We present results on the inspiral, merger, and post-merger evolution of a
neutron star - neutron star (NSNS) system. Our results are obtained using the
hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our
numerical methods, we evolve an equal-mass system for $\approx 22$ orbits
before merger. This waveform is the longest waveform obtained from fully
general-relativistic simulations for NSNSs to date. Such long (and accurate)
numerical waveforms are required to further improve semi-analytical models used
in gravitational wave data analysis, for example the effective one body models.
We discuss in detail the improvements to SpEC's ability to simulate NSNS
mergers, in particular mesh refined grids to better resolve the merger and
post-merger phases. We provide a set of consistency checks and compare our
results to NSNS merger simulations with the independent BAM code. We find
agreement between them, which increases confidence in results obtained with
either code. This work paves the way for future studies using long waveforms
and more complex microphysical descriptions of neutron star matter in SpEC.