An efficient semi-Lagrangian algorithm for simulation of corona discharges: the position-state separation method

TL;DR

This paper introduces the position-state separation method (POSS), an efficient semi-Lagrangian algorithm for simulating corona discharges that combines Eulerian and Lagrangian schemes to achieve low computational cost and high accuracy.

Contribution

The paper presents a novel semi-Lagrangian algorithm, POSS, that effectively solves convection-dominated equations in corona discharge modeling without flux correction, improving efficiency and robustness.

Findings

POSS has linear time complexity with respect to the number of unknowns.

It allows larger time steps than CFL in certain conditions.

Demonstrated excellent performance in various numerical experiments.

Abstract

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.