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In this paper, we present a high order conservative semi-Lagrangian (SL)Hermite weighted essentially non-oscillatory (HWENO) method for the Vlasovequation based on dimensional splitting [Cheng and Knorr, Journal ofComputational Physics, 22(1976)]. The major advantage of HWENO reconstruction,compared with the original WENO reconstruction, is compact. For the splitone-dimensional equation, to ensure local mass conservation, we propose a highorder SL HWENO scheme in a conservative flux-difference form, following thework in [J.-M. Qiu and A. Christlieb, Journal of Computational Physics,v229(2010)]. Besides performing dimensional splitting for the original 2Dproblem, we design a proper splitting for equations of derivatives to ensurelocal mass conservation of the proposed HWENO scheme. The proposed fifth orderSL HWENO scheme with the Eulerian CFL condition has been tested to work well incapturing filamentation structures without introducing oscillations. Weintroduce WENO limiters to control oscillations when the time stepping size islarger than the Eulerian CFL restriction. We perform classical numerical testson rigid body rotation problem, and demonstrate the performance of our schemevia the Landau damping and two-stream instabilities when solving theVlasov-Poisson system.

A conservative semi-Lagrangian HWENO method for the Vlasov equation