Implement general EOS equations in Riemann Solver

[psharda]

Resolves #337 and #271 and #278
Includes #339

[psharda]

@BenWibking I implemented equation A.5a of Kershaw+1998 to find $C^{*}_{\rho}$ for arbitrary EOS. I have kept $C^{*}_{P}$ the same as before (so, it is only applicable for ideal gas EOS). Now, for gamma_law, dedr = 0 in microphysics. So, equation A.5a of Kershaw reduces to: $C^{*}_{\rho} = \frac{1}{2} \left(I^{-} + I^{+} \right)$. However, since both $I^{-}$ and $I^{+}$ are > 0 for several Hydro test problems, I don't obtain $C^{*}_{\rho} = 0$ as we'd expect for ideal gas. Why?

All the tests (except for HydroSMS) pass anyway, which I don't understand. Is the issue here that equation A5.a is an approximate equation, or that I changed $C^{*}_{\rho}$ but not $C^{*}_P$?

[psharda]

Ugh, why are my $$ not working above to display inline equations

[BenWibking]

All the tests (except for HydroSMS) pass anyway, which I don't understand. Is the issue here that equation A5.a is an approximate equation, or that I changed $C_{\rho}$ but not $C_P$?

The issue is the A.5a is approximate.

For reasons I don't fully understand (but have seen in experimenting with different ways to calculate the wavespeeds for ideal gases), the HydroSMS test is very sensitive to the wavespeed estimates. So I don't think this is anything to worry about.

[BenWibking]

Hmm. It does look bad though:

It doesn't get much better unless I add a huge amount of artificial viscosity, which is not something I'd want to do in a real simulation.

Let's hope it's less oscillatory once you use the numerical approximation for $C_P^{\star}$.

[psharda]

hydro_sms_1.0000.pdf
The oscillations seem less, but the spike is larger.

[psharda]

This is how it was before:

[BenWibking]

@BenWibking does Microphysics also have (∂2P∂2ρ)s

Not sure. You'll have to ask Mike.

[psharda]

hmm, I pushed some more commits but they haven't appeared here.

[BenWibking]

Wow, it looks basically perfect:

[psharda]

Wow, it looks basically perfect:

Woah, didn't expect that. It's even better than what we had before this PR.

[psharda]

/azp run

[psharda]

all tests will pass now. any more comments @BenWibking ?

[BenWibking]

As long as the GPU tests pass, it looks good to me.