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SuperNu simulates time-dependent radiation transport in local thermodynamic equilibrium with matter. It applies the methods of Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) for static or homologously expanding spatial grids. The radiation field affects material temperature but does not affect the motion of the fluid. SuperNu may be applied to simulate radiation transport for supernovae with ejecta velocities that are not affected by radiation momentum. The physical opacity calculation includes elements from Hydrogen up to Cobalt. SuperNu is motivated by the ongoing research into the effect of variation in the structure of progenitor star explosions on observables: the brightness and shape of light curves and the temporal evolution of the spectra. Consequently, the code may be used to post-process data from hydrodynamic simulations. SuperNu does not include any capabilities or methods that allow for non-trivial hydrodynamics.