How much flooding would an asteroid impact in the Indian Ocean cause?
This simulation uses the same impact point of an asteroid in the Indian Ocean as in the video • Simulation of an asteroid impact in t... , but instead of being reflecting, the Earth's continent are assumed here to have a large index of refraction - the wave speed is assumed to be 25 times smaller over land than on the open seas. I'm afraid Bangladesh does not fare very well...
The simulation can be seen as a crude model of the effect of a meteor impact. Note however that several factors, such as the Coriolis force, dissipation, shallow areas near the coast, and ice sheets are not taken into account. The vertical scale has been exaggerated to make the waves and mountain ranges more visible. The point of view follows a polar orbit.
To make this simulation, I used the so-called Blue Marble Earth map, available at https://en.wikipedia.org/wiki/File:Bl... , in 2,560 × 1,280 resolution. I identified the dominant color of the Oceans, and declared all pixels having a nearby color as being in the domain of the wave, while the other pixels' color is used to draw the continents. A few areas of shallow sea with a different color appear therefore as parts of the land masses.
The land masses have been drawn with a varying altitude, which has been greatly exaggerated for visibility. The altitudes are taken from the digital elevation model (DEM) available in the file https://commons.wikimedia.org/wiki/Fi... , also in 2,560 × 1,280 resolution.
Simulating the wave equation on a sphere is rather similar to the planar case, except that the Laplacian is written in spherical coordinates. A difficulty is that the Laplacian is singular at the poles of the sphere, which induces some numerical instability. The fix used here is a combination of a regularization of the Laplacian at the poles and an averaging procedure around the poles. While it avoids blow-up, it does not completely prevent the north pole from deforming the wave.
The video has four parts, showing the same simulation with two different color schemes two different playback speeds:
Wave height: 0:00
Average energy: 1:44
Wave height (time lapse): 3:44
Average energy (time lapse): 4:19
In the first and third parts, the color hue and the radial coordinate show the wave height. In the second and fourth part, they show the energy, averaged from the beginning of the simulation. In parts 2 and 4, the playback speed has been multiplied by a factor 3.
Edit: As pointed out in a comment, a (controversial) hypothesis made by a group of Earth scientist proposes that prehistoric sand dune formations in Madagascar and western Australia are the result of a mega-tsunami caused by an asteroid impact in the Indian Ocean, at a location not too far from the one used in this simulation. See https://en.wikipedia.org/wiki/Burckle...
Render time: 1 hour 35 minutes
Color scheme: Parts 1 and 3 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric firing
https://github.com/BIDS/colormap
Parts 2 and 4 - Parula, originally from Matlab
https://www.mathworks.com/help/matlab...
Music: Despair and Triumph by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/...
Source: http://incompetech.com/music/royalty-...
Artist: http://incompetech.com/
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!
#asteroidimpact #asteroid #wave_equation
