High-order accurate implicit scheme for drift-diffusion equations and application to dielectric barrier discharges

A computational model based on fractional step methods for solving DBD discharge plasma kinetics is presented. Governing equations consist of continuity equations of charged particles in drift diffusion approximation, as well as Poisson equation for self-consistent electric field. We used a Strang splitting procedure for temporal discretization, in order to decouple drift and diffusion effects from chemical production ones. Fluxes of charged particles are discretized in space by Scharfetter Gummel scheme. We verify consistency of our numerical approach by discussing its convergence in time. Obtained solutions are benchmarked with results present in literature. Samples of numerical experiments of DBD discharge in pure nitrogen at atmospherical pressure, under different power supply types (DC and Gaussian pulse voltages) are shown.