Add some basic notes on time stepping design

[mwarusz]

• Documentation:
  • Design document has been generated and added to the docs
  • Documentation has been built locally and changes look as expected

[philipwjones]

Should have added this to the original design doc, but to follow up on my comments during the call, we need a requirement for the full ocean model to be able to mix time stepping schemes, not only by variable but also by individual tendencies. For example, we will always do vertical mixing with a fully implicit scheme. And for tracers, we may use a different scheme for advection (sometimes consistent with momentum, but maybe SLT brings its own) vs mixing terms. And of course barotropic splitting which will add its own complications.

[philipwjones]

This document might be ok for version-0, but I really think it would benefit from thinking about, and designing for the full complexity of the final model. This includes adding requirements for

• barotropic splitting, both implicit and explicit-subcycling
• separate momentum and tracer timesteps (tracer super-cycling)
• support for regional timesteps?
• blending time integration schemes as needed in a consistent way

I don't think this current design will be able to support any of this unless doStep becomes the analog of the mpas time_integration_xxxxx routines for every possible combination of options. I'd like to see a little more thought up front about how to more flexibly support all these options. I realize with the time crunch we may need to put something simple in place now, so understand if we need to do so.

[mwarusz]

@philipwjones
I agree that the design I proposed is probably too restrictive and requires more thought. I am converting this PR to a draft for now.