分辨率优化的混合WENO格式

doi:10.19596/j.cnki.1001-246x.7664

计算物理 ›› 2018, Vol. 35 ›› Issue (4): 397-404.DOI: 10.19596/j.cnki.1001-246x.7664

分辨率优化的混合WENO格式

郭元¹, 田奇¹, 梁贤¹, 李新亮^2,3

1. 北方民族大学数学与信息科学学院, 宁夏银川 750021;
2. 中国科学院大学工程科学学院, 北京 100049;
3. 中国科学院力学研究所高温气体动力学国家重点实验室, 北京 100190

收稿日期:2017-03-23 修回日期:2017-05-25 出版日期:2018-07-25 发布日期:2018-07-25
通讯作者: 梁贤,E-mail:gavin.liang@featech.com.cn
作者简介:郭元(1993-),男,硕士,从事高精度数值方法研究,E-mail:szwdgy9806@163.com
基金资助:
国家自然科学基金（11472010，91441103，11372330，11472278）、国家重点研发计划（2016YFA0401200）、民用飞机专项科研（MJ-2015-F-028）及科学挑战专题项目（JCKY2016212A501）资助

A Hybrid WENO Scheme for Resolution Optimization

GUO Yuan¹, TIAN Qi¹, LIANG Xian¹, LI Xinliang^2,3

1. School of Mathematics and Information Science, Beifang University for Nationalities, Yinchuan 750021, China;
2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China;
3. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Received:2017-03-23 Revised:2017-05-25 Online:2018-07-25 Published:2018-07-25

摘要/Abstract

摘要： 为提高有限差分格式的分辨率，利用傅里叶分析对WENO格式进行色散及耗散优化，并给出优化的线性权重.用优化后的WENO格式与保单调格式（MP）进行加权混合，得到新的加权混合WENO格式（H-WENO）.通过一维激波管问题、Shu-Osher问题及二维双Mach反射问题及R-T不稳定性问题对格式进行数值测试.结果显示，新格式具有强健的激波捕捉能力和对小尺度波结构的高分辨率，与原WENO格式相比改进明显.

关键词: 混合格式, 数值耗散, 色散, 保单调, 优化

Abstract: To improve finite difference scheme, Fourier analysis is used to optimize dispersion and dissipation of WENO scheme. And optimal linear weights are given. A class of hybrid schemes is designed by combing optimized WENO schemes with monotonicity-preserving scheme. A weighted hybrid WENO scheme(H-WENO) is obtained. The scheme is tested with one-dimensional shock tube problem, Shu-Osher problem, two-dimensional Mach reflection problem and R-T instability problem. It shows that the scheme has strong ability to capture shock wave and high resolution for small scale wave structure, which is improved obviously compared with original WENO scheme.

Key words: hybrid scheme, numerical dissipation, numerical dispersion, monotonicity-preserving, optimize

中图分类号:

O354.5

郭元, 田奇, 梁贤, 李新亮. 分辨率优化的混合WENO格式[J]. 计算物理, 2018, 35(4): 397-404.

GUO Yuan, TIAN Qi, LIANG Xian, LI Xinliang. A Hybrid WENO Scheme for Resolution Optimization[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(4): 397-404.

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分辨率优化的混合WENO格式

A Hybrid WENO Scheme for Resolution Optimization

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