标题： 多时刻对流方案用于Vlasov模拟 显示英文标题

标题： Multi-Moment Advection scheme for Vlasov simulations

摘要： 我们提出了一种新的数值方案，用于求解对流方程，并将其应用于Vlasov模拟。 该方案不仅处理轮廓的点值，还将其零阶到二阶分段矩作为依赖变量，以更好地保持信息熵的守恒。 我们开发了一维和二维方案，并表明与现有其他方案相比，它们在合理使用计算资源的情况下提供了非常准确的解决方案。 二维方案可以准确求解高斯轮廓的刚体旋转问题，在超过一百个旋转周期内几乎没有数值扩散。 这对于磁化等离子体的Vlasov模拟至关重要。 本文展示了该一维和二维方案在静电和电磁Vlasov模拟中的应用，并进行了一些基准测试。 显示英文摘要

摘要： We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one- and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.