Mechanisms of plasmoid drift following massive material injection are studied via 3D non-linear MHD modelling with the JOREK code, using a transient neutral source deposited at the low field side midplane of a JET H-mode plasma to clarify basic processes and compare with existing theories. The simulations confirm the important role of the propagation of shear Alfv\'en wave (SAW) packets from both ends of the plasmoid (``SAW braking'') and the development of external resistive currents along magnetic field lines (``P\'egouri\'e braking'') in limiting charge separation and thus the $\mathbf{E}\times \mathbf{B}$ plasmoid drift, where $\mathbf{E}$ and $\mathbf{B}$ are the electric and magnetic fields, respectively. The drift velocity is found to be limited by the SAW braking on the few microseconds timescale for cases with relatively small source amplitude while the P\'egouri\'e braking acting on a longer timescale is shown to set in earlier with larger toroidal extent of the source, both in good agreement with existing theories. The simulations also identify the key role of the size of the $\mathbf{E}\times \mathbf{B}$ flow region on plasmoid drift and show that the saturated velocity caused by dominant SAW braking agrees well with theory when considering an effective pressure within the $\mathbf{E}\times \mathbf{B}$ flow region. The existence of SAWs in the simulations is demonstrated and the 3D picture of plasmoid drift is discussed.
