Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System

Abstract

In this study, we advance the classic implicit moment method (IMM) particle simulation approach for the coupled Vlasov--Ampère system. We extend the IMM concept by (1) enforcing discrete consistency between the moment and kinetic system by introducing the concept of discrete consistency term and (2) efficiently converging the moment and kinetic system within a time step using a density normalized stress tensor. The new approach is energy conserving and is second-order accurate in time. The advantageous accuracy properties of the scheme are demonstrated with several numerical experiments including the challenging case of an ion acoustic shockwave problem.