A higher-order accurate algorithm based on two-dimensional unstructured mesh for simulation of charge transportation in solid dielectrics.

In a high voltage direct current (HVDC) transmission system, the devices like HVDC cable and its accessory, HVDC bush play important roles in power transmission and power transformation. The local electric field could be greatly enhanced due to the space charge accumulation in the insulation, which significantly influences the electrical performance of the electric devices. In this paper, an algorithm for solving the charge coupled systems of solid dielectrics is presented. The algorithm is based upon a finite element method (FEM) solving the Poisson equation and a finite volume method (FVM) discretizing the transportation equation on a cell-centered tessellation. Both FEM and FVM share a set of unstructured mesh. The study focuses on the capability of different upwind schemes on capture of charge density step. The numerical experiment results show that in contrast to conventional methods that constrain charge densities to piecewise constants within a cell, a higher-order approximation of charge density is obtained by reconstructing the charge densities gradient in the control volumes. And the oscillation could be avoided when a limiter function is adopted to make sure that no new extrema created between the central cell and the neighbor cells. The influences of time step, total calculation time, and the mesh structured or not are also investigated. The results show that the algorithm could provide enough accuracy when suitable time step and time duration are adopted with unstructured mesh. [ABSTRACT FROM PUBLISHER]