A high-order energy-conserving semi-Lagrangian discontinuous Galerkin method for the Vlasov-Ampère system

In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin (ECSLDG) method for the Vlasov-Ampère system. The method employs a semi-Lagrangian discontinuous Galerkin scheme for spatial discretization of the Vlasov equation, achieving high-order accuracy while removing the Courant-Friedrichs-Lewy (CFL) constraint. To ensure total energy conservation, we incorporate the energy-conserving technique proposed by Liu et al. Temporal accuracy is further enhanced through a high-order operator splitting strategy, yielding a method that is high-order accurate in both space and time. The resulting ECSLDG scheme is unconditionally stable and conserves both mass and energy at the fully discrete level, regardless of spatial or temporal resolution. Numerical experiments demonstrate the accuracy, stability, and conservation properties of the proposed method. In particular, the method achieves more accurate enforcement of Gauss’s law and improved numerical fidelity over low-order schemes, especially when using a large CFL number.