<div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr">Hi Roland,<div><br clear="all"></div></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">> I generally suggest shifting the grid so that the closest gridpoint<br>
> to the origin is (dx/2, dy/2, dz/2), where dx,dy,dz are the<br>
> resolutions on the finest grid. I've used this trick many times to<br>
> stabilize evolutions. Also you may want to try the ShiftedKerrSchild<br>
> thorn (in the ETK), which enables a radial offset that shrinks the BH<br>
> coordinate size but at the same time kills off enormous constraint<br>
> violations near r=0. Unlike the existing KerrSchild thorn(s), this<br>
> one uses the standard Kerr-Schild metric written in spherical<br>
> coordinates and does the basis xform.<br>
Right, I had completely forgotten about that one. Thank you. So<br>
ShifterKerrSchild is actually different from Exact with its<br>
Kerr_KerrSchild__epsilon parameter (ie it would do proper coordinate<br>
transformation r -> r+r0 rather than just add r0 in some of the 1/r<br>
terms)?<br></blockquote><div><br></div><div>KerrSchild_radial_shift sets r0. </div><div><br></div><div>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):<br></div><div>Basic equations (takes a minute to load):</div><div><a href="https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-ADM_Initial_Data-ShiftedKerrSchild.ipynb" target="_blank">https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-ADM_Initial_Data-ShiftedKerrSchild.ipynb<br></a></div><div>Numerical validation (takes a minute to load):</div><div><a href="https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_Shifted_KerrSchild_initial_data.ipynb" target="_blank">https://mybinder.org/v2/gh/zachetienne/nrpytutorial/master?filepath=Tutorial-Start_to_Finish-BSSNCurvilinear-Setting_up_Shifted_KerrSchild_initial_data.ipynb<br></a></div><div> <br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
Note that the goal is use it only as ID and not to reset the metric at<br>
each time so I will have to modify ShifterKerrSchild a bit.<br></blockquote><div><br></div><div>Should be a pretty simple change.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<br>
Yours,<br>
Roland<br>
<br>
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</blockquote></div></div></div></div></div>