Multidimensional VlasovPoisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes

Understand

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.