Abstract. We have developed numerical techniques to treat CR acceleration at shocks in multidimensional MHD simulations of astrophysical objects. These allow us to study production, transport and emissions produced by CRs inside very complex and unsteady flows. Here we report results of 3D supersonic jet simulations designed to model radio galaxy formation. Initial findings demonstrate several important physical points: (1) The flows, including the jets, are highly unsteady. Clear jet termination shocks are uncommon, so that CRs are accelerated more by a complex web of shocks in the flow "head". (2) The energy spectrum of the accelerated CRs is spatially and temporally complex, and not simply the canonical "strong-shock" power law. (3) Magnetic fields within the "backflow cocoon" are highly intermittent, so conventional "aging" models, based on synchrotron losses are not reliable