A positivity-preserving scheme for the simulation of streamer discharges in non-attaching and attaching gases

TL;DR

This paper introduces a finite difference scheme that guarantees positivity of particle densities in streamer discharge simulations, effectively handling both attaching and non-attaching gases with improved numerical stability.

Contribution

A novel positivity-preserving finite difference scheme using operator splitting for accurate streamer discharge simulation in cylindrical coordinates.

Findings

Scheme successfully preserves positivity in simulations

Effective in both attaching and non-attaching gases

Numerical examples validate scheme's robustness

Abstract

Assumed having axial symmetry, the streamer discharge is often described by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation. Without additional care for a stricter CFL condition or special treatment to the negative source term, popular methods used in streamer discharge simulations, e.g., FEM-FCT, FVM, cannot ensure the positivity of the particle densities for the cases in attaching gases. By introducing the positivity-preserving limiter proposed by Zhang and Shu \cite{ppl} and Strang operator splitting, this paper proposed a finite difference scheme with a provable positivity-preserving property in cylindrical coordinate system, for the numerical simulation of streamer discharges in non-attaching and attaching gases. Numerical examples in non-attaching gas (N$_2$) and attaching gas (SF$_6$) are given to illustrate the effectiveness of the scheme.