Relativistic hadrons and leptons are ubiquitous constituents in astrophysical plasmas. Their presence reflects the breakdown of thermodynamic behaviors in collisionless plasmas, particularly at shocks. They can carry substantial energy, and their electromagnetic emissions often provide most of the information available about conditions in such environments. We have developed efficient and practical numerical approaches to computational simulations of the generation and transport of these so-called cosmic-rays. Here we report on a new method and its application for simulating relativistic electrons in supersonic MHD flows, particularly as it applies to radio galaxies. Additionally, we have developed tools that enable us to synthesize astronomical observations of our simulated objects that can be used to study them in ways identical to those of observational astronomers, thus enabling more meaningful comparisons of dynamical simulations with observations than has been possible before. (C) 2002 Elsevier Science B.V. All rights reserved