High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
复制标题
DOI：
10.1007/s42967-021-00150-5
复制
发表时间：
2021-08
影响因子：
1.6
通讯作者：
A. Christlieb;M. Link;Hyoseon Yang;Ruimeng Chang
中科院分区：
文献类型：
--
作者：
A. Christlieb;M. Link;Hyoseon Yang;Ruimeng Chang
本文提出了一种基于非多项式函数空间的半拉格朗日（SL）方法来求解Vlasov方程。我们发现，一个非多项式函数为基础的计划是适合的具体目标问题。为了解决等离子体问题的相空间模型中出现的问题，我们开发了一个加权基本无振荡（韦诺）计划使用三角多项式。特别地，非多项式韦诺方法能够在尖锐梯度或不连续性附近实现改进的精度。此外，为了获得不仅在空间而且在时间上的高阶精度，建议在时间上应用高阶分裂格式。我们的目标是介绍整个SL算法与高阶分裂在时间和高阶韦诺重建在空间上解决Vlasov-Poisson系统。一些数值实验证明所提出的方法在具有高阶收敛性和捕获非光滑解的鲁棒性。一个关键的观察是，该方法可以捕获相位结构，需要两倍的分辨率与基于多项式的方法。在6D中，这将是一个巨大的节省。
In this paper, we present a semi-Lagrangian (SL) method based on a non-polynomial function space for solving the Vlasov equation. We find that a non-polynomial function based scheme is suitable to the specifics of the target problems. To address issues that arise in phase space models of plasma problems, we develop a weighted essentially non-oscillatory (WENO) scheme using trigonometric polynomials. In particular, the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities. Moreover, to obtain a high-order of accuracy in not only space but also time, it is proposed to apply a high-order splitting scheme in time. We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system. Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions. A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method. In 6D, this would represent a significant savings.