Multidimensional VlasovPoisson 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 three-stage 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 $128^3\times 128^3$ mesh grids have been successfully performed on a massively parallel computer.

27 pages, 21 figures. Accepted for publication in Astrophysical Journal

References in corpus (3)

• Collisionless Stellar Hydrodynamics as an Efficient Alternative to N-body Methods
• Boltzmann moment equation approach for the numerical study of anisotropic stellar disks
• Multi-Moment Advection scheme for Vlasov simulations

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