  GenASiS (General Astrophysical Simulation System) is a new code being
developed initially and primarily, though by no means exclusively, for the
simulation of core-collapse supernovae on the world's leading capability
supercomputers. This paper---the first in a series---demonstrates a centrally
refined coordinate patch suitable for gravitational collapse and documents
methods for compressible nonrelativistic hydrodynamics. We benchmark the
hydrodynamics capabilities of GenASiS against many standard test problems; the
results illustrate the basic competence of our implementation, demonstrate the
strengths and limitations of the HLLC relative to the HLL Riemann solver in a
number of interesting cases, and provide preliminary indications of the code's
ability to scale and to function with cell-by-cell fixed-mesh refinement.
