  Radio relics are diffuse synchrotron sources that illuminate shock waves in
the intracluster medium. In recent years, radio telescopes have provided
detailed observations about relics. Consequently, cosmological simulations of
radio relics need to provide a similar amount of detail. In this methodological
work, we include information on adiabatic compression and expansion, which have
been neglected in the past in the modelling of relics. In a cosmological
simulation of a merging galaxy cluster, we follow the energy spectra of shock
accelerated cosmic-ray electrons using Lagrangian tracer particles. On board of
each tracer particle, we compute the temporal evolution of the energy spectrum
under the influence of synchrotron radiation, inverse Compton scattering, and
adiabatic compression and expansion. Exploratory tests show that the total
radio power and, hence, the integrated radio spectrum are not sensitive to the
adiabatic processes. This is attributed to small changes in the compression
ratio over time.
