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 - <p style="text-align: justify;">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.</p>