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三阶WENO-Z格式精度分析及其改进格式

徐维铮 吴卫国

徐维铮, 吴卫国. 三阶WENO-Z格式精度分析及其改进格式[J]. 应用数学和力学, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011
引用本文: 徐维铮, 吴卫国. 三阶WENO-Z格式精度分析及其改进格式[J]. 应用数学和力学, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011
XU Weizheng, WU Weiguo. Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. doi: 10.21656/1000-0887.390011
Citation: XU Weizheng, WU Weiguo. Precision Analysis of the 3rd-Order WENO-Z Scheme and Its Improved Scheme[J]. Applied Mathematics and Mechanics, 2018, 39(8): 946-960. 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
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

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

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

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