  The high order fluid model developed in the preceding paper is employed here
to study the propagation of negative planar streamer fronts in pure nitrogen.
The model consists of the balance equations for electron density, average
electron velocity, average electron energy and average electron energy flux.
These balance equations have been obtained as velocity moments of Boltzmann's
equation and are here coupled to the Poisson equation for the space charge
electric field. Here the results of simulations with the high order model, with
a PIC/MC (Particle in cell/Monte Carlo) model and with the first order fluid
model based on the hydrodynamic drift-diffusion approximation are presented and
compared. The comparison with the MC model clearly validates our high order
fluid model, thus supporting its correct theoretical derivation and numerical
implementation. The results of the first order fluid model with local field
approximation, as usually used for streamer discharges, show considerable
deviations. Furthermore, we study the inaccuracies of simulation results caused
by an inconsistent implementation of transport data into our high order fluid
model. We also demonstrate the importance of the energy flux term in the high
order model by comparing with results where this term is neglected. Finally,
results with an approximation for the high order tensor in the energy flux
equation is found to agree well with the PIC/MC results for reduced electric
fields up to 1000 Townsend, as considered in this work.
