  An efficient algorithm without flux correction for simulation of corona
discharges is proposed. The algorithm referred to as the position-state
separation method (POSS) is used to solve convection-dominated continuity
equations commonly present in corona discharges modelling. 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 CFL time step. These special
features enable POSS to have great potential in modeling of corona discharges
in long interelectrode gaps and for long simulation times.
