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In this paper, we extended the recent work of Liu and Becerra to employ the position-state separation (POSS) method to simulate filamentary streamer discharges. POSS is a semi-Lagrangian method, which solves convection-dominated continuity equations without numerical flux correction. An improved interpolation strategy for POSS is here introduced to overcome the excessive numerical diffusion of the method when very small time step is used. Several benchmark tests in the literature are used to validate the improved method. Numerical experiments show that POSS is an accurate, efficient, and robust numerical method to simulate streamer discharges in arbitrary geometries when combined with finite-element method. [ABSTRACT FROM PUBLISHER]

An efficient algorithm without flux correction for the simulation of corona discharges is proposed. The algorithm referred to as the position-state separation (POSS) method is used to solve convection-dominated continuity equations commonly present in corona discharges modeling. The proposed solution method combines an Eulerian scheme for the solution of the convective acceleration, the diffusion and the reaction subproblems, and a Lagrangian scheme for the solution of the linear convection subproblem. Several classical numerical experiments in different dimensions and coordinate systems are conducted to demonstrate the excellent performance of POSS regarding low computational cost, robustness, and high resolution. It is shown that the time complexity of the method when dealing with the convection of charged particles increases linearly with the number of unknowns. For the simulation of corona discharges where local electric fields do not change strongly in time, the time step of POSS could be much larger than the Courant–Friedrichs–Lewy time step. These special features enable POSS to have great potential in the modeling of corona discharges in long interelectrode gaps and for long simulation times. [ABSTRACT FROM AUTHOR]