Three-dimensional (3-D) images are presented for the propagation of streamers in a short uniform gap in air at atmospheric pressure. Results are obtained through a self-consistent solution of the hydrodynamic diffusion-drift model, which includes Poisson's equation and the continuity equations for the charged particles. A 3-D extension of the finite element-flux corrected transport (FE-FCT) algorithm with the incorporation of a new subgridding scheme for the efficient calculation of secondary effects, such as photoionization, is utilized to obtain these 3-D simulation images. Index Terms-Finite element flux corrected transport (FE-FCT), gas discharge, numerical simulation, plasma, streamers, threedimensional.A CHARACTERIZATION of gas discharge phenomena, such as streamers and coronas, requires in its simplest form the solution of the continuity equations for electrons, positive ions and negative ions coupled with Poisson's equation [1]. The complete characterization of such processes requires the use of three-dimensional (3-D) models, due to their inherently complex nature. There was a need, therefore, to develop new numerical methods to overcome computational restrictions associated with the time consuming, transient and shock-like nature of these phenomena, such as the duration of calculations, the complexity of the domains, and the need for accurate solutions. The development of the finite element-flux corrected transport (FE-FCT) algorithm by the authors [2], which leads to improvements in computing efficiency and accuracy due mainly to the unstructured nature of the finite element (FE) grids, in conjunction with the advent of more powerful computers, has opened up the road to the solution of complex gas discharge problems in fully 3-D form and to a better understanding of the processes involved. Furthermore, the special treatment (namely the subgridding scheme) of computationally very demanding and very important processes, such as photoionization and photoemission, which is central to the development of gas discharges, has made possible their inclusion in the new 3-D model.The formulation described in [2] for the solution of gas discharge problems in air is used here and extended to take into account the third dimension in space, secondary processes such as photoionization, photoemission, and secondary ionization, due to ion impact at the cathode surface, through the incorporation of the subgridding scheme [3]. Ionization, recombination, attachment, transport, and diffusion mechanisms are also considered. The solution procedure consists of the following steps. Given an initial charge at time , the field is calculated through the solution of Poisson's equation; this is then used to update the transport parameters, which are fed to the continuity equations to establish the charge densities at time . Having the charge densities at , the field at can be calculated, and finally, after establishing the transport parameters at , the charge densities are updated for time . This procedure is repeated until the whole...
