A comparison of numerical methods for charge transport simulation in insulating materials

Bipolar charge transport (BCT) model has been widely used to simulate time/space evolution of space charges in insulating materials. The BCT simulations are performed to investigate the relationships between space charge accumulation and conduction, electroluminescence (EL), charge packet formation, electrical breakdown, and surface potential decay (SPD) properties. Accordingly, the charge advection-reaction equation that contains shocks or high gradient regions should be solved by highly accurate and stable numerical methods to obtain high resolution. We use Runge-Kutta discontinuous Galerkin (RKDG) method and finite differential weighted essentially non-oscillatory (WENO) method to resolve the charge advection-reaction equation. Then, we calculate the SPD properties and space charge profiles of corona charged low-density polyethylene (LDPE) at various initial surface potentials. The simulated results of the two schemes are compared with analytical SPD results, and also compared with each other. It is found that the simulated SPD curves of RKDG and WENO in the case of single carrier injection are both consistent with the analytical results. Moreover, in the case of both single carrier injection and bipolar carrier injection, WENO scheme is more accurate than RKDG scheme at a given spatial discretization.