  Particle acceleration is an ubiquitous phenomenon in astrophysical and space
plasma. Diffusive shock acceleration (DSA) and stochastic turbulent
acceleration are known to be the possible mechanisms for producing very high
energetic particles, particularly in weakly magnetized regions. An interplay of
different acceleration processes along with various radiation losses is
typically observed in astrophysical sources. While DSA is a systematic
acceleration process that energizes particles in the vicinity of shocks,
stochastic turbulent acceleration (STA) is a random energizing process, where
the interaction between cosmic ray particles and electromagnetic fluctuations
results in particle acceleration. This process is usually interpreted as a
biased random walk in energy space, modelled through a Fokker-Planck equation.
In the present work, we describe a novel Eulerian algorithm, adopted to
incorporate turbulent acceleration in the presence of DSA and radiative
processes like synchrotron and Inverse-Compton emission. The developed
framework extends the hybrid Eulerian-Lagrangian module in a full-fledged
relativistic Magneto-hydrodynamic (RMHD) code PLUTO. From our validation tests
and case studies, we showcase the competing and complementary nature of both
acceleration processes. Axisymmetric simulations of an RMHD jet with this
extended hybrid framework clearly demonstrate that emission due to shocks is
localized while that due to turbulent acceleration originates in the backflow
and is more diffuse, particularly in the high energy X-ray band.
