The unsteady flow around a forced rolling hull section with and without bilge keels is computed using URANS code ReFRESCO. In this paper, extensive studies have been carried out in the dependence on grid resolution and time-step size on the linear roll viscous-damping coefficient. The influence of the grid resolution on the viscous-damping coefficient is significant, and relatively fine grids should be used to obtain a grid-converged solution. The coefficient estimates decrease with grid refinement. The influence of the time step is smaller. The numerical results obtained for the rectangular hull with sharp bilges have been compared to classical experimental data by Ikeda. A very good agreement has been found, with deviations lower than 10% for several amplitudes and two periods. For this case, it is confirmed that the viscous-damping coefficient is linear with the roll amplitude. The numerical results obtained for the rectangular hull with triangular-shaped bilge keels have also been compared to available experimental data. A reasonable agreement between ReFRESCO results and the experimental data is found for dimensionless frequencies lower than 0.7. For these values a deviation from the experimental values lower than 10% is observed. For higher dimensionless frequencies, the calculated viscous-damping coefficient highly overestimates the model-tests results, which is expected to be related to non-linear free-surface effects. The viscous damping calculated is linear with the frequency, which is not true for the experiments for frequencies higher than 0.7. For the hull section with bilge keels, a preliminary study on possible scale effects has been performed. One calculation has been carried out for a full-scale Reynolds number corresponding to a geometrical scale factor of 50. The preliminary results showed that the pressure and vorticity fields are very similar for model and full scale. The difference in viscous damping coefficient between model and full scale is of 1.85%.