The Convergence of Particle-in-Cell Schemes for Cosmological Dark Matter Simulations

Understand

Particle methods are a ubiquitous tool for solving the Vlasov-Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter in an expanding universe.

• However, these methods are known to produce poor results on idealized test problems, particularly at late times, after the particle trajectories have crossed.
• To investigate this, we have performed a series of one- and two-dimensional "Zel'dovich Pancake" calculations using the popular Particle-in-Cell (PIC) method.
• We find that PIC can indeed converge on these problems provided the following modifications are made.