Title: 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.