Modeling of Streamer in Gas by FEM and Semi-Lagrangian Method

Determining the likelihood of occurrence, growth and extinction of partial discharges between two conductors is a key point when designing electrical devices such as transformers, electrical machines or busbars. The continuity equations governing both time- and position-dependence of charged particle densities makes it possible to build the most comprehensive model of partial discharge development in gas. Known in the literature as fluid model, plasma model or even electrohydrodynamic model, it consists of a set of advection-diffusion-reaction type equations strongly coupled to Poisson’s equation that still remains challenging to solve by means of FEM due to numerical instability. This paper deals with the modeling of spatio-temporal growth of partial discharge inside gas using FEM and stabilized by a semi-Lagrangian method. The main contribution lies in the development of the weak formulation of the state problem in the general case for the electro-hydrodynamic problem. The simulation based on this formulation of the POSS method is validated for a streamer discharge.