Navier-Stokes simulations of liquid beryllium (Be) flows over the straight edge of plasma-facing components are carried out in conditions emulating upper dump plate (UDP) melting observed experimentally in JET. The results demonstrate the existence of three main hydrodynamic regimes featuring various degrees of downstream flow attachment to the underlying solid surface. Transitions between these regimes are characterized by critical values of the Weber number, which quantifies the relative strength of fluid inertia and surface tension, thereby providing a general stability criterion that can be applied to any instance of transient melt events in fusion devices. The predictive capabilities of the model are tested by comparing numerical output with JET data regarding the morphology of the frozen melt layers and the location of Be droplets splashed onto nearby vacuum vessel surfaces as a result of disruption current quench plasmas interacting with the solid Be tiles protecting the upper main chamber regions. Simulations accounting for the coupling between fluid flow and heat transfer confirm the key role played by re-solidification as a stabilizing process, as previously found through macroscopic melt dynamics calculations performed with the MEMOS-U code. The favourable agreement found between the simulations and the general characteristics of the JET Be UDP melt splashing give confidence that the same approach can be applied to estimate the possibility of such mechanisms occurring during disruptions on ITER.