Uniformly accurate Particle-in-Cell method for the long time solution of the two-dimensional Vlasov–Poisson equation with uniform strong magnetic field

• Published in: Journal of computational physics Vol. 346; pp. 172 - 190
• Main Authors: Crouseilles, Nicolas, Lemou, Mohammed, Méhats, Florian, Zhao, Xiaofei
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.10.2017; Elsevier Science Ltd
• Subjects: Accuracy; Computational physics; Four dimensional; Highly oscillatory; Kinetic models; Magnetic fields; Mathematical problems; Particle in cell technique; Particle-in-Cell; Poisson distribution; Poisson equation; Two-scale formulation; Uniformly accurate; Vlasov–Poisson equation; Four dimensional; Particle-in-Cell; Kinetic models; Vlasov–Poisson equation; Highly oscillatory; Uniformly accurate; Two-scale formulation
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2017.06.011

In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov–Poisson system subject to a uniform strong external magnetic field. To do so, we consider a Particle-in-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method.