5 ms·

Could you write a blogpost-style article on how to model the shallow water wave equation on a sphere? The article would start with the simplest possible method,

• neumann 2y ago
  If you are interested in this, I'd recommend following an openfoam tutorial, c++ though. You could do SWE with finite elements, but generally finite volumes would be your choice to handle any potential discontinuities and is more stable and accurate for practical problems. Here is a tutorial. https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPilqvist/johanPilqvistReport.pdf https://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2010/johanPi...
  • akomtu 2y ago
    I'm looking for something like this, but more advanced. The common problem with such tutorials is that they stop with the simplest geometry (square) and the simplest finite difference method. What's unclear to me is how do I model the spherical geometry without exploding the complexity of the solution. I know that a fully custom mesh with a pile of formulas for something like beltrami-laplace operator would work, but I want something more elegant than this. For a example, can I use the Fibbonacci spiral to generate a uniform spherical mesh, and then somehow compute gradients and the laplacian? I suspect that the stability of FE or FV methods is rooted in the fact that the FE functions slightly overlap, so computing the next step is a lot like using an implicit FD scheme, or better, a variation of the compact FD scheme. However I'm interested in how an adept in the field would solve this problem in practice. Again, I'm aware that there are methods of solving such systems (Jacobi, etc.), but those make the solution 10x more complex, buggier and slower.
• fastasucan 2y ago
  Interesting that this reads almost like an chatgpt prompt.
  • gwern 2y ago
    Lazy people have been lazy forever. I stumbled across an example of this the other day from the 1990s, I think, and was shocked how much the student emails sounded like LLM prompts: https://www.chiark.greenend.org.uk/~martinh/poems/questions.html https://www.chiark.greenend.org.uk/~martinh/poems/questions....
    • MichaelZuo 2y ago
      It reminds me of the old joke that half of the students are below average…
      • wombatpm 2y ago
        Expect in Lake Woebegone, all of the children are above average
      • meindnoch 2y ago
        But that's not true, unless by "average" you mean the median.
        • KeplerBoy 2y ago
          Normally, it's all the same.
          • meindnoch 2y ago
            Only if the distribution has zero skewness. Unless "normally" you mean the normal distribution, which indeed has zero skewness.
            • KeplerBoy 2y ago
              Yes, it was a admittedly bad pun.
    • pixelpoet 2y ago
• CamperBob2 2y ago
  "As an AI language model, I am happy to comply with your request ( https://chatgpt.com/share/6727b644-b2e0-800b-b613-322072d9d33f https://chatgpt.com/share/6727b644-b2e0-800b-b613-322072d9d3... ), but good luck finding a data set to verify it, LOL."
• sampo 2y ago
  > Could you write a blogpost-style article on how to model the shallow water wave equation on a sphere? Typically, Finite Volume Method is used for fluid flow problems. It is possible to use Finite Element Methods, but it is rare.