An inventive multi-scale, multiphysics modeling approach and comparative analysis of distinctive features of planar ionization waves in air: I. Negative streamers

A multiscale-multiphysics model of two different patterns of negative discharge (droplets and branches) based on the well-known electro-hydrodynamic equations in a two-dimensional non-axisymmetric configuration is developed to investigate the main features of the negative discharge (e.g. bifurcation, stochastic branching, and evolution of all charged particles including positive and negative ions and electrons). We discuss the challenges behind the finite-element-based streamer models and illustrate the robustness and efficiency of introduced three different meshing techniques via coupled fixed and adaptively refined meshes in terms of the accuracy of results and computational burden. The capability of the model in representing an outstanding spatial resolution of the streamer propagation and its stages is demonstrated under both uniform and non-uniform electric fields. A further required extension of the presented model for the representation of the positive streamer is presented in part II of this series paper. Also, in this part, the distinctive characteristics of both positive and negative streamers are presented, and the different features achieved from the model are thoroughly discussed and compared with the prior experimental results.