High-Order Accurate Conservative Finite Difference Methods for Vlasov Equations in 2D+2V

Abstract

This manuscript discusses discretization of the Vlasov--Poisson system in 2D+2V phase space using high-order accurate conservative finite difference algorithms. One challenge confronting direct kinetic simulation is the significant computational cost associated with the high-dimensional phase space description. In the present work we advocate the use of high-order accurate schemes as a mechanism to reduce the computational cost required to deliver a given level of error in the computed solution. We pursue a discretely conservative finite difference formulation of the governing equations, and discuss fourth- and sixth-order accurate schemes. In addition, we employ a minimally dissipative nonlinear scheme based on the well-known WENO (weighted essentially nonoscillatory) approach. Verification of the full formulation is performed using the method of manufactured solutions. Results are also presented for the physically relevant scenarios of Landau damping, and growth of transverse instabilities from an imposed plane wave.