Vortex ring example simulation

[EdoAlvarezR]

In this PR I have updated test/vortex.jl to work with the latest changes in main, and added a script under /example-vortexring.jl with a vortex ring simulation.

To run the simulation, just run the following in the terminal:

julia path/to/FastMultipole/scripts/example-vortexring.jl

The vortex ring simulation shows that the FMM is introducing some spurious calculations that throw down the structure of the ring:

The spurious calculations become obvious at the boundaries of the clusters, and increasing the expansion order does not seem to have an effect in decreasing the error that is introduced by the FMM:

As a reference, here is the same simulation without the FMM (just the direct! function):

It is unclear if at this point there is something wrong in the implementation of the FMM, or perhaps the FMM is introducing numerical-precision noise that throws off the symmetry of the problem. In the case of the later, there isn't much to do about it, and perhaps Pedrizzeti's relaxation would help smooth away such numerical noise.

[rymanderson]

It looks like the convect! function fails to set lamb_helmholtz=true, which is required for vector potential problems, and likely what is leading the simulation to fail. There might be other issues in the example file vortex.jl, since I created that example very early on in the development of FastMultipole, and have since changed the way FastMultipole returns the velocity gradient (before I returned the entire hessian of the potential functions). I haven't tested the time integration in over a year. I'll take a look and will reopen this pull request after that's fixed.

[rymanderson]

Incidentally, I have already incorporated FastMultipole into the derivatives branch of FLOWVPM, and the vortex ring tests work there.
https://github.com/byuflowlab/FLOWVPM.jl/blob/master/test/runtests_singlevortexring.jl
https://github.com/byuflowlab/FLOWVPM.jl/blob/master/test/runtests_leapfrog.jl

[rymanderson]

The unsort! operation was broken due to faulty access functions in the vortex.jl example file, so particles were getting scrambled. I fixed that, and it looks like it works. Note that this is with an expansion order of 4.