发表机构
Uppsala University（乌普萨拉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种用于Vlasov-Maxwell系统的高阶迎风SBP有限差分方法，在GPU上实现无矩阵计算，保证质量守恒和动量保持，并通过基准问题验证其精度与鲁棒性。
AI 中文摘要
本文提出了一种用于在2D2V相空间中求解Vlasov-Maxwell系统的高阶、稳定的求和分部（SBP）有限差分方法。当解变得不光滑并发展出细尺度丝状结构时（这是高维Vlasov-Maxwell模拟中的典型情况），用于平流项的中央SBP算子不稳定。为解决此问题，该方法使用高阶迎风SBP算子进行稳定化。时间积分采用高阶显式Runge-Kutta方法。我们证明了全离散格式精确守恒质量，并在截断误差阶内保持动量。此外，我们在现代GPU架构上提出了该方法的无矩阵实现。通过求解一系列具有挑战性的基准问题，验证了所提格式的精度、鲁棒性和性能。
英文摘要
In this paper, we present a high-order, stable summation-by-parts (SBP) finite difference method for solving the Vlasov-Maxwell system in a 2D2V phase space. Central SBP operators for the advection terms are not stable when the solution becomes non-smooth and fine-scale filamentary structures develop, as is typical in high-dimensional Vlasov-Maxwell simulations. To address this issue, the method is stabilized using high-order upwind SBP operators. High-order explicit Runge-Kutta methods are employed for time integration. We prove that the fully discrete scheme exactly conserves mass and preserves momentum up to truncation error. Furthermore, we present a matrix-free implementation of the method on modern GPU architectures. A range of challenging benchmark problems is solved to demonstrate the accuracy, robustness, and performance of the proposed scheme.
Comments26 pages, 7 figures
