Feature: Generalized EOS Support

[baperry2]

Implement support for detailed chemistry simulations with SRK (or other non-ideal EOS). Extension of the low-Mach projection methods used in PeleLMeX from ideal gasses to real gas equations of state was described in J. Bell, @drummerdoc, et al, JCP, 2004: https://www.sciencedirect.com/science/article/pii/S0021999103005783

Preliminary thoughts on what would be required to adapt PeleLMeX:

• The key difference is the modified divergence constraint. The infrastructure exists in PeleLMeX to modify the divu calculation based on EOS for Manifold EOS. However, some of the necessary thermodynamic partial derivatives are not currently supported and would have to be added to the SRK EOS in PelePhysics (some derivation needed):
  

• $\frac{\partial p}{\partial T}|_{\rho,Y_k}$,

• $\frac{\partial p}{\partial \rho}|_{T,Y_k}$,

• $\xi_k = \frac{\partial h}{\partial Y_k}|_{p,T,Y_j}$,

• $\frac{\partial p}{\partial X_k}|_{T,\rho,Y_j}$,

• There are several places where ideal gas behavior is assumed in that H and Cp depend only on T,Y and not rho or P. Many calls like eos.TY2Cp and eos.HY2T will have to be suitably modified. PelePhysics does not currently support all of these, but does support analogs with E instead of H, so adding them shouldn't be too difficult. Perhaps some simplification is also possible by noting that P is constant throughout the domain.

• For SRK, the driving force terms for diffusion are more complex, nonlinear, and pressure-dependent. It may be difficult to integrate these into the implicit diffusion solve that uses AMReX's linear solvers. This may be the trickiest part form an implementation perspective. See PeleC explicit implementation here: https://github.com/AMReX-Combustion/PeleC/blob/c9a0f87a99f3728283ad9b01b3f1a9c3a51dca79/Source/Diffterm.H#L78

Additionally, it should be noted that manifold-based combustion models with non-ideal EOS are supported, so long as the data used to generate the manifold had non-ideal EOS (e.g., as supported by Cantera).

[drummerdoc]

Thanks Bruce! Excellent summary. Couple of minor/trivial comments

• Consider relabeling this capability as "Generalized EOS support"
• For the diffusion, we almost certainly will need to structure this as a linearized/lagged nonlinear solve, and could perhaps incorporate it too into the "SDC" iteration framework (rather than iterate to convergence as we do for the T solve). I don't anticipate that would lead to any significant errors, but it does require some thought.
• It's possible, and possibly much simpler, to evaluate the required partial derivatives numerically. We may want to set that up regardless as a way to help debug any analytic expressions created. Also, it might be useful to interact with Bell, Zingale, Katz etc for thoughts on the impact of the cost and accuracy of those terms in the context of table-based EOSs, etc, and any hidden constraints/requirements that may have arisen in the context of astrophysical works along these lines.

[baperry2]

Another low Mach code where some of this has been implemented/documented, perhaps we can take some stuff from here:

https://github.com/AMReX-FHD/LowMachFHD/blob/master/staggered_grid/exec/energy/doc/DesignDocument.tex