  We describe a new hybrid framework to model non-thermal spectral signatures
from highly energetic particles embedded in a large-scale classical or
relativistic MHD flow. Our method makes use of \textit{Lagrangian} particles
moving through an Eulerian grid where the (relativistic) MHD equations are
solved concurrently. Lagrangian particles follow fluid streamlines and
represent ensembles of (real) relativistic particles with a finite energy
distribution. The spectral distribution of each particle is updated in time by
solving the relativistic cosmic ray transport equation based on local fluid
conditions. This enables us to account for a number of physical processes, such
as adiabatic expansion, synchrotron and inverse Compton emission. An accurate
semi-analytically numerical scheme that combines the method of characteristics
with a Lagrangian discretization in the energy coordinate is described.
  In presence of (relativistic) magnetized shocks, a novel approach to
consistently model particle energization due to diffusive shock acceleration
has been presented. Our approach relies on a refined shock-detection algorithm
and updates the particle energy distribution based on the shock compression
ratio, magnetic field orientation and amount of (parameterized) turbulence. The
evolved distribution from each \textit{Lagrangian} particle is further used to
produce observational signatures like emission maps and polarization signals
accounting for proper relativistic corrections. We further demonstrate the
validity of this hybrid framework using standard numerical benchmarks and
evaluate the applicability of such a tool to study high energy emission from
extra-galactic jets.
