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一种三阶WENO-Z格式改进方法

徐维铮 孔祥韶 郑成 吴卫国

徐维铮, 孔祥韶, 郑成, 等 . 一种三阶WENO-Z格式改进方法[J]. 北京航空航天大学学报, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863
引用本文: 徐维铮, 孔祥韶, 郑成, 等 . 一种三阶WENO-Z格式改进方法[J]. 北京航空航天大学学报, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863
XU Weizheng, KONG Xiangshao, ZHENG Cheng, et al. An improved method for third-order WENO-Z scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863(in Chinese)
Citation: XU Weizheng, KONG Xiangshao, ZHENG Cheng, et al. An improved method for third-order WENO-Z scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863(in Chinese)

一种三阶WENO-Z格式改进方法

doi: 10.13700/j.bh.1001-5965.2016.0863
基金项目: 

国防基础科研项目 B1420133057

国家自然科学基金 51409202

中央高校基本科研业务费专项资金 2016-YB-016

详细信息
    作者简介:

    徐维铮 男, 博士研究生。主要研究方向:高精度激波捕捉格式、约束空间爆炸波数值模拟程序开发

    孔祥韶 男, 博士, 硕士生导师。主要研究方向:舰船抗爆、抗冲击

    通讯作者:

    孔祥韶, E-mail: kongxs@whut.edu.cn

  • 中图分类号: V221.3

An improved method for third-order WENO-Z scheme

Funds: 

National Defense Basic Research Program B1420133057

National Natural Science Foundation of China 51409202

the Fundamental Research Funds for the Central Universities 2016-YB-016

More Information
  • 摘要:

    高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义。在三阶WENO-Z格式(WENO-Z3)基础上,通过构造不同形式的全局光滑因子得到WENO-Z3N1、WENO-Z3N2、WENO-Z3N3格式。选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用等经典算例,考察了3种格式(WENO-Z3N1、WENO-Z3N2、WENO-Z3N3)的计算性能。根据泰勒级数展开,理论推导给出3种格式的精度分析。通过探讨各格式理论精度与实际计算精度之间的关系得到如下结论:3种格式在连续解非极值点处的理论精度对实际计算性能起决定性的作用,并通过双马赫反射问题进一步验证该结论的可靠性。本文的研究给出一种三阶WENO-Z格式的改进方法,合理构造全局光滑因子使得格式在连续解非极值点处满足设计精度的要求。

     

  • 图 1  Sod激波管计算结束后密度曲线局部放大图

    Figure 1.  Partial enlarged details of density curves after calculation for Sod shock tube

    图 2  双爆轰波碰撞计算结束后密度曲线局部放大图

    Figure 2.  Partial enlarged details of density curves after calculation for interacting blast waves

    图 3  激波与熵波相互作用计算结束后密度曲线局部放大图

    Figure 3.  Partial enlarged details of density curves after calculation for shock entropy wave interaction

    图 4  双马赫反射马赫杆附近局部放大图

    Figure 4.  Density contours of enlarged portion near Mach stems for the double Mach reflection problem

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出版历程
  • 收稿日期:  2016-11-10
  • 录用日期:  2017-01-20
  • 刊出日期:  2017-12-20

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