Volume 15, Issue 1
A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases

Chijie Zhuang & Rong Zeng

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

Published online: 2014-01

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  • 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 (N2) and attaching gas (SF6) are given to illustrate the effectiveness of the scheme.

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@Article{CiCP-15-153, author = {}, title = {A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {1}, pages = {153--178}, 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 (N2) and attaching gas (SF6) are given to illustrate the effectiveness of the scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210213.300413a}, url = {http://global-sci.org/intro/article_detail/cicp/7091.html} }
TY - JOUR T1 - A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases JO - Communications in Computational Physics VL - 1 SP - 153 EP - 178 PY - 2014 DA - 2014/01 SN - 15 DO - http://doi.org/10.4208/cicp.210213.300413a UR - https://global-sci.org/intro/article_detail/cicp/7091.html KW - AB -

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 (N2) and attaching gas (SF6) are given to illustrate the effectiveness of the scheme.

Chijie Zhuang & Rong Zeng. (2020). A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases. Communications in Computational Physics. 15 (1). 153-178. doi:10.4208/cicp.210213.300413a
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