An efficient algorithm without flux correction for simulation of coronadischarges is proposed. The algorithm referred to as the position-stateseparation method (POSS) is used to solve convection-dominated continuityequations commonly present in corona discharges modelling. The proposedsolution method combines an Eulerian scheme for the solution of the convectiveacceleration, the diffusion and the reaction subproblems, and a Lagrangianscheme for the solution of the linear convection subproblem. Several classicalnumerical experiments in different dimensions and coordinate systems areconducted to demonstrate the excellent performance of POSS regarding lowcomputational cost, robustness, and high-resolution. It is shown that the timecomplexity of the method when dealing with the convection of charged particlesincreases linearly with the number of unknowns. For the simulation of coronadischarges where local electric fields do not change strongly in time, the timestep of POSS could be much larger than the CFL time step. These specialfeatures enable POSS to have great potential in modeling of corona dischargesin long interelectrode gaps and for long simulation times.
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