The hydrogen ionization and dissociation front around an ultraviolet radiation source should merge when the ratio of ionizing photon flux to gas density is sufficiently low and the spectrum is sufficiently hard. This regime is particularly relevant to the molecular knots that are commonly found in evolved planetary nebulae, such as the Helix Nebula, where traditional models of photodissociation regions have proved unable to explain the high observed luminosity in H_2 lines. In this paper we present results for the structure and steady-state dynamics of such advection-dominated merged fronts, calculated using the Cloudy plasma/molecular physics code. We find that the principal destruction processes for H_2 are photoionization by extreme ultraviolet radiation and charge exchange reactions with protons, both of which form H_2^+, which rapidly combines with free electrons to undergo dissociative recombination. Advection moves the dissociation front to lower column densities than in the static case, which vastly increases the heating in the partially molecular gas due to photoionization of He^0, H_2, and H^0. This causes a significant fraction of the incident bolometric flux to be re-radiated as thermally excited infrared H_2 lines, with the lower excitation pure rotational lines arising in 1000 K gas and higher excitation H_2 lines arising in 2000 K gas, as is required to explain the H_2 spectrum of the Helix cometary knots.
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