[Users] UIUC's GRMHD Primitives (Recovery) Solver

[Zach Etienne]

Dear ET folks,

I had a recent discussion with Tanja Bode about the GRMHD primitives solver
in Maya/ET. It seems both of our primitives (recovery) solvers (aka
conservative-to-primitives routines) are based on the open-source HARM
code, and there is a real push now to get GRMHD working in ET. The Illinois
group would like to become more involved in contributing to the ET
community, and as a show of our support, I am sending this email. I have
discussed the situation with Stu Shapiro, who is happy to contribute and
has permitted me to attach our HARM-based primitives solver to this email.
This code is GPL version 2 or 3 (whichever you prefer to maximize
compatibility with ET and the existing HARM license). As you are already
familiar with HARM's solver, we include no documentation. The current
solver can handle Gamma-law equations of state. It will require some work,
but it should be straightforward to extend the solver to arbitrary
equations of state.

The solver contains a driver with some quality-control features, like
taking a norm of how much the conservatives have changed before and after
the solver. It also contains a standalone version, so that when the solver
fails during a run, it can dump a file with all the information necessary
to rerun the solver *independently of the evolution code* and debug the
solver. It also outputs benchmarks (# primitives/second) by default each
time it is called. Finally, it includes all of the fixes our group has
developed over the years (see appendix in Etienne et al., Phys. Rev. D 85,
064029 (2012)) to assess and repair the physicality of conservatives
*before* going through the Newton-Raphson routine, as well as fixing
unphysical primitives when they appear. With these features, we have some
confidence in the robustness of our solver.

There are parts of the code where you'll find commented-out lines, as
evidence that a lot of tweaking has gone into this. As with all of our
codes, this solver is a work in progress. As we haven't used it, we haven't
updated the standalone solver in a while, so you may need to port some of
the features from primitives_generic.C if you would like to use the
standalone version.

-Zach, on behalf of the Illinois group
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