Fix bulk modulus calculation in spiner EOS

[pdmullen]

Fixes a (potential) bug in Spiner EOS bulk modulus calculation.

PR Summary

Despite the bulk modulus being a required table in a SpinerDependsRhoT or SpinerDependsRhoSie EOS file, it is overwritten by functions fixBulkModulus_ and calcBMod_, respectively. Inside these functions, the bulk modulus formulae assume dpdrho to be $\partial P / \partial \rho \; \vert{T}$. However, I believe (please check me) that spiner expects that the tables provided correspond to $\partial P / \partial \rho \; \vert{e}$. This PR changes the bulk modulus formula to reflect this. There is this trick that eos_spiner plays wherein if $\partial P / \partial e \; \vert{\rho} < 0$, it modifies the bulk modulus calculation. I tried to preserve this behavior by defining $\partial P / \partial \rho \; \vert{T}$ in terms of thermodynamic derivatives (please double check me...).

PR Checklist

• [ ] Adds a test for any bugs fixed. Adds tests for new features.
• [ ] Format your changes by using the make format command after configuring with cmake.
• [ ] Document any new features, update documentation for changes made.
• [x] Make sure the copyright notice on any files you modified is up to date.
• [x] After creating a pull request, note it in the CHANGELOG.md file.
• [ ] LANL employees: make sure tests pass both on the github CI and on the Darwin CI

If preparing for a new release, in addition please check the following:

• [ ] Update the version in cmake.
• [ ] Move the changes in the CHANGELOG.md file under a new header for the new release, and reset the categories.

[Yurlungur]

Thanks for catching this @pdmullen ! I'm going to trigger tests on Darwin.

[chadmeyer]

Looking at this now. I think this might be OK, but I want to make sure (and perhaps also ensure that this is what we want).

Let's agree that $c^2 = \left.\frac{\partial P}{\partial \rho}\right|_{e}+\frac{P}{\rho^2}\left.\frac{\partial P}{\partial e}\right|_{\rho}$. Is that what is being done in both of these cases? I ask because one of these cases is DependsRhoT and the other one is DependsRhoSie, so I'm not sure what was tabulated (is it the same between them?).

Is that what it is? I'm thinking so, but I might need to dig into Sesame2Spiner to be sure.

[Yurlungur]

Is that what it is? I'm thinking so, but I might need to dig into Sesame2Spiner to be sure.

I had the same confusion. I thought Sesame2Spiner was tabulating $dP/d\rho |_T$ but it turns out it's tabulating $dP/d\rho |_e$.

[jhp-lanl]

Is that what it is? I'm thinking so, but I might need to dig into Sesame2Spiner to be sure.

I had the same confusion. I thought Sesame2Spiner was tabulating dP/dρ|T but it turns out it's tabulating dP/dρ|e.

I think the another issue is that Sesame2Spiner gets density-energy derivatives for density-temperature tables via thermodynamic identities and then uses another thermodynamic identity on them to get the bulk modulus. I would propose (for the future) to just ask for the bulk modulus directly via the EOS_BSt_DT table.

This would be advantageous for two reasons: 1) it avoids roundoff due to unnecessary multiplications and additions and 2) it can leverages the effort that the EOSPAC folks put into making sure that EOSPAC returns the most accurate bulk modulus possible.

[pdmullen]

Is that what it is? I'm thinking so, but I might need to dig into Sesame2Spiner to be sure.

I had the same confusion. I thought Sesame2Spiner was tabulating dP/dρ|T but it turns out it's tabulating dP/dρ|e.

I think the another issue is that Sesame2Spiner gets density-energy derivatives for density-temperature tables via thermodynamic identities and then uses another thermodynamic identity on them to get the bulk modulus. I would propose (for the future) to just ask for the bulk modulus directly via the EOS_BSt_DT table.

This would be advantageous for two reasons: 1) it avoids roundoff due to unnecessary multiplications and additions and 2) it can leverages the effort that the EOSPAC folks put into making sure that EOSPAC returns the most accurate bulk modulus possible.

I'd add that it feels a bit weird for SpinerEOS to demand a bulk modulus field in tables when it actually just recomputes them from thermodynamic derivatives. Maybe a future MR could optionally enroll "bulk modulus correction/fixing". That way if a user wants to use bulk moduli as directly computed from EOSPAC, they could set correct_bulk_mod = false (or similar).

[jhp-lanl]

I think this looks ready for merging

[Yurlungur]

@jhp-lanl @pdmullen agreed regarding using the bulk modulus from eospac. I'll make an issue.