Numerical modelling of atmospheric pressure gas discharges leading to plasma production

In this paper, we give a detailed review of recent work carried out on the numerical characterization of non-thermal gas discharge plasmas in air at atmospheric pressure. First, we briefly describe the theory of discharge development for dielectric barrier discharges, which is central to the production of non-equilibrium plasma, and we present a hydrodynamic model to approximate the evolution of charge densities. The model consists of the continuity equations for electrons, positive and negative ions coupled to Poisson's equation for the electric field. We then describe features of the finite element flux corrected transport algorithm, which has been developed to specifically aim for accuracy (no spurious diffusion or oscillations), efficiency (through the use of unstructured grids) and ease of extension to complex 3D geometries in the framework of the hydrodynamic model in gas discharges. We summarize the numerical work done by other authors who have applied different methods to various models and then we present highlights of our own work, which includes code validation, comparisons with existing results and modelling of radio frequency systems, dc discharges, secondary effects such as photoionization and plasma production in the presence of dielectrics. The extension of the code to 3D for more realistic simulations is demonstrated together with the adaptive meshing technique, which serves to achieve higher efficiency. Finally, we illustrate the versatility of our scheme by using it to simulate the transition from non-thermal to thermal discharges.