Add support for omega sphere transport tests

[cbegeman]

Add omega support for the sphere_transport test suite

Checklist

• Testing comment in the PR documents testing used to verify the changes

[cbegeman]

Testing

Test suite has been run on chrysalis, intel-impi with omega. All tests fail because they do not meet the order of convergence.

rotation_2d has 1st order convergence
correlated_tracers_2d, divergent_2d and nondivergent_2d do not converge

I tried reducing the time step by a factor of 2 and it did not affect convergence rates.

[xylar]

@cbegeman, could you post images of the beginning and end states at the highest resolution? It could really be that the centered advection we currently have is not convergent for these more rigorous tracer tests with small-scale tracer or velocity-field structure.

This, in turn, would point to the urgency of higher-order tracer advection that we discussed on Monday.

[cbegeman]

This test suite appears to be performing appropriately for Omega.

rotation_2d is the case that is closest to the cosine_bell test case; cosine bell tracer distribution and a rotational field. It has convergence of 1.685 whereas the cosine_bell case has convergence of 1.364. For MPAS-Ocean with 2nd order advection, the rotation_2d case has convergence of 1.711 and the cosine_bell case has convergence of 1.364.

[xylar]

Thanks @cbegeman. This looks good to me. The code also looks good. Let me know when you think this is ready for review.

[xylar]

@cbegeman, this looks excellent! Thanks for taking the time to work on this.

I was able to run all 8 tests (icos and qu, all 4 test types) as well as the viz for icos/rotation_2d (I didn't try the other 7 viz cases) on Chyrsalis with Omega from the current develop branch.

I took a look at the viz output and it's pretty clear why convergence is poor -- the oscillations that you showed above at 60 km are much worse for both coarser resolutions and for tracer3 (the slotted cylinder). e.g.:

[cbegeman]

Yes. I ran MPAS-Ocean with centered tracer advection and the behavior is similar.

[cbegeman]

@xylar Thanks for reviewing!