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Multi-moment advection scheme for Vlasov simulations

机译：Vlasov模拟的多矩对流方案

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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.
机译：我们提出了一种新的数值方法来求解平流方程及其在弗拉索夫模拟中的应用。该方案不仅将轮廓的点值而且将其零阶至二阶分段矩都视为因变量，以更好地保存信息熵。我们已经开发出一维和二维方案，并表明与其他现有方案相比，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。二维方案可以在数百个旋转周期内精确地解决高斯轮廓的实体旋转问题，而数值扩散很小。这对于磁化等离子体的Vlasov模拟至关重要。通过一些基准测试，介绍了一维和二维方案在静电和电磁Vlasov模拟中的应用。

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