Experiments of the flow in precessing containers have repeatedly shown a rapid breakdown to turbulence, which remains unexplained to date. We present direct numerical simulations closely modelled after the experiments of Manasseh (JFM 243, 1992). Despite the four times lower Reynolds number of 4780, we still observe a transition with the same characteristics as in the experiment. Analysis of the flow state preceding the breakdown shows a relatively clean and simple overturning flow, and a strong azimuthal mean flow. Contrary to observations by Manasseh, we find no flow reversals before or during the breakdown.