研究成果・発表論文

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

Tanaka, Satoshi,   Yoshikawa, Kohji,   Minoshima, Takashi,   & Yoshida, Naoki

要旨
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 the 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$× \128\$^3$ mesh grids have been successfully performed on a massively parallel computer.