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address rotation source in spherical 2d coordinate #2967

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PR summary

This addresses #2927 regarding the rotation bit.
I mainly separated get_omega() to return magnitude of the angular frequency,
then made get_omega_vec() to depend on j, since $\Omega \hat{z} = \Omega[\cos(\theta) \hat{r} - \sin(\theta) \hat{\theta})]$.
To deal with the problem of position vector, I just made sure r is (r,0,0) before the cross_product call.
I also made computing dt_omega_matrix into a separate function since omega vector now varies.

PR motivation

PR checklist

  • test suite needs to be run on this PR
  • this PR will change answers in the test suite to more than roundoff level
  • all newly-added functions have docstrings as per the coding conventions
  • the CHANGES file has been updated, if appropriate
  • if appropriate, this change is described in the docs

@zingale zingale mentioned this pull request Sep 26, 2024
14 tasks
@zhichen3 zhichen3 marked this pull request as ready for review December 8, 2024 00:40
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