用于Vlasov模拟的一类基于混合HWENO的转秩直线法

doi:10.52396/JUST-2021-0007

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (3): 202-215.DOI: 10.52396/JUST-2021-0007

用于Vlasov模拟的一类基于混合HWENO的转秩直线法

王恺鹏, 蒋琰^*, 张梦萍

中国科学技术大学数学科学学院,安徽合肥 230026

收稿日期:2021-01-04 修回日期:2021-03-20 出版日期:2021-03-31 发布日期:2021-11-16
通讯作者: * E-mail: jiangy@ustc.edu.cn

A hybrid HWENO-based method of lines transpose approach for Vlasov simulations

Wang Kaipeng, Jiang Yan^*, Zhang Mengping

School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Received:2021-01-04 Revised:2021-03-20 Online:2021-03-31 Published:2021-11-16
Contact: *E-mail: jiangy@ustc.edu.cn

摘要/Abstract

摘要： 在隐式转秩直线法(MOL^T) 框架下,针对一维线性输运方程设计了一类新型的混合Hermite加权本质无震荡(HWENO)格式,并进一步用于求解Vlasov-Poisson (VP) 方程组.相较于之前的基于加权本质无震荡(WENO)的MOL^T方法 [J. Comput. Phys., 2016,327:337-367],该新方法主要有两个优点:第一,在满足相同精度的情况下,HWENO格式比WENO格式使用更窄的模版;第二,该方法可以自动调节选取线性格式或HWENO格式.因此,混合HWENO方法既保持了WENO方法的简便性和鲁棒性,同时,又能在光滑区域减小计算误差,降低计算时间,提高计算效率.我们将设计的算法用于模拟一系列基准算例,以展示其鲁棒性和高效性.

关键词: 转秩直线法, 隐式时间离散, HWEMO方法, 混合方法, Vlasov-Poisson方程组

Abstract: A new type hybrid Hermite weighted essentially non-oscillatory (HWENO) schemes in the implicit method of lines transpose (MOL^T) framework is designed for solving one-dimensional linear transport equations and further applied to the Vlasov-Poisson (VP) simulations via dimensional splitting. Compared with the WENO-based MOL^T method given in J. Comput. Phys. [2016, 327: 337-367], the new proposed hybrid HWENO-based MOL^T scheme has two advantages. The first is the HWENO schemes using the stencils narrower than those of the WENO schemes with the same order of accuracy. The second is that the schemes can adapt between the linear scheme and the HWENO scheme automatically. In summary, the hybrid HWENO scheme keeps the simplicity and robustness of the simple WENO scheme, while it has higher efficiency with less numerical errors in smooth regions and less computational costs as well. Benchmark examples are given to demonstrate the robustness and good performance of the proposed scheme.

Key words: method of lines transpose, implicit time discretization, HWENO methodology, hybrid scheme, Vlasov-Poisson system

中图分类号:

O242.1

王恺鹏, 蒋琰, 张梦萍. 用于Vlasov模拟的一类基于混合HWENO的转秩直线法[J]. 中国科学技术大学学报, 2021, 51(3): 202-215.

WANG Kaipeng, JIANG Yan, ZHANG Mengping. A hybrid HWENO-based method of lines transpose approach for Vlasov simulations[J]. Journal of University of Science and Technology of China, 2021, 51(3): 202-215.

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用于Vlasov模拟的一类基于混合HWENO的转秩直线法

A hybrid HWENO-based method of lines transpose approach for Vlasov simulations

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