  Particle acceleration by turbulence plays a role in many astrophysical
environments. The non- linear evolution of the underlying cosmic-ray spectrum
is complex and can be described by a Fokker-Planck equation, which in general
has to be solved numerically. We present here an implementation to compute the
evolution of a cosmic-ray spectrum coupled to turbulence considering isotropic
particle pitch-angle distributions and taking into account the relevant
particle energy gains and losses. Our code can be used in run time and
post-processing to very large astrophysical fluid simulations. We also propose
a novel method to compress cosmic- ray spectra by a factor of ten, to ease the
memory demand in very large simulations. We show a number of code tests, which
firmly establish the correctness of the code. In this paper we focus on
relativistic electrons, but our code and methods can be easily extended to the
case of hadrons. We apply our pipeline to the relevant problem of particle
acceleration in galaxy clusters. We define a sub-grid model for compressible
MHD-turbulence in the intra- cluster-medium and calculate the corresponding
reacceleration timescale from first principles. We then use a
magneto-hydrodynamic simulation of an isolated cluster merger to follow the
evolution of relativistic electron spectra and radio emission generated from
the system over several Gyrs.
