Volume 10, Issue 4
A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

Nicolas Crouseilles & Thomas Respaud

Commun. Comput. Phys., 10 (2011), pp. 1001-1026.

Published online: 2011-10

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  • Abstract

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampère's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

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@Article{CiCP-10-1001, author = {}, title = {A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations}, journal = {Communications in Computational Physics}, year = {2011}, volume = {10}, number = {4}, pages = {1001--1026}, abstract = {

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampère's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.210410.211210a}, url = {http://global-sci.org/intro/article_detail/cicp/7472.html} }
TY - JOUR T1 - A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations JO - Communications in Computational Physics VL - 4 SP - 1001 EP - 1026 PY - 2011 DA - 2011/10 SN - 10 DO - http://dor.org/10.4208/cicp.210410.211210a UR - https://global-sci.org/intro/article_detail/cicp/7472.html KW - AB -

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampère's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

Nicolas Crouseilles & Thomas Respaud. (2020). A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations. Communications in Computational Physics. 10 (4). 1001-1026. doi:10.4208/cicp.210410.211210a
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