  We present numerical simulations of energetic flows propagating through the
debris cloud of a binary neutron star (BNS) merger. Starting from the scale of
the central engine, we use a moving-mesh hydrodynamics code to simulate the
complete dynamical evolution of the produced relativistic jets. We compute
synchrotron emission directly from the simulations and present multi-band light
curves of the early (sub-day) through late (weeks to years) afterglow stages.
Our work systematically compares two distinct models for the central engine,
referred to as the narrow and wide engine scenario, which is associated with a
successful structured jet and a quasi-isotropic explosion respectively. Both
engine models naturally evolve angular and radial structure through
hydrodynamical interaction with the merger debris cloud. They both also result
in a relativistic blast wave capable of producing the observed multi-band
afterglow data. However, we find that the narrow and wide engine scenario might
be differentiated by a new emission component that we refer to as a merger
flash. This component is a consequence of applying the synchrotron radiation
model to the shocked optically thin merger cloud. Such modeling is appropriate
if injection of non-thermal electrons is sustained in the breakout relativistic
shell, for example by internal shocks or magnetic reconnection. The rapidly
declining signature may be detectable for future BNS mergers during the first
minutes to day following the GW chirp. Furthermore, its non-detection for the
GRB170817A event may disfavor the wide, quasi-isotropic explosion model.
