Hi Roland,

> I generally suggest shifting the grid so that the closest gridpoint
> to the origin is (dx/2, dy/2, dz/2), where dx,dy,dz are the
> resolutions on the finest grid. I've used this trick many times to
> stabilize evolutions. Also you may want to try the ShiftedKerrSchild
> thorn (in the ETK), which enables a radial offset that shrinks the BH
> coordinate size but at the same time kills off enormous constraint
> violations near r=0. Unlike the existing KerrSchild thorn(s), this
> one uses the standard Kerr-Schild metric written in spherical
> coordinates and does the basis xform.
Right, I had completely forgotten about that one. Thank you. So
ShifterKerrSchild is actually different from Exact with its
Kerr_KerrSchild__epsilon parameter (ie it would do proper coordinate
transformation r -> r+r0 rather than just add r0 in some of the 1/r
terms)?

KerrSchild_radial_shift sets r0.

For more documentation, my Master's student George Vopal developed as part of his Master's research project a couple of interactive NRPy+ tutorial modules on the shifted Kerr-Schild solution (even confirming constraint convergence to zero in a standalone code):

Basic equations (takes a minute to load):

https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-ADM_Initial_Data-ShiftedKerrSchild.ipynb

Numerical validation (takes a minute to load):

https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_Shifted_KerrSchild_initial_data.ipynb

Note that the goal is use it only as ID and not to reset the metric at
each time so I will have to modify ShifterKerrSchild a bit.

Should be a pretty simple change.

Yours,
Roland

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