@Article{CiCP-10-1001,
author = {Nicolas Crouseilles and Thomas Respaud},
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 = {<p style="text-align: justify;">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&#39;s equation, or equivalently under charge conservation, the Amp<span style="text-align: justify;">è</span>re&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.210410.211210a},
url = {http://global-sci.org/intro/article_detail/cicp/7472.html}
}