Empyreal092
commented
5 months ago Thanks! I have heard of these works and maybe I should mention them in Section 1.1.4. I heard they have simulated Moosinesq convection.
In my limit research, the volume penalty method is not perfect. For example in Eric's paper they achive second order accuracy, which is far from the ideal of a spectral method (spectral in space). I am also not sure how difficult it is to use it for different equation sets. Does it work nicely with 2D Euler type where we need to do an elliptic inversion? It seems these are research level questions and not suited for a pedagodical note like this one.
Also immersed boundary methods of the Courant variety is a different method.
This is very random comment and probably not helpful, but I was reading your section 1.1.4 and remembering something that one of the Dedalus devs had mentioned years ago. He had told me that boundaries are no problem, as they can always be put in using immersed boundary methods: https://www.math.ucla.edu/~ehester/project/volume-penalty-method/ . I seem to remember that these also used to be an example where some flow was solved in a box, where the box was embedded inside a sphere (and basically part of the sphere was solid). However, I can't seem to locate this example anymore. Edit: Ok located it here: https://arxiv.org/pdf/1903.12642.pdf