SIMBAD references

We describe a new hybrid framework to model non-thermal spectral signatures from highly energetic particles embedded in a large-scale classical or relativistic magnetohydrodynamic (MHD) flow. Our method makes use of 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 the presence of (relativistic) magnetized shocks, a novel approach to consistently model particle energization due to diffusive shock acceleration is 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 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 extragalactic jets.