Nils Berglund | Simulation of an asteroid impact between Ireland and Newfoundland @NilsBerglund | Uploaded October 2024 | Updated October 2024, 2 hours ago.
This new simulation of an asteroid impact assumes the asteroid falls into the North Atlantic ocean about halfway between Ireland and Newfoundland, more to the north than in the previous simulation youtu.be/cr3rCxjWL4k of a North Atlantic impact. The simulation includes a respawning of tracer particles, which gives a better idea of the velocity field.
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: 0:16
Original speed, 3D: 0:32
Original speed, 2D: 1:38
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 26 minutes
2D parts - 2 hours 18 minutes
Color scheme: Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
github.com/BIDS/colormap
Music: "The Arid Land" by Sir Cubworth@SirCubworth
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
This new simulation of an asteroid impact assumes the asteroid falls into the North Atlantic ocean about halfway between Ireland and Newfoundland, more to the north than in the previous simulation youtu.be/cr3rCxjWL4k of a North Atlantic impact. The simulation includes a respawning of tracer particles, which gives a better idea of the velocity field.
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: 0:16
Original speed, 3D: 0:32
Original speed, 2D: 1:38
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 26 minutes
2D parts - 2 hours 18 minutes
Color scheme: Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
github.com/BIDS/colormap
Music: "The Arid Land" by Sir Cubworth@SirCubworth
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
