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

Abstract: In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin(ECSLDG) method for the Vlasov-Ampere 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 energy conservation and eliminate the need to resolve the plasma period, we adopt an energy-conserving time discretization introduced by Liu et al. [J. Comput. Phys., 492 (2023), 112412]. 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.