Investigation of the purely hyperbolic maxwell system for divergence cleaning in discontinuous galerkin based particle-in-cell methods

Abstract

For the Particle-In-Cell (PIC) method which is used to simulate non-neutral plasma the charge conservation is violated. To solve this problem several approaches have been suggested. In this paper we shall investigate the hyperbolic divergence cleaning method. It has been proposed in two different manners, one enforcing only Gauss’ law and another considering both Gauss’ law and the magnetic monopole divergence constraint. We shall investigate the differences between the two approaches with numerical simulations of a quasi 2D diode with the PIC method and a pure Maxwell equations example satisfying the charge conservation in its initial conditions. We use a discontinuous Galerkin FEM-type space discretization method to solve the Maxwell equations. The results of the numerical investigations are presented and the advantages or disadvantages of both approaches w.r.t. performance and quality are discussed.