The motion of flux into ring-shaped bulk high-temperature superconductors during pulsed-field magnetization (PFM) renders finite element modelling of the process more complicated than for disk-shaped bulks. The collision of two opposite-moving flux fronts within the bulk creates a thermal shock which, if poorly modelled, pollutes the numerical solution. In this work, the H-formulation is coupled with a thermal model to simulate the dynamics of ring-bulk PFM. The results are firstly validated against Brandt's analytical equations for a simple zero-field-cooled magnetization case, then extended to analyze PFM under more realistic material assumptions. The limitations, and ways to address these, of finite element modelling to predict the behavior of ring-shaped bulks during PFM are explored.