  In recent years, dynamical relativistic jet simulation techniques have
progressed to a point where it is becoming possible to fully numerically
resolve gamma-ray burst (GRB) blast-wave evolution across scales. However, the
modeling of emission is currently lagging behind and limits our efforts to
fully interpret the physics of GRBs. In this work we combine recent
developments in moving-mesh relativistic dynamics with a local treatment of
non-thermal emission in a new code: GAMMA. The code involves an arbitrary
Lagrangian-Eulerian approach only in the dominant direction of fluid motion
which avoids mesh entanglement and associated computational costs. Shock
detection, particle injection and local calculation of their evolution
including radiative cooling are done at runtime. Even though GAMMA has been
designed with GRB physics applications in mind, it is modular such that new
solvers and geometries can be implemented easily with a wide range of potential
applications. In this paper, we demonstrate the validity of our approach and
compute accurate broadband GRB afterglow radiation from early to late times.
Our results show that the spectral cooling break shifts by a factor of ~ 40
compared to existing methods. Its temporal behavior also significantly changes
from the previously calculated temporary steep increase after the jet break.
Instead, we find that the cooling break does not shift with time between the
relativistic and Newtonian asymptotes when computed from our local algorithm.
GAMMA is publicly available at: https://github.com/eliotayache/GAMMA.
