标题： 保正的高阶半拉格朗日谱体积法求解Vlasov-Poisson方程 显示英文标题

标题： The positivity-preserving high-order semi-Lagrangian spectral volume method for Vlasov-Poisson equations

摘要： 本文提出了一种新的高阶半拉格朗日（SL）谱体积（SV）方法，并通过算子分裂技术研究了其在非线性 Vlasov-Poisson（VP）模拟中的应用。所提出的算法结合了半拉格朗日法和谱体积法的优点，表现出强稳定性、在大时间步长下的鲁棒性、空间上的任意高阶精度、局部质量守恒以及正性保持能力。对应用于一维和二维输运方程、Vlasov-Poisson 系统以及包括朗道阻尼和双流不稳定现象在内的经典基准问题的 SLSV 方法进行了数值研究，证实了我们算法在处理复杂非线性现象方面的有效性、准确性和鲁棒性。 显示英文摘要

摘要： In this paper, a novel high order semi-Lagrangian (SL) spectral volume (SV) method is proposed and studied for nonlinear Vlasov-Poisson (VP) simulations via operator splitting. The proposed algorithm combines both advantages of semi-Lagrangian and spectral volume approaches, exhibiting strong stability, robustness under large time steps, arbitrary high-order accuracy in space, local mass conservation, and positivity preservation. Numerical study of the SLSV method applied to the one-dimensional and two-dimensional transport equations, the Vlasov-Poisson system, the classical benchmark problems including Landau damping and two-stream instabilities is conducted, confirming the effectiveness, accuracy, and robustness of our algorithm in addressing complex nonlinear phenomena.