[Users] Proposal: Modify HydroBase to Support Staggered A-Fields

[Zach Etienne]

Dear ET folks,

I have written a small thorn that converts HydroBase and ADMBase variables
into the variables IllinoisGRMHD needs to perform a GRMHD evolution. This
conversion works just fine on all variables... except the vector potential.

As you may be aware, IllinoisGRMHD requires that A_t (=\sqrt{\gamma} \Phi),
A_x, A_y, and A_z each be staggered differently (a la Table I of
http://arxiv.org/abs/1007.2848).

However, HydroBase does not support defining such staggered A-fields. Thus
it is currently impossible to modify/create GRMHD initial data thorns so
that vector potential data produced by them can be directly read in by
IllinoisGRMHD. For example, if an initial data thorn only outputs the
vector potential on grid vertices, then an interpolation will need to be
performed to staggered gridpoints. This will introduce truncation errors
that, depending on the A-field structure and needed grid resolutions, may
be severe. I conclude that this is _not_ The Right Strategy. The Right
Strategy would not break any existing thorn as a first step, either.

So as a first step, I believe we should modify HydroBase so that
1) A new set of four, 3-timelevel groups are defined, one for each
component of the vector potential
2) The prolongation type can be specified differently for each of the four
vector potential gridfunction groups, allowing for arbitrary staggerings of
the single variable within each of these groups.

Variables in these groups will be read in by IllinoisGRMHD and can be used
directly for evolutions.

Regarding the longer-term strategy, we could either

1) modify Carpet so that different components of Avec() (the current
3-vector potential group in HydroBase) can accept different
prolongation/restriction operators (then modifying IllinoisGRMHD to accept
this new vector gridfunction), or

2) just keep the four, 3-timelevel groups and phase out Avec() and Aphi
altogether.

Even the latter strategy would not be difficult to implement in current
publicly available thorns:

After a simple grep, I could only find a single initial data thorn that
actually sets Avec, so the needed changes to public initial data thorns
should be minimal. Further, I am under the impression that Avec evolutions
are not yet supported in GRHydro anyway, and found only about 40 references
to the Avec() gridfunctions within GRHydro, so renaming these variables to
a new style would be trivial.

Please let me know your thoughts regarding this proposal. The IllinoisGRMHD
code announcement paper is nearing completion, and at least having the
infrastructure for this code in place by the next ET release would be
great. In this regard, I have already asked Erik if he would be willing to
merge the staggered prolongation/restriction code into the mainline Carpet
for the next ET release. The soft freeze is Nov 10, these new features
affect none of Carpet's other functionality, and I have thoroughly tested
these new features with GRMHD evolutions, verifying that they work well.

Please consider the possibility of adding these small infrastructure
enhancements prior to the freeze.

Sincerely,

-Zach

*     *     *
Zachariah Etienne
Assistant Professor of Mathematics
West Virginia University
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