Properly extend shape map into interior region #6477
+981
−573
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This is only allowed when the inner surface is spherical and when we are using the "regular" transition (i.e. not reversed).
Proposed changes
Fixes #6451.
A previous PR (#6359) attempted to extend the shape map into the excision, but did so incorrectly. This PR implements this correctly. In order to do this, the meaning of the transition function had to be changed slightly. Previously, the shape map was
and the transition function was$f(r, \theta, \phi)$ . The functional form of the shape map hasn't changed, but now it reads
where$G(r, \theta, \phi)$ is the transition. The $1/r$ factor was just absorbed into the transition function because the full $G$ is different inside the excision, not just $f$ .
Also, the transition function inside the excisions is
which is different than it is in SpEC. The transition defined in SpEC causes the jacobian to be undefined at the center of the shape map, which means the full frame velocity of all the maps can't be computed at the center of the shape map. This new transition inside the excision allows for this and has the correct behavior.
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