  We present a comparison between several simulation codes designed to study
the core-collapse supernova mechanism. We pay close attention to controlling
the initial conditions and input physics in order to ensure a meaningful and
informative comparison. Our goal is three-fold. First, we aim to demonstrate
the current level of agreement between various groups studying the
core-collapse supernova central engine. Second, we desire to form a strong
basis for future simulation codes and methods to compare to. Lastly, we want
this work to be a stepping stone for future work exploring more complex
simulations of core-collapse supernovae, i.e., simulations in multiple
dimensions and simulations with modern neutrino and nuclear physics. We compare
the early (first ~500ms after core bounce) spherically-symmetric evolution of a
20 solar mass progenitor star from six different core-collapse supernovae
codes: 3DnSNe-IDSA, AGILE-BOLTZTRAN, FLASH, F{\sc{ornax}}, GR1D, and
PROMETHEUS-VERTEX. Given the diversity of neutrino transport and hydrodynamic
methods employed, we find excellent agreement in many critical quantities,
including the shock radius evolution and the amount of neutrino heating. Our
results provide an excellent starting point from which to extend this
comparison to higher dimensions and compare the development of hydrodynamic
instabilities that are crucial to the supernova explosion mechanism, such as
turbulence and convection.
