Add support for a general EOS

[BenWibking]

This requires the ability to compute:

• temperature $T(\rho, e)$
• pressure $P(\rho, e)$
• specific internal energy $e(\rho, P)$
• adiabatic sound speed $a^2 = (\partial P / \partial \rho)_s$
• additional thermodynamic derivatives (needed to calculate the Roe-averaged wavespeeds used by the Riemann solver; see eqs. 4.9-4.12 and Appendix A of [3])
  • $\partial P / \partial \rho$
  • $\partial P / \partial e$

From these, we can derive:

• isentropic compressibility $K_s = -(1/V) (\partial V / \partial P)_s = \rho a^2$ (used in shock flattening)

[1] Glaister, P. Journal of Computational Physics, Volume 74, Issue 2, p. 382-408. https://ui.adsabs.harvard.edu/abs/1988JCoPh..74..382G/abstract

[3] Kershaw et al., Computer Methods in Applied Mechanics and Engineering, Volume 158, Issues 1–2, 1998, p. 81-116. https://doi.org/10.1016/S0045-7825(97)00228-4

[BenWibking]

The fundamental derivative $\mathcal{G}$ is also useful for constructing a nonlinear wavespeed estimate [2], since it is proportional to $(\partial^2 P / \partial \rho^2)_s$.

[2] https://doi.org/10.1016/S0045-7930(98)00033-4

[psharda]

Continuing from #271 , we can now include gamma_law EOS from Microphysics. So, now we have to see if gamma_law can compute all the things you list above. I don't know what was the conclusion of your conversation with Mike on this? Are you or Mike going to modify gamma_law EOS to compute everything listed above?

[BenWibking]

Well, I'm not sure what the conclusion was either... 😆

It looks like the gamma_law EOS (https://github.com/AMReX-Astro/Microphysics/blob/main/EOS/gamma_law/actual_eos.H) computes all the derivatives that are needed, yes.

It might be necessary to check that the behavior is consistent for other EOSes. For instance, Mike said that state.cs is not set to $(\partial P / \partial \rho)_s$ for the helmholtz equation of state. So it might require some careful checking to make sure that everything is defined as expected in all cases, in case someone decides to use a stellar matter EOS in Quokka for some reason :)

[psharda]

Well, we have only built support for gamma_law and primordial_chem EOS in our new function setup_target_for_microphysics_compilation. If the user gives any other EOS, CMake will throw an error.

Okay, since gamma_law has everything you need already, we can now modify EOS.hpp to just use Microphysics. Do we need the EOS_Traits struct?

[psharda]

Also, looks like we will need to insert preCalculateInitialConditions() function in all Quokka tests, to initialize microphysics routines (just like we do for primordial chem):

template <> void RadhydroSimulation<ShocktubeProblem>::preCalculateInitialConditions()
{
    // initialize microphysics routines
    init_extern_parameters();
    eos_init();
    network_init();
}

I wonder if there is a better way to do this. Can you initialize them in EOS.hpp directly instead of in test.cpp?

[BenWibking]

Okay, since gamma_law has everything you need already, we can now modify EOS.hpp to just use Microphysics. Do we need the EOS_Traits struct?

No, we can get rid of that.

[BenWibking]

Also, looks like we will need to insert preCalculateInitialConditions() function in all Quokka tests, to initialize microphysics routines (just like we do for primordial chem):

template <> void RadhydroSimulation<ShocktubeProblem>::preCalculateInitialConditions()
{
  // initialize microphysics routines
  init_extern_parameters();
  eos_init();
  network_init();
}

I wonder if there is a better way to do this. Can you initialize them in EOS.hpp directly instead of in test.cpp?

Yeah, we should initialize this in RadhydroSimulation.hpp before the simulation starts.

[psharda]

Okay, since gamma_law has everything you need already, we can now modify EOS.hpp to just use Microphysics. Do we need the EOS_Traits struct?

No, we can get rid of that.

I did that, but ran into a bunch of errors from hydro_system.hpp radiation_system.hpp Cloudy_Cooling.hpp that use EOS_Traits. I had to modify a bunch of stuff to get rid of the errors. I will push my changes soon so you can check.

[psharda]

Resolved by #338