Multidimensional Vlasov–Poisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes

Abstract

We develop new numerical schemes for Vlasov-Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is also preserved. We adopt an efficient semi-Lagrangian time integration scheme that is more accurate and computationally less expensive than the threestage TVD Runge-Kutta integration. We apply our spatially fifth-and seventh-order schemes to a suite of simulations of collisionless self-gravitating systems and electrostatic plasma simulations, including linear and nonlinear Landau damping in one dimension and Vlasov-Poisson simulations in a six-dimensional phase space. The high-order schemes achieve a significantly improved accuracy in comparison with the third-order positive-flux-conserved scheme adopted in our previous study. With the semi-Lagrangian time integration, the computational cost of our high-order schemes does not significantly increase, but remains roughly the same as that of the third-order scheme. Vlasov-Poisson simulations on 128 3 ×128 3 mesh grids have been successfully performed on a massively parallel computer.

Editorial: Adaptive Kinetic-Fluid Models for Plasma Simulations on Modern Computer Systems

“…It is shown that the spatial and velocity resolutions should be adapted together rather than independently for optimal efficiency. This contributes to the ongoing discussion [4][5][6][7], of splitting vs non-splitting methods for mesh adaptation in phase space.…”

A Mean-field Approach to Simulating the Merging of Collisionless Stellar Systems Using a Particle-based Method

“…In order to reveal how faithfully the SCF simulations shown here can follow the true evolution, the most desirable approach may be a comparison of the simulations with the SCF code to those with a six-dimensional phase-space code developed by Yoshikawa et al (2013), which has been touched up by Tanaka et al (2017), or with that based on a moving adaptive simplicial tessellation method devised by Sousbie & Colombi (2016), since no gravitational softening is included in these codes. In fact, Yoshikawa et al (2013) have presented a sample simulation of merging two identical King spheres.…”

Highly accurate monotonicity-preserving Semi-Lagrangian scheme for Vlasov-Poisson simulations

“…However, this limiter has limitation of Courant-Friedrichs-Lewy (CFL) condition. It has been applied recently to the Semi-Lagrangian method and for the Vlasov-Poisson system [49]. Note also that an extension work of [48] has been made [21] to give more relaxation space.…”