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Volume 32, Issue 3
A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates

Yi Wang, Jiexing Zhang & Guoxi Ni

DOI: 10.4208/cicp.OA-2022-0033

Commun. Comput. Phys., 32 (2022), pp. 779-809.

Published online: 2022-09

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  • Abstract

Many configurations in plasma physics are axisymmetric, it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates. In this paper, a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed, our algorithm is based on Strang splitting. The equation is divided into two parts, one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme, and the other is the acceleration part solved by a Runge-Kutta solver. The asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration. Numerical results show it can capture the process from non-equilibrium to equilibrium state by Coulomb collisions, and numerical accuracy is obtained.

  • Keywords

Vlasov-BGK-Poisson equations, cylindrical coordinates, gas-kinetic scheme, asymptotic preserving property, Coulomb collisions.

  • AMS Subject Headings

65M08, 65M06, 35Q99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-779, author = {Wang , YiZhang , Jiexing and Ni , Guoxi}, title = {A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {3}, pages = {779--809}, abstract = {

Many configurations in plasma physics are axisymmetric, it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates. In this paper, a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed, our algorithm is based on Strang splitting. The equation is divided into two parts, one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme, and the other is the acceleration part solved by a Runge-Kutta solver. The asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration. Numerical results show it can capture the process from non-equilibrium to equilibrium state by Coulomb collisions, and numerical accuracy is obtained.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0033}, url = {http://global-sci.org/intro/article_detail/cicp/21045.html} }
TY - JOUR T1 - A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates AU - Wang , Yi AU - Zhang , Jiexing AU - Ni , Guoxi JO - Communications in Computational Physics VL - 3 SP - 779 EP - 809 PY - 2022 DA - 2022/09 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0033 UR - https://global-sci.org/intro/article_detail/cicp/21045.html KW - Vlasov-BGK-Poisson equations, cylindrical coordinates, gas-kinetic scheme, asymptotic preserving property, Coulomb collisions. AB -

Many configurations in plasma physics are axisymmetric, it will be more convenient to depict them in cylindrical coordinates compared with Cartesian coordinates. In this paper, a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed, our algorithm is based on Strang splitting. The equation is divided into two parts, one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme, and the other is the acceleration part solved by a Runge-Kutta solver. The asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch configuration. Numerical results show it can capture the process from non-equilibrium to equilibrium state by Coulomb collisions, and numerical accuracy is obtained.

Wang , YiZhang , Jiexing and Ni , Guoxi. (2022). A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates. Communications in Computational Physics. 32 (3). 779-809. doi:10.4208/cicp.OA-2022-0033
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