Numerical predictions using the large eddy simulation (LES) and RANS methods have been performed on a mixing vessel stirred by a Rushton impeller at Re = 40,000. The finite volume method in an unstructured mesh consisting of around 490,000 computational cells was used. For the LES method, the subgrid-scale effects were modelled using the standard Smagorinsky model, while for the RANS method the standard k-epsilon model was used. The interaction between the rotating impeller and the static baffles was accounted for using the sliding-deforming mesh methodology. Comparisons were made between the predictions and previously reported phase-resolved LDA measurements of mean and rms velocities, as well as turbulent kinetic energy. The results obtained with the LES approach capture well both the overall as well as the detailed flow features (such as the trailing vortices) and show very substantial improvement in comparison to RANS predictions with the standard k-epsilon model. The global turbulent energy dissipation rate (epsilon) across the vessel volume was also well predicted by the LES, to within 15% of the measured value; in contrast, e was underpredicted by 45% with the RANS model. The local values of E in the impeller stream also compare well with measured values.