Thanks, Brian!
I'm developing my own
fluid dynamical simulation software from scratch, but stuff is non-trivial, so I'm serving myself of the shoulders of giants from a methodological point of view. Like in many other cases, you can really understand things only, if you implement them yourself. Better if you even develop the required methods yourself, and go through all the flaws and glitches you can make. The time step in
the excerpt I've submitted to missionjuno is 1 hour, but the full version is calculated with fixed steps of 6 minutes. In order to keep the file size within reasonable limits, I've taken just each 10th image, and reduced it by a factor of 2. The method is grid-free on an inviscid flat 2D
Biot-Savart approach with a
stream-function-derived 2D
vorticity field of the south polar region of PJ19 as initial condition of an initial value problem. Algorithmic complexity is O(tnē), with n the number of 4th order "Gauss-
mollified" "
vortons" and t the number of time-steps. I'm using single-step multi-stage explicit
Runge-Kutta methods with fixed time-steps of order 4 or 5 for numerical integration of the ODEs.
Dormand-Prince methods are useful to test for the quality of the convergence of the integration.
I'm working on a
2-spherical version in order to get a little more realistic. Simulating on the precise IAU Jupiter 2-spheroid might be algorithmically expensive, and difficult to implement, because of the according
geodesic problem. I'm exploring how far I can go within reasonable computational and implementation costs. Even the 2-sphere simulation is much slower(but still O(tnē)) than the flat euclidean 2D plane.
There is much more to tell, maybe within a presentation on one of the conferences this year, provided I'll get an abstract submitted in time.
Finite volume methods on a grid appear less suitable in a very turbulent regime. They tend to get numerically unstable for large
Reynolds numbers unless very short time steps are applied (see
von Neumann criteria).
Some simulations of turbulence favor
VIC (vortex in cell) methods. I've still to decide, whether I'll test this family of methods, too. But those hybrid methods are more difficult to understand, and I'm not yet quite sure, whether I'd been able to modify the required
Poisson solver for non-euclidean geometry within short time, if necessary. So, my first choice is the above approach, which I already understand sufficiently well to modify it according to my requirements.
If you are interested in a good introductory paper, I'd recommend
Cottet & al "Vortex Methods, Theory and Practice".