An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations

TL;DR

This paper introduces an adaptive, high-order phase-space remapping method for solving 2D Vlasov-Poisson equations, improving accuracy and efficiency in plasma simulations by regularizing particle distributions and preserving positivity.

Contribution

It presents a novel adaptive remapping algorithm with high-order interpolation for 2D Vlasov-Poisson equations, including a positivity-preserving technique and parallel scalability analysis.

Findings

Successfully applied to classical plasma problems in 1D

Demonstrates improved accuracy over traditional PIC methods

Shows good parallel scalability on large computers

Abstract

The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.