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一种健壮的混合Roe黎曼求解器
引用本文:胡立军,袁礼,翟健.一种健壮的混合Roe黎曼求解器[J].计算力学学报,2019,36(6):818-824.
作者姓名:胡立军  袁礼  翟健
作者单位:衡阳师范学院 数学与统计学院, 衡阳 421002,中国科学院 数学与系统科学研究院计算数学与科学工程计算研究所, 北京 100190,曙光信息产业(北京)有限公司, 北京 100193
摘    要:使用Roe格式计算多维流动问题时,在强激波附近会出现数值激波不稳定现象。带有剪切粘性的HLLEC格式不仅可以捕捉接触间断,而且表现出很好的稳定性。混合Roe格式和HLLEC格式来消除数值激波不稳定性。在强激波附近,通过激波面法向和网格界面法向的夹角来定义开关函数,使得数值通量在激波面横向切换成HLLEC格式。在其余地方,数值通量依然使用Roe格式来计算。数值试验表明,混合格式不仅消除了Roe格式的数值激波不稳定性,还最大程度地减少了HLLEC格式所带来的剪切耗散,保留了Roe格式高分辨率的优点。

关 键 词:无粘可压缩流  Roe格式  HLLEC格式  Roe-HLLEC格式  数值激波不稳定性
收稿时间:2018/9/30 0:00:00
修稿时间:2018/12/28 0:00:00

A robust hybrid Roe Riemann solver
HU Li-jun,YUAN Li,ZHAI Jian.A robust hybrid Roe Riemann solver[J].Chinese Journal of Computational Mechanics,2019,36(6):818-824.
Authors:HU Li-jun  YUAN Li  ZHAI Jian
Institution:School of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, China,Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Dawning Information Industry Co., Ltd, Beijing 100193, China
Abstract:Numerical shock instabilities will occur near strong shock waves when using Roe scheme to compute multidimensional flow problems.The HLLEC scheme with shear viscosity can not only resolve contact discontinuities,but also show good stability in numerical computation.We combine the Roe scheme and the HLLEC scheme to eliminate the numerical shock instabilities.In the vicinity of strong shock waves,the switching function is defined by the angle between the normal directions of the shock front and the cell interface,so that the numerical flux is switched to the HLLEC scheme in the transverse direction of the shock front.In other places,numerical flux is still evaluated by the Roe scheme. Numerical experiments show that the hybrid scheme proposed here can not only eliminate the shock instabilities of Roe scheme,but also reduce the shear dissipation brought by the HLLEC scheme to the greatest extent,preserving the advantage of high resolution of Roe scheme.
Keywords:inviscid compressible flows  Roe scheme  HLLEC scheme  Roe-HLLEC scheme  numerical shock instabilities
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