resolution of g-modes

[higl]

With the test_stability problem we found out, that maestro is not doing very well around peaks in the brunt-vaisala frequency (N). We attributed this to unresolved (reflected, interacting ....) g-modes in these areas.

Fabian Miczek proposed a much simpler test setup in his PhD thesis where one follows a single g-mode in a stably stratified ideal gas with constant N. Such a wave should move at a constant amplitude with constant speed, which gives us the chance to compare the code to this analytic solution.

I set up this problem (g_wave_package) in my fork in the commit 9ee6406 . (including a notebook for a quick first analysis)

An amplitude decrease is somewhat expected due to numerical dissipation, but the one found here seems a bit large. On the other hand, it looks like we can resolve the speed rather well (at least for small dt), but for some reason the wave splits and moves in both directions (which might explain the amplitude decrease).

[zingale]

can you do a PR with this problem and the script to produce the plot comparing to analytic?