Investigating, predicting and optimising practical magnetisation techniques for charging bulk superconductors is a crucial prerequisite to their use as high performance ‘psuedo’ permanent magnets. The leading technique for such magnetisation is the pulsed field magnetisation (PFM) technique, in which a large magnetic field is applied via an external magnetic field pulse of duration of the order of milliseconds. Recently ‘giant field leaps’ have been observed during charging by PFM: this effect greatly aids magnetisation as flux jumps occur in the superconductor leading to magnetic flux suddenly intruding into the centre of the superconductor. This results in a large increase in the measured trapped field at the centre of the top surface of the bulk sample and full magnetisation. Due to the complex nature of the magnetic flux dynamics during the PFM process, simple analytical methods, such as those based on the Bean critical state model, are not applicable. Consequently, in order to successfully model this process, a multi-physical numerical model is required, including both electromagnetic and thermal considerations over short time scales. In this paper, we show that a standard numerical modelling technique, based on a 2D axisymmetric finite-element model implementing the $H$-formulation, can model this behaviour. In order to reproduce the observed behaviour in our model all that is required is the insertion of a bulk sample of high critical current density, $Jc$. We further explore the consequences of this observation by examining the applicability of the model to a range of previously reported experimental results. Our key conclusion is that the ‘giant field leaps’ reported by Weinstein $et\; al$ and others need no new physical explanation in terms of the behaviour of bulk superconductors: it is clear the ‘giant field leap’ or flux jump-assisted magnetisation of bulk superconductors will be a key enabling technology for practical applications.