaches zero, and then increases linearly again. The singularity happens where the wave speed vanishes. A corrected version will be released in a couple of days. This video has two parts, showing the same evolution with two different color gradients: Wave height: 0:00 Averaged wave energy: 1:07 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. There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, slightly below the path of the particle. Render time: 34 minutes 41 seconds Compression: crf 23 Color scheme: Part 1 - Twilight by Bastian Bechtold https://github.com/bastibe/twilight Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt https://github.com/BIDS/colormap Music: Led Foot by Ethan Meixsell 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 Marco Mancini and Julian Kauth for helping me to accelerate my code! #wave #Cherenkov$

Growing quasicrystals from pentagons in a central gravity field

Magnetized squishy squares clogging a funnel