Can you enlighten me on the issues that influence the choices among (i) “smoothed particle hydrodynamics,” (ii) “adaptive mesh refinement,” or (iii) a “moving, unstructured mesh?” A grid-based structure certainly seems correct, but the finer points of implementation are not apparent. I would be completely satisfied with a list of references rather than a detailed answer. Thank you for taking the time.
All three are actively in use in astrophysics, even just within the "galaxy formation" community. So you can imagine, many debates about this topic. There have been recent reviews of note:
https://www.annualreviews.org/doi/abs/10.1146/annurev-astro-082214-122309 (on grid codes)
https://arxiv.org/abs/1109.2219 (on sph)
both discuss the moving mesh as well, although the main paper for this is for the AREPO code: https://arxiv.org/abs/0901.4107
Also this paper highlights some interesting differences between grid and particle techniques: