高精度格式非线性权的统计谱特性分析

doi:10.19596/j.cnki.1001-246x.7812

计算物理 ›› 2019, Vol. 36 ›› Issue (2): 127-140.DOI: 10.19596/j.cnki.1001-246x.7812

• • 下一篇

高精度格式非线性权的统计谱特性分析

李理^1,2, 刘晓艳², 李新亮², 田保林¹, 梁贤³, 哈金才³

1. 北京应用物理与计算数学研究所, 北京 100088;
2. 中国科学院大学, 北京 100049;
3. 北方民族大学, 数学与信息科学学院, 宁夏 750021

收稿日期:2017-12-11 修回日期:2018-03-09 出版日期:2019-03-25 发布日期:2019-03-25
通讯作者: 田保林,E-mail:tian_baolin@iapcm.ac.cn;哈金才,E-mail:hjcnx@163.com
作者简介:李理(1988-),男(回族),博士,主要从事计算流体力学高精度数值方法研究,E-mail:lilili606@163.com
基金资助:
中国博士后科学基金（2016M600967）、国家自然科学基金（11702029，11771054，U1730118，11801036）及科学挑战专题（TZ2016001）资助项目

On Statistical Spectral Property of Nonlinear Weights in High Order Schemes

LI Li^1,2, LIU Xiaoyan², LI Xinliang², TIAN Baolin¹, LIANG Xian³, HA Jincai³

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China;
3. College of Mathematics & Information Science, Beifang University, Ningxia 750021, China

Received:2017-12-11 Revised:2018-03-09 Online:2019-03-25 Published:2019-03-25

摘要/Abstract

摘要： 分析激波捕捉格式/混合格式中常用的非线性权和激波识别器在谱空间中的性质.设计一套分析非线性权和激波识别器在傅里叶空间性质的统计谱特性分析方法；利用该方法对不同的非线性权和激波识别器在傅里叶空间的性质进行详细分析，给出不同非线性权和激波识别器的统计特性，并比较优劣.分析方法和结论有助于深入理解非线性格式/混合格式在数值计算中的表现，并为设计高分辨率非线性格式提供理论支撑.

关键词: 非线性权, 激波识别器, 傅里叶分析, 激波捕捉格式

Abstract: Fourier property of nonlinear weights and limiters in wave-space are analyzed. Firstly, a statistical method is designed to analyze Fourier property of nonlinear weights. Secondly, averaged values and deviations of nonlinear weights are shown, and values with change of wave-number are analyzed. It is helpful to comprehension of nonlinear schemes. The method is a guidance for designing shock-capture schemes.

Key words: nonlinear weights, shock sensors, Fourier analysis, shock-capture schemes

中图分类号:

O354

李理, 刘晓艳, 李新亮, 田保林, 梁贤, 哈金才. 高精度格式非线性权的统计谱特性分析[J]. 计算物理, 2019, 36(2): 127-140.

LI Li, LIU Xiaoyan, LI Xinliang, TIAN Baolin, LIANG Xian, HA Jincai. On Statistical Spectral Property of Nonlinear Weights in High Order Schemes[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 127-140.

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高精度格式非线性权的统计谱特性分析

On Statistical Spectral Property of Nonlinear Weights in High Order Schemes

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