We present a model for the radio evolution of supernova remnants (SNRs) obtained by using three-dimensional (3D) hydrodynamic simulations, coupled with nonlinear kinetic theory of cosmic ray (CR) acceleration in SNRs. We model the radio evolution of SNRs on a global level, by performing simulations for wide range of the relevant physical parameters, such as the ambient density, the supernova (SN) explosion energy, the acceleration efficiency and the magnetic field amplification (MFA) efficiency. We attribute the observed spread of radio surface brightnesses for corresponding SNR diameters to the spread of these parameters. In addition to our simulations of type Ia SNRs, we also considered SNR radio evolution in denser, nonuniform circumstellar environment, modified by the progenitor star wind. These simulations start with the mass of the ejecta substantially higher than in the case of a type Ia SN and presumably lower shock speed. The magnetic field is understandably seen as very important for the radio evolution of SNRs. In terms of MFA, we include both resonant and non-resonant modes in our large scale simulations, by implementing models obtained from first-principles, particle-in-cell (PIC) simulations and non-linear magnetohydrodynamical (MHD) simulations. We test the quality and reliability of our models on a sample consisting of Galactic and extragalactic SNRs. Our simulations give $Sigma-D$ slopes between -4 and -6 for the full Sedov regime. Recent empirical slopes obtained for the Galactic samples are around -5, while for the extragalactic samples are around -4.
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