Abstract: The observed properties of galaxy clusters are the result of a non-linear interaction between many physical processes including gravity, hydrodynamics, magnetic fields, turbulence, radiation, galaxy formation and feedback, and cosmology. This provides a unique "cosmic laboratory" with which we can learn about our Universe. In particular, galaxy clusters are hosts to cosmic shocks, which propagate through the intracluster medium as a signature of structure formation. It is believed that at these shock fronts, magnetic field inhomogeneities in a compressing flow may lead to the acceleration of cosmic ray electrons and ions. These relativistic particles decay and radiate through a variety of mechanisms, and have observational signatures in radio, hard X-ray, and Gamma-ray wavelengths. The construction of several new low frequency radio telescopes have begun observations of aEurooeradio relicsaEuro, which are thought to be the result of synchrotron emission from shock accelerated electrons. I will present recent work using adaptive mesh refinement MHD simulations of galaxy clusters using Enzo and analyzed with yt, that explain many of the observed properties of these radio relics including polarization fraction and direction of the radiation. I will also present preliminary work of combining a numerical library for momentum-space transport of cosmic rays with Enzo, where we can follow the spectral evolution of these high energy particles along with their spatial transport.