An Adaptive, High-Order Phase-Space Remapping for the Two Dimensional Vlasov--Poisson Equations

Abstract

The numerical solution of the high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to 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 using a local redistribution technique. While the one dimensional algorithm has been well established [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537], we present the two dimensional algorithm and its parallel implementation in this paper. A performance study of the parallel implementation is included. We discuss the scalability of the algorithm on massively parallel computers.