High-order fluid model for streamer discharges: II. Numerical solution and investigation of planar fronts

Abstract

The high-order fluid model developed in part I of this series 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 particle-in-cell/Monte Carlo (PIC/MC) 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.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

“…The salient feature of their theory is the fact that the heat flux term in the energy balance equation was explicitly neglected, but this, unfortunately, is of questionable accuracy. We will illustrate in streamer simulations in our second paper [76] that the energy flux plays an important role in determining the streamer behavior. Thus, particular care should be taken with the closure through specification of the energy flux.…”

“…We will see that the closure of this equation is not a straight forward process, and we will discuss some approximations made in the literature. The results of a second order model and of our high order model for planar streamer fronts will be compared in our second paper [76].…”

An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries

“…In this paper we will consider the minimal fluid model where the electrons and ions are described only by their average densities, and the momentum equations are closed by imposing drift and diffusion velocities to be functions of the electric field. Certainly, improvements to this model are possible by using Euler equations for the electrons, as is done in [39,40,41].…”

Advanced fluid modeling and PIC/MCC simulations of low-pressure ccrf discharges

“…In Refs. [37,38] it has been shown that the four-moment model proposed in Ref. [29] is more accurate than conventional fluid approaches for the theoretical description of negative streamer fronts in nitrogen and neon, while the classical fluid model using the local field approximation (LFA) [39,40] gives reasonably good results under these conditions, too [38].…”