  Late activity of the central engine is often invoked in order to explain the
flares observed in the early X-ray afterglow of gamma-ray bursts, either in the
form of an active neutron star remnant or (fall-back) accretion onto a black
hole. However, these scenarios are not always plausible, in particular when
flares are delayed to very late times after the burst. Recently, a new scenario
was proposed that suggests X-ray flares can be the result of the passing of a
long-lived reverse shock through a stratified ejecta, with the advantage that
it does not require late-time engine activity. In this work, we numerically
demonstrate this scenario to be physically plausible, by performing
onedimensional simulations of ejecta dynamics and emission using our novel
moving-mesh relativistic hydrodynamics code. Improved efficiency and precision
over previous work enables the exploration of a broader range of setups. We can
introduce a more physically realistic description of the circumburst medium
mass density. We can also locally trace the cooling of electrons when computing
the broadband emission from these setups. We show that the synchrotron cooling
timescale can dominate the flare decay time if the stratification in the ejecta
is constrained to a localised angular region inside the jet, with size
corresponding to the relativistic causal connection angle, and that it
corresponds to values reported in observations. We demonstrate that this
scenario can produce a large range of observed flare times, suggesting a
connection between flares and initial ejection dynamics rather than with
late-time remnant activity.
