| 分辨率优化的混合WENO格式 |
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| 引用本文： | 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. |
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| 作者姓名： | 郭元 田奇 梁贤 李新亮 |
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| 作者单位： | 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 |
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| 基金项目： | 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 |
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| 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.
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| 关 键 词： | 混合格式 数值耗散 色散 保单调 优化 |
| 收稿时间： | 2017-03-23 |
| 修稿时间： | 2017-05-25 |
A Hybrid WENO Scheme for Resolution Optimization |
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| 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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| Authors: | GUO Yuan TIAN Qi LIANG Xian LI Xinliang |
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| Institution: | 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 |
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| 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. |
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| Keywords: | hybrid scheme numerical dissipation numerical dispersion monotonicity-preserving optimize |
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