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We describe a new hybrid framework to model non-thermal spectral signaturesfrom highly energetic particles embedded in a large-scale classical orrelativistic MHD flow. Our method makes use of \textit{Lagrangian} particlesmoving through an Eulerian grid where the (relativistic) MHD equations aresolved concurrently. Lagrangian particles follow fluid streamlines andrepresent ensembles of (real) relativistic particles with a finite energydistribution. The spectral distribution of each particle is updated in time bysolving the relativistic cosmic ray transport equation based on local fluidconditions. This enables us to account for a number of physical processes, suchas adiabatic expansion, synchrotron and inverse Compton emission. An accuratesemi-analytically numerical scheme that combines the method of characteristicswith a Lagrangian discretization in the energy coordinate is described.  In presence of (relativistic) magnetized shocks, a novel approach toconsistently model particle energization due to diffusive shock accelerationhas been presented. Our approach relies on a refined shock-detection algorithmand updates the particle energy distribution based on the shock compressionratio, magnetic field orientation and amount of (parameterized) turbulence. Theevolved distribution from each \textit{Lagrangian} particle is further used toproduce observational signatures like emission maps and polarization signalsaccounting for proper relativistic corrections. We further demonstrate thevalidity of this hybrid framework using standard numerical benchmarks andevaluate the applicability of such a tool to study high energy emission fromextra-galactic jets.

A Particle Module for the PLUTO code: II - Hybrid Framework for Modeling Non-thermal emission from Relativistic Magnetized flows