An implicit time integration approach for simulation of corona discharges

Abstract

Corona discharge is a type of electric discharge that occurs when a small conductor carries a voltage strong enough to ionize the surrounding air. The resultant ions are drifted by the electric field and transfer their momentum to neutral particles via elastic collisions, creating a flow effect known as ionic wind that has promising application in flow control. Over the last two decades, a large amount of numerical works have been realized to study this effect. However, simulation of corona discharges with explicit time integration usually requires an excessive amount of time to finish, ranging from days to months in two dimensions, depending on mesh size and physical end time. The reason lies in the profound disparity between physical time scales in a discharge: for example, electron density evolves on the order of picoseconds while the time scale of airflow dynamics is on the order of milliseconds. The objective of this work is therefore to reduce the CPU time of corona discharges. We propose an implicit time strategy in the scope of the Local Field Approximation plasma model. We investigate some algorithms, namely the Lie operator splitting, the Douglas-Rachford method and a nonlinear variant of the Gauss-Seidel algorithm, to solve the system of discrete equations, which are adapted to take into consideration a constraint on the electron density. This constraint is introduced to compensate for sources of electrons from physical processes that are not accounted for in the plasma model; it is expressed by a minimum density, or floor density, imposed on the electrons. Therefore, simplified plasma models can be employed for discharge simulations, for instance a four-specie, four-reaction model is used in this article. The investigation is done on a one-dimensional wire-to-wire corona discharge. After having identified the most suitable algorithm, we carry on to two-dimensional simulations and compare the numerical results with experiment data for different levels of floor density.