Commun. Comput. Phys., 15 (2014), pp. 153-178.


A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases

Chijie Zhuang 1, Rong Zeng 1*

1 State Key Lab of Power Systems, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China.

Received 21 February 2013; Accepted (in revised version) 30 April 2013
Available online 26 July 2013
doi:10.4208/cicp.210213.300413a

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 [15] and Strang operator splitting, this paper proposes 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 (F_6) are given to illustrate the effectiveness of the scheme.

AMS subject classifications: 65Z05, 65M06, 68U20

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Key words: WENO finite difference, positivity-preserving, streamer discharge, numerical simulation.

*Corresponding author.
Email: chijie@tsinghua.edu.cn (C. Zhang), zengrong@tsinghua.edu.cn (R. Zeng)
 

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