Prague Relativistic Astrophysics

David Hubber

Smoothed Particle Hydrodynamics (SPH) and Adaptive Mesh Refinement
(AMR) codes have been used for the past 20+ years to investigate
various astrophysical problems such as star formation and cosmological
simulations. While often championed for their strengths, both methods
have noticable weaknesses that can undermine their achievements. We
discuss recent attempts in the literature to improve our understanding
of how, why and when SPH and AMR agree and disagree, and how this
knowledge can be used to inform us better on when to trust numerical
simulations and how to improve them in the future. We explore some of
the present and future algorithmic developments of these two methods,
and what kinds of problems we will be able to attack in the next
decade, as well as other methods that may become powerful tools for
numerical astrophysics.