In this article we present a fluid model for the numerical simulation of electric charge transport and accumulation inside a polymeric solid dielectric material. The model is bipolar and dynamic, that is, the dynamics of two kinds of charge carriers, electrons and holes, are simulated over time. The considered transport mechanisms are drift due to electric field and diffusion due to charge carriers' concentration gradients. Source and sink terms for the species are described by means of trapping, detrapping and recombination coefficients. We describe the implementation of a finite-volume one-dimensional solver written in Fortran 90, based on the described model. We use the code to simulate the charging process of a dielectric specimen under an HVDC field. The effect of several model parameters on the temporal behavior of the computed polarization current is investigated by performing a sensitivity analysis. Starting from the parameter values suggested by other authors, we isolate two distinct sets of values that allow to fit an experimentally measured polarization current.