Multi-Dimensional Vlasov-Poisson Simulations with High-Order Monotonicity and Positivity Preserving Schemes [CL]

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 which 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.

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S. Tanaka, K. Yoshikawa, T. Minoshima, et. al.
Wed, 1 Mar 17

Comments: 24 pages, 19 figures. Submitted to the Astrophysical Journal