Applicability analysis of the prevailing algorithms for reliable solution of the bipolar charge transport model

Abstract

For space charge simulation inside the insulating materials as to characterize the dielectric performance, apart from accuracy of the equivalent physical and mathematical models themselves, corresponding algorithms to be adopted are also crucial for a reliable solution. However, no clear boundary has so far been defined regarding applicability of the prevailing algorithms. According to the injected charge density calculated by the Schottky law, it indicates the law is no longer applicable for the situation under low electric fields, for which cases a threshold electric field is proposed by the authors as the charge injection valve. Further, the algorithms commonly used are fully accounted for different cases. Numerical simulation of a specific waveform and the results based on symmetrical parameters are firstly used to verify the accuracy of the simulation process. A comparison based on dissymmetrical parameters demonstrates that, though the QUICKEST algorithm used for the convection equation presents good applicability while either the finite difference method (FDM) or the boundary element method (BEM) is used for the Poisson’s equation, the deviation between the two methods will enlarge with increased simulation time. According to the authors’ research, it is more appropriate to use BEM combined with the finite differential weighted essentially non-oscillatory (WENO) algorithm for a reliable solution. To elucidate the difference of the QUICKEST and the WENO algorithms, further computation below the threshold electric field is implemented, which indicates the QUICKEST algorithm is no longer applicable for long-term simulation. Hence, a preferable combination WENO + BEM presents the best choice for solving the bipolar charge transport model.