一种改进的Roe格式及其稳定性分析  

A Modified Roe Scheme and Stability Analysis

作　　者：胡立军 赵昆磊 HU Lijun;ZHAO Kunlei(College of Mathematics and Statistics,Hengyang Normal University,Hengyang,Hunan 421002,P.R.China;LSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China)

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421002 [2]中国科学院数学与系统科学研究院科学和工程计算国家重点实验室,北京100190

出　　处：《应用数学和力学》2020年第10期1110-1124,共15页Applied Mathematics and Mechanics

摘　　要：低耗散的激波捕捉方法,包括流行的Roe格式,在计算多维强激波问题时会遭遇激波不稳定现象的困扰,这会严重影响格式对于高超声速流动问题的精确模拟.对Roe格式进行小扰动分析,结果表明:激波面纵向所有物理量的扰动均会衰减,而横向的密度扰动和剪切速度扰动不会衰减.在横向数值通量上增加与熵波和剪切波相对应的黏性来抑制Roe格式不稳定现象的发生.为了防止不合适的黏性影响格式对于接触间断和剪切层的分辨率,定义两个开关函数,使得黏性仅仅添加在激波层亚声速区的横向数值通量上.数值测试的结果表明:改进的Roe格式不仅保留了原始Roe格式高分辨率的优点,而且具有更好的鲁棒性,消除了激波不稳定现象.Low dissipation shock⁃capturing methods,including the popular Roe scheme,will encounter the shock instability phenomenon in the computation of the multidimensional strong shock wave problems.This will seriously affect the schemes’accurate simulation of the hyper⁃sonic flow problems.The small perturbation analysis of the Roe scheme was carried out.The results show that,all perturbations in the longitudinal direction of the shock front are damped,but the perturbations of density and shear velocity in the transverse direction are undamped.The viscosities corresponding to the entropy wave and shear wave were added to the flux trans⁃verse to the shock front to suppress instability of the Roe scheme.To prevent the improper vis⁃cosity from influencing the resolution of contact discontinuity and shear layers,2 switching functions were defined,so that the viscosity was only added to the transverse flux in the sub⁃sonic region of the shock layer.The numerical tests show that,the modified Roe scheme not only retains the merit of high resolution of the original Roe scheme,but also has better robust⁃ness and eliminates the shock wave instability.

关 键 词：高超声速流 Roe格式 小扰动分析 数值黏性 激波不稳定性 

分 类 号：O354[理学—流体力学] O241.82[理学—力学]