Скачать с ютуб Wave protection comparison 8: "golden spiral" versus Poisson disc sampling with a step input в хорошем качестве

Wave protection comparison 8: "golden spiral" versus Poisson disc sampling with a step input

Like the video    • Wave protection comparison 7: "Golden...  , this simulation compares the "golden spiral" (or "sunflower") grid, and a Poisson disc sampling arrangement, both with about 160 obstacles. This time, however, the initial state is not a sharply localised planar wave, but a "step function", that could model a sudden rise of water level, due for instance to a breaking dam. I made the obstacles refracting instead of reflecting, with an index of refraction of 5. This is because the purely reflecting (Dirichlet) boundary conditions I often used do not give a very realistic result in this setting. One should rather use some type of Neumann boundary condition (vanishing derivative instead of vanishing wave height), which are however harder to implement with the discretization method used here. There is also some dissipation inside the circles. The colors represent the wave height: orange and yellow means high water, violet means a lower water level than at rest. The numbers in the four corners and at the top and bottom show the total energy in areas at the left and at the right of the obstacles, as well as in the area occupied by obstacles, compared to the energy of the incoming wave. There are periodic boundary conditions on the top and bottom sides of the displayed domain, and absorbing boundary conditions on the sides, which however don't work perfectly, explaining why you see some waves reflected from the boundary. Music: "Crater Laker" by the Mini Vandals‪@theminivandals1840‬ 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 my colleague Marco Mancini for helping me to accelerate my code!