一种治愈强激波数值不稳定性的混合方法

胡立军; 袁礼

doi:10.3879/j.issn.1000-0887.2015.05.004

一种治愈强激波数值不稳定性的混合方法

doi: 10.3879/j.issn.1000-0887.2015.05.004

胡立军,
袁礼

中国科学院数学与系统科学研究院计算数学所;科学与工程计算国家重点实验室(中国科学院), 北京 100190

基金项目: 国家重点基础研究发展计划（973计划）(2010CB731505)；国家自然科学基金(面上项目)（10972230）；创新群体项目(11321061)；国际(地区)合作与交流项目(11261160486)

详细信息

作者简介:
胡立军（1985—），男，湖南人，博士生(E-mail: hulijun@lsec.cc.ac.cn);袁礼（1963—），男，重庆人，研究员，博士，博士生导师(通讯作者. E-mail: lyuan@lsec.cc.ac.cn).

中图分类号: O354;O241.82
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- 被引次数: 0
出版历程
- 收稿日期: 2014-07-04
- 修回日期: 2015-01-13
- 刊出日期: 2015-05-15

Analysis of Numerical Shock Instability and a Hybrid Curing Method

HU Li-jun,
YUAN Li

LSEC(Chinese Academy of Sciences); Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China

Funds: The National Basic Research Program of China (973 Program)(2010CB731505)；The National Natural Science Foundation of China（General Program)（10972230）

摘要

摘要: HLLC（Harten-Lax-Leer-contact）格式是一种高分辨率格式，能够准确捕捉激波、接触间断和稀疏波.但是使用HLLC格式计算多维问题时，在强激波附近会出现激波不稳定现象.FORCE（first-order centred）格式在强激波附近表现出很好的稳定性，并且其数值耗散比HLL（Harten-Lax-Leer）格式小.分析了HLLC格式和FORCE格式在特定流动条件下的稳定性，构造了HLLC-FORCE混合格式并且进一步结合开关函数来消除HLLC格式的激波不稳定现象.数值试验表明新构造的混合格式不仅能够消除HLLC格式的激波不稳定现象，还最大程度地保留HLLC格式高分辨率的优点.
- 数值激波不稳定性 /
- 稳定性分析 /
- HLLC-FORCE混合格式 /
- MUSCL重构
Abstract: HLLC is a high resolution scheme, which can capture shock, contact discontinuity and rarefaction wave accurately. But when it is used to calculate multidimensional problems, the phenomenon of numerical shock instability may appear near the strong shock. Compared with the HLLC scheme, the FORCE scheme is stable near the strong shock, and the related numerical dissipation is lower than that of the HLL scheme. The stability of HLLC and FORCE under special conditions was analyzed, a hybrid scheme combining the HLLC and FORCE schemes in a special way was constructed, and a switching function to invoke the hybrid scheme in the transverse direction of the shock wave was defined. Numerical experiments demonstrate that the hybrid scheme not only presents good stability near the strong shock, but also retains the high resolution of HLLC.
- numerical shock instability /
- analysis of stability /
- HLLC-FORCE hybrid scheme /
- MUSCL reconstruction

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参考文献(19)

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