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Volume 35, Issue 3
An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality

Chuwen Ma & Shi Jin

DOI: 10.4208/cicp.OA-2023-0133

Commun. Comput. Phys., 35 (2024), pp. 724-760.

Published online: 2024-04

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  • Abstract

An implicit, asymptotic-preserving and energy-charge-conserving (APECC) Particle-In-Cell (PIC) method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral regime. Charge conservation is enforced by particle orbital averaging and fixed sub-time steps. The truncation error depending on the number of sub-time steps is further analyzed. The temporal discretization is chosen by the Crank-Nicolson method to conserve the discrete energy exactly. The key step in the asymptotic-preserving iteration for the nonlinear system is based on a decomposition of the current density deduced from the Vlasov equation in the source of the Maxwell model. Moreover, we show that the convergence is independent of the quasi-neutral parameter. Extensive numerical experiments show that the proposed method can achieve asymptotic preservation and energy-charge conservation.

  • Keywords

Vlasov-Maxwell, quasi-neutrality, asymptotic-preserving, energy-charge conservation.

  • AMS Subject Headings

65M06, 78A25, 78A35, 78-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-35-724, author = {Ma , Chuwen and Jin , Shi}, title = {An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality}, journal = {Communications in Computational Physics}, year = {2024}, volume = {35}, number = {3}, pages = {724--760}, abstract = {

An implicit, asymptotic-preserving and energy-charge-conserving (APECC) Particle-In-Cell (PIC) method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral regime. Charge conservation is enforced by particle orbital averaging and fixed sub-time steps. The truncation error depending on the number of sub-time steps is further analyzed. The temporal discretization is chosen by the Crank-Nicolson method to conserve the discrete energy exactly. The key step in the asymptotic-preserving iteration for the nonlinear system is based on a decomposition of the current density deduced from the Vlasov equation in the source of the Maxwell model. Moreover, we show that the convergence is independent of the quasi-neutral parameter. Extensive numerical experiments show that the proposed method can achieve asymptotic preservation and energy-charge conservation.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0133}, url = {http://global-sci.org/intro/article_detail/cicp/23058.html} }
TY - JOUR T1 - An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality AU - Ma , Chuwen AU - Jin , Shi JO - Communications in Computational Physics VL - 3 SP - 724 EP - 760 PY - 2024 DA - 2024/04 SN - 35 DO - http://doi.org/10.4208/cicp.OA-2023-0133 UR - https://global-sci.org/intro/article_detail/cicp/23058.html KW - Vlasov-Maxwell, quasi-neutrality, asymptotic-preserving, energy-charge conservation. AB -

An implicit, asymptotic-preserving and energy-charge-conserving (APECC) Particle-In-Cell (PIC) method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral regime. Charge conservation is enforced by particle orbital averaging and fixed sub-time steps. The truncation error depending on the number of sub-time steps is further analyzed. The temporal discretization is chosen by the Crank-Nicolson method to conserve the discrete energy exactly. The key step in the asymptotic-preserving iteration for the nonlinear system is based on a decomposition of the current density deduced from the Vlasov equation in the source of the Maxwell model. Moreover, we show that the convergence is independent of the quasi-neutral parameter. Extensive numerical experiments show that the proposed method can achieve asymptotic preservation and energy-charge conservation.

Chuwen Ma & Shi Jin. (2024). An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality. Communications in Computational Physics. 35 (3). 724-760. doi:10.4208/cicp.OA-2023-0133
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