发表机构
Iowa State University（爱荷华州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多物种Vlasov-Ampère系统，提出一种基于半拉格朗日间断伽辽金框架的高阶保正动力学求解器，采用算子分裂和局部限制器确保正性，并在多种标准测试案例中验证了其精度与鲁棒性。
AI 中文摘要
我们为多物种Vlasov-Ampère系统开发了一种高阶且保正的动力学求解器，该系统构建在半拉格朗日间断伽辽金（SLDG）框架内。该方法旨在广泛条件下实现高效与精确，包括具有强离子-电子尺度分离的刚性、多尺度机制。相空间通过高阶间断伽辽金有限元离散；时间步进通过高阶算子分裂和一系列一维、无条件稳定的半拉格朗日更新来处理。为提高精度和效率，每个等离子体物种在不同的相空间网格上表示。在每个单元上，对每个物种应用局部保正限制器，以防止虚假下冲并严格确保下一时间步单元平均值的正性。所得方法的准确性和鲁棒性在几个标准的单物种和双物种测试案例中得到验证，包括制造解、双流不稳定性、弱和强朗道阻尼、离子声波传播、离子声激波形成以及KEEN波动力学。
英文摘要
We develop a high-order and positivity-preserving kinetic solver for the multi-species Vlasov-Ampère system that is built within a semi-Lagrangian discontinuous Galerkin (SLDG) framework. The method is designed for efficiency and accuracy across a broad range of conditions, including stiff, multi-scale regimes with strong ion-electron scale separation. Phase space is discretized via high-order discontinuous Galerkin finite elements; time stepping is handled via high-order operator splitting and a series of one-dimensional, unconditionally stable, semi-Lagrangian updates. To improve both accuracy and efficiency, each plasma species is represented on a different phase-space mesh. On every element and for each species, local positivity-preserving limiters are applied to prevent spurious undershoots and rigorously ensure positivity of the cell averages at the next time step. The accuracy and robustness of the resulting method are verified on several standard single- and two-species test cases, including manufactured solutions, two-stream instability, weak and strong Landau damping, ion-acoustic wave propagation, ion-acoustic shock formation, and KEEN wave dynamics.
Comments39 pages, 8 figures, 3 tables
