标题： 高阶能量守恒半拉格朗日间断伽辽金方法求解Vlasov-Ampere系统 显示英文标题

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

摘要： 本文提出了一种高阶能量守恒半拉格朗日间断伽辽金（ECSLDG）方法，用于求解Vlasov-Ampere系统。该方法采用半拉格朗日间断伽辽金格式对Vlasov方程的空间进行离散化，在实现高精度的同时去除了Courant-Friedrichs-Lewy（CFL）约束。为了确保能量守恒并消除对等离子体周期的解析需求，我们采用了刘等人引入的能量守恒时间离散化方法[《计算物理杂志》，492 (2023), 112412]。通过高阶算子分裂策略进一步提高了时间精度，从而得到一个时空均具有高阶精度的方法。所得的ECSLDG格式在空间和时间上都是无条件稳定的，并且在完全离散的层面上保持质量和能量守恒，与空间或时间分辨率无关。数值实验表明了所提方法的精度、稳定性和守恒性质。特别是，该方法在使用大CFL数时，能够更准确地执行高斯定律并提高数值保真度，超过低阶方案。 显示英文摘要

摘要： 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.