Numerical simulations on the melt flow down the keyhole front during fibre laser welding are presented here. The calculations confirm the existence of melt waves previously observed by high speed imaging, with velocities ranging between 4-10 m/s. The simulations provide spatial and temporal information on the temperature and flow fields, particularly within the melt film volume, which cannot be observed by high speed imaging. The ablation pressure achieves high values around wave-peaks and at the bottom of the front, just before droplets are sheared off. The simulation results provide explanations on the main liquid transport mechanisms within the keyhole based on information on the temperature, velocity and pressure field and on the geometrical front conditions.