三阶WENO-Z格式精度分析及其改进格式

徐维铮; 吴卫国

doi:10.21656/1000-0887.390011

三阶WENO-Z格式精度分析及其改进格式

doi: 10.21656/1000-0887.390011

徐维铮^1,2,
吴卫国^1,2

¹武汉理工大学高性能舰船技术教育部重点实验室, 武汉 430063;²武汉理工大学交通学院船舶、海洋与结构工程系, 武汉 430063

基金项目: 国防基础研究项目(B1420133057);国家自然科学基金(51409202);中央高校基本科研业务费(2016-YB-016)

详细信息

作者简介:
徐维铮(1991—)，男，博士生(E-mail: xuweizheng@whut.edu.cn);吴卫国(1960—)，男，教授，博士生导师(通讯作者. E-mail: mailjt@163.com).

中图分类号: O357.1
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出版历程
- 收稿日期: 2018-01-03
- 修回日期: 2018-01-29
- 刊出日期: 2018-08-15

Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme

XU Weizheng^1,2,
WU Weiguo^1,2

¹Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, P.R.China;²Department of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan 430063, P.R.China

Funds: The National Natural Science Foundation of China(51409202)

摘要

摘要: 首先通过理论推导给出了三阶WENO格式(WENO-JS3格式)满足收敛精度的充分条件.采用Taylor(泰勒)级数展开的方法，分析发现传统的三阶WENO-Z格式(WENO-Z3格式)在光滑流场极值点处精度降低.为了提高WENO-Z3格式在极值点处的计算精度，根据收敛精度的充分条件构造一种改进的三阶WENO-Z格式(WENO-NZ3格式)，并综合权衡计算精度和计算稳定性确定所构造格式的参数.通过两个典型的精度测试，验证了WENO-NZ3格式在光滑流场极值点区域逼近三阶精度.选用Sod激波管、激波与熵波相互作用、Rayleigh-Taylor不稳定性、二维Riemann(黎曼)问题经典算例，进一步证实了本文提出的WENO-NZ3格式相较其他格式（WENO-JS3、WENO-Z3、WENO-N3），不仅提高了计算精度，而且提高了对复杂流场结构的分辨率.
- 三阶WENO格式 /
- 光滑因子 /
- Taylor展开 /
- 高精度 /
- 高分辨率 /
- 双曲守恒律
Abstract: Firstly, the sufficient conditions for the 3rd-order WENO scheme satisfying the convergence precision were deduced. Based on the Taylor series method, the precision of the conventional 3rd-order WENO-Z scheme in the smooth flow field was analyzed. It was found that at the critical points, the 3rd-order WENO-Z scheme fails to achieve the convergence precision. In order to improve the precision near the critical points for the 3rd-order WENO-Z scheme, an improved 3rd-order WENO-Z scheme (WENO-NZ3) was constructed in view of the balance between precision and stability to finally determine the parameters. The improvement of the precision was verified through 2 typical numerical tests. What is more, the Sod shock wave tube, the shock-entropy wave interaction, the Rayleigh-Taylor instability and the 2D Riemann problem were calculated to confirm that the WENO-NZ3 scheme performs better than the conventional WENO schemes like WENO-JS3, WENO-Z3 and WENO-N3.
- 3rd-order WENO scheme /
- smoothness indicator /
- Taylor expansion /
- high precision /
- high resolution /
- hyperbolic conservation law

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