Influence of different algorithms on the simulation of space charge packet migration in polyethylene

Numerous numerical simulations and analysis were performed to understand the phenomenon of space charge packets. In theory, the simulation of charge packet transport is based on the three physics principles: transport equation, continuity equation and Poisson's equation. As a key equation to simulate charge packet problem, it's very important to select an appropriate numerical algorithm to solve transport equation. For the sake of simplicity, supposed there is no charge injection at the electrode, without trapping and de-trapping process, and neglecting the influence of small charge packet on the applied electric field, three algorithms, FTCS Scheme, First Order Upwinding Scheme and QUICKEST Scheme, are used for solving transport equation. The results show that when the charge packet migrates across the sample, its amplitude becomes larger and the width gets narrower by using the FTCS, however, smaller and broader by the First Order Upwinding Scheme. By comparison, the charge packet can almost keep its shape by the QUICKEST Scheme, but with a relatively lower computing efficiency. When combining the objective and subjective evaluation results, it seems that QUICKEST is the most suitable compromise for the transport equation.