Add entropy-stable dg operators

[MTCam]

Adds ESDG continued from @thomasgibson's previous work. (#573).

The main pieces are:

• euler.py
  • Stand-alone entropy_stable_euler_operator
  • Options to use entropy-stable
• inviscid.py
  • Entropy conserving flux routines:
    - entropy_conserving_flux_chandrashekar (single gas only, passive scalars ok)
    - entropy_conserving_flux_renac (supports mixtures)
  • Facial flux drivers:
    - entropy_stable_inviscid_facial_flux_rusanov ESDG Rusanov-type flux with dissipation
    - entropy_stable_inviscid_facial_flux. General ESDG flux, dissipation optional
• navierstokes.py
  • Rearranged to use inviscid_fluid_operator = {None, euler_operator, entropy_stable_euler_operator} for inviscid terms (default is None, meaning - do inline inviscid terms)
  • Options to use entropy-stable for inviscid terms
• gas_model.py
  • Utilities to convert from conservative to/from entropy variables CV <--> EV (move to EOS?)
  • Utilities to create CV from projected EV
• Examples
  • Added ESDG option to all examples
  • Some work better than others - but we should have the option available so we can exercise/debug it

Review guide:

• There is a lot of repeated code in the giant gob of examples. The review will go easier/quicker by looking at some representative examples, instead of giving them all detailed attention. Here are some representative examples:
  • Simple case: pulse-mpi.py
  • Complex case: thermally-coupled-mpi.py

Questions for the review:

• Is the scope and purpose of the PR clear?
  • The PR should have a description.
  • The PR should have a guide if needed (e.g., an ordering).
• Is every top-level method and class documented? Are things that should be documented actually so?
• Is the interface understandable? (I.e. can someone figure out what stuff does?) Is it well-defined?
• Does the implementation do what the docstring claims?
• Is everything that is implemented covered by tests?
• Do you see any immediate risks or performance disadvantages with the design? Example: what do interface normals attach to?

[tulioricci]

Some comments/questions.

[tulioricci]

Wondering if we should mix esdg_euler with plain_euler or simply let the driver/navierstokes operator handle which one to use. I have a preference to keep them separate.

[MTCam]

I will push back on this a bit. We have in excess of 20 examples to change. Adding the necessary constructs to all drivers to do in in the driver-side is an onerous undertaking. On the other hand, letting the driver specify use_esdg=True and factoring out the rest into this common code reduces the total amount of code required by a lot , makes it easier to read, and much easier to use.

[tulioricci]

👍