北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (11): 1576-1580.doi: 10.13700/j.bh.1001-5965.2013.0734

• 论文 • 上一篇    下一篇

三阶中心无振荡格式性能分析

李彦苏, 阎超, 屈峰, 于剑   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2014-01-08 出版日期:2014-11-20 发布日期:2014-12-02
  • 作者简介:李彦苏(1990-),女,江苏南通人,博士生,yansu_li@126.com.
  • 基金资助:

    国家重点基础研究发展计划资助项目(2009CB724104)

Analysis for centered nonoscillatory scheme of third order

Li Yansu, Yan Chao, Qu Feng, Yu Jian   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-01-08 Online:2014-11-20 Published:2014-12-02

摘要:

三阶中心无振荡格式Cn3(Centered nonoscillatory scheme of third order)使用对称模板构造具有三阶精度的插值公式.利用单调区域与精确区域修正原始插值参数,该格式能够获得间断附近无振荡、光滑区域高精度的计算结果.通过一维和二维典型算例,将Cn3格式与三阶和五阶WENO格式(Weighted Essentially Non-Oscillatory schemes)进行比较,重点分析了3种格式的间断分辨率、计算稳定性和数值耗散性.分析可见,Cn3格式能够精确、稳定地捕捉激波和接触间断,同时对光滑流动区域的小尺度流动结构保持较低的耗散,值得进一步研究及推广应用.

关键词: 高精度格式, WENO格式, 间断分辨率, 稳定性, 数值耗散性

Abstract:

Choosing symmetric stencils, a centered nonoscillatory scheme of third order scheme (Cn3) constructs a formula which achieves third-order accuracy. A modification of the original estimates, in the reconstruction procedure, was undertaken by employing a monotonicity region as well as an accuracy one. After the very modification, the Cn3 scheme not only obtained nonoscillatory results near discontinuities but also achieved high-accuracy calculation in smooth regions. By using several typical one- and two-dimensional test cases, Cn3 scheme was compared with the weighted essentially non-oscillatory (WENO) schemes of third and fifth order. The properties of capturing discontinuities, stability/robustness and numerical dissipation were significantly considered. The results of the numerical experiments confirm that Cn3 scheme has the ability to suppress spurious numerical oscillations near shocks and contact discontinuities when sharply capturing them, which indicates its characteristics of stability and accuracy, and has low dissipation in smooth region at the same time. Cn3 scheme is worth of further study and application.

Key words: high-accuracy scheme, WENO schemes, discontinuities capturing, stability, numerical dissipation

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