Volume 24, Issue 4
Numerical Simulations for the Quasi-3D Fluid Streamer Propagation Model: Methods and Applications

Chijie Zhuang, Mengmin Huang & Rong Zeng

Commun. Comput. Phys., 24 (2018), pp. 1259-1278.

Published online: 2018-06

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  • Abstract

In this work, we propose and compare four different strategies for simulating the fluid model of quasi-three-dimensional streamer propagation, consisting of Poisson’s equation for the particle velocity and two continuity equations for particle transport in the cylindrical coordinate system with angular symmetry. Each strategy involves one method for solving Poisson’s equation, a discontinuous Galerkin method for solving the continuity equations, and a total variation-diminishing RungeKutta method in temporal discretization. The numerical methods for Poisson’s equation include discontinuous Galerkin methods, the mixed finite element method, and the least-squares finite element method. The numerical method for continuity equations is the Oden-Babuˇska-Baumann discontinuous Galerkin method. A slope limiter for the DG methods in the cylindrical coordinate system is proposed to conserve the physical property. Tests and comparisons show that all four strategies are compatible in the sense that solutions to particle densities converge. Finally, different types of streamer propagation phenomena were simulated using the proposed method, including double-headed streamer in nitrogen and SF6 between parallel plates, a streamer discharge in a point-to-plane gap.

  • Keywords

Streamer discharge, mixed finite element method, least-squares finite element method, discontinuous Galerkin method, fluid model.

  • AMS Subject Headings

65Z05, 65M06, 68U20

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COPYRIGHT: © Global Science Press

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@Article{CiCP-24-1259, author = {}, title = {Numerical Simulations for the Quasi-3D Fluid Streamer Propagation Model: Methods and Applications}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {1259--1278}, abstract = {

In this work, we propose and compare four different strategies for simulating the fluid model of quasi-three-dimensional streamer propagation, consisting of Poisson’s equation for the particle velocity and two continuity equations for particle transport in the cylindrical coordinate system with angular symmetry. Each strategy involves one method for solving Poisson’s equation, a discontinuous Galerkin method for solving the continuity equations, and a total variation-diminishing RungeKutta method in temporal discretization. The numerical methods for Poisson’s equation include discontinuous Galerkin methods, the mixed finite element method, and the least-squares finite element method. The numerical method for continuity equations is the Oden-Babuˇska-Baumann discontinuous Galerkin method. A slope limiter for the DG methods in the cylindrical coordinate system is proposed to conserve the physical property. Tests and comparisons show that all four strategies are compatible in the sense that solutions to particle densities converge. Finally, different types of streamer propagation phenomena were simulated using the proposed method, including double-headed streamer in nitrogen and SF6 between parallel plates, a streamer discharge in a point-to-plane gap.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.13}, url = {http://global-sci.org/intro/article_detail/cicp/12327.html} }
TY - JOUR T1 - Numerical Simulations for the Quasi-3D Fluid Streamer Propagation Model: Methods and Applications JO - Communications in Computational Physics VL - 4 SP - 1259 EP - 1278 PY - 2018 DA - 2018/06 SN - 24 DO - http://dor.org/10.4208/cicp.2018.hh80.13 UR - https://global-sci.org/intro/cicp/12327.html KW - Streamer discharge, mixed finite element method, least-squares finite element method, discontinuous Galerkin method, fluid model. AB -

In this work, we propose and compare four different strategies for simulating the fluid model of quasi-three-dimensional streamer propagation, consisting of Poisson’s equation for the particle velocity and two continuity equations for particle transport in the cylindrical coordinate system with angular symmetry. Each strategy involves one method for solving Poisson’s equation, a discontinuous Galerkin method for solving the continuity equations, and a total variation-diminishing RungeKutta method in temporal discretization. The numerical methods for Poisson’s equation include discontinuous Galerkin methods, the mixed finite element method, and the least-squares finite element method. The numerical method for continuity equations is the Oden-Babuˇska-Baumann discontinuous Galerkin method. A slope limiter for the DG methods in the cylindrical coordinate system is proposed to conserve the physical property. Tests and comparisons show that all four strategies are compatible in the sense that solutions to particle densities converge. Finally, different types of streamer propagation phenomena were simulated using the proposed method, including double-headed streamer in nitrogen and SF6 between parallel plates, a streamer discharge in a point-to-plane gap.

Chijie Zhuang, Mengmin Huang & Rong Zeng. (2020). Numerical Simulations for the Quasi-3D Fluid Streamer Propagation Model: Methods and Applications. Communications in Computational Physics. 24 (4). 1259-1278. doi:10.4208/cicp.2018.hh80.13
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