Asymptotic-Preserving Particle-In-Cell method for the Vlasov–Poisson system near quasineutrality

• Published in: Journal of computational physics Vol. 229; no. 16; pp. 5630 - 5652
• Main Authors: Degond, Pierre, Deluzet, Fabrice, Navoret, Laurent, Sun, An-Bang, Vignal, Marie-Hélène
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 2010; Elsevier
• Subjects: Asymptotic properties; Asymptotic-Preserving scheme; Computation; Computational techniques; Debye length; Discretization; Exact sciences and technology; Mathematical methods in physics; Mathematical models; Mathematics; Numerical Analysis; Particle in cell technique; Physics; Plasma; Plasma frequencies; Plasma Physics; Quasineutral limit; Stability; Vlasov–Poisson; Asymptotic-Preserving scheme; Plasma; Quasineutral limit; Debye length; Vlasov–Poisson; Space-time; Discretization; Digital simulation; Calculation; Vlasov equation; Vlasov-Poisson; Calculation methods; quasineutral limit; asymptotic preserving scheme; plasma
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.04.001

This paper deals with the numerical resolution of the Vlasov–Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, Classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an “Asymptotic-Preserving” PIC scheme which is not subjected to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and space steps, this method provides a consistent PIC discretization of the quasineutral Vlasov equation. We perform several one-dimensional numerical experiments which provide a solid validation of the method and its underlying concepts, and compare the method with Classical PIC and Direct-Implicit methods.