Suppressing spurious oscillations and particle noise in particle-in-cell simulations

Abstract: Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used in PIC codes to solve Maxwell's equations produces spurious oscillations near discontinuities, which can lead to unphysical solutions. In this work, we present numerical techniques to address these challenges within the semi-implicit PIC code FLEKS, which is based on the Gauss's Law-satisfying Energy-Conserving Semi-Implicit Particle-in-Cell method (GL-ECSIM). First, we introduce a Lax-Friedrichs-type diffusion term with a flux limiter into the Maxwell solver to suppress unphysical oscillations near discontinuities. Second, we propose a novel approach for calculating the current density in the comoving frame, which significantly reduces particle noise in simulations with fast plasma flows. Numerical tests are presented to demonstrate the effectiveness of these methods in mitigating spurious oscillations and noise in shock and magnetic reconnection simulations.