北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (12): 2400-2405.doi: 10.13700/j.bh.1001-5965.2016.0863

• 论文 • 上一篇    下一篇

一种三阶WENO-Z格式改进方法

徐维铮1,2, 孔祥韶1,2, 郑成1,2, 吴卫国1,2   

  1. 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, 武汉 430063
  • 收稿日期:2016-11-10 修回日期:2017-01-20 出版日期:2017-12-20 发布日期:2017-04-13
  • 通讯作者: 孔祥韶 E-mail:kongxs@whut.edu.cn
  • 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。
  • 基金资助:
    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)

An improved method for third-order WENO-Z scheme

XU Weizheng1,2, KONG Xiangshao1,2, ZHENG Cheng1,2, WU Weiguo1,2   

  1. 1. Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, China;
    2. School of Transportation, Wuhan University of Technology, Wuhan 430063, China
  • Received:2016-11-10 Revised:2017-01-20 Online:2017-12-20 Published:2017-04-13
  • Supported by:
    National Defense Basic Research Program (B1420133057); National Natural Science Foundation of China (51409202);the Fundamental Research Funds for the Central Universities (2016-YB-016)

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。

关键词: 三阶WENO-Z格式, 全局光滑因子, 精度分析, 低耗散, 高分辨率

Abstract: High resolution shock capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. WENO-Z3N1, WENO-Z3N2 and WENO-Z3N3 schemes were constructed through different global smoothness indicators based on the third-order WENO-Z scheme (WENO-Z3 scheme). Several classical examples such as sod problem, interacting blast wave and shock entropy wave interaction were simulated to investigate the computing performance of the three schemes (WENO-Z3N1, WENO-Z3N2, WENO-Z3N3). Precision of the three schemes was analyzed theoretically according to Taylor series expansion. It is concluded that theoretical precision of the three schemes at non-critical points plays the important role in the actual computing performance after discussion on the relationship between the theoretical precision and actual calculation accuracy. Double Mach reflection problem was conducted to further verify the reliability of the above conclusion. The research in the present paper gives an improved method for third-order WENO-Z scheme:global smoothness indicators should be reasonably constructed to make scheme satisfy the requirement of design precision at non-critical points in the smooth flow fields.

Key words: third-order WENO-Z scheme, global smoothness indicator, precision analysis, low dissipation, high resolution

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