There is growing theoretical and observational evidence that protoplanetary disc evolution may be significantly affected by the canonical levels of far-ultraviolet (FUV) radiation found in a star-forming environment, leading to substantial stripping of material from the disc outer edge even in the absence of nearby massive stars. In this paper, we perform the first full radiation hydrodynamic simulations of the flow from the outer rim of protoplanetary discs externally irradiated by such intermediate strength FUV fields, including direct modelling of the photon-dominated region which is required to accurately compute the thermal properties. We find excellent agreement between our models and the semi-analytic models of Facchini et al. (2016) for the profile of the flow itself, as well as the mass-loss rate and location of their ‘critical radius’. This both validates their results (which differed significantly from prior semi-analytic estimates) and our new numerical method, the latter of which can now be applied to elements of the problem that the semi-analytic approaches are incapable of modelling. We also obtain the composition of the flow, but given the simple geometry of our models we can only hint at some diagnostics for future observations of externally irradiated discs at this stage. We also discuss the potential for these models as benchmarks for future photochemical–dynamical codes.