一种健壮的低耗散通量分裂格式  

A Robust and Low-Dissipation Flux Splitting Scheme

作　　者：胡立军 袁礼[2] 翟健 HU Lijun;YUAN Li;ZHAI Jian(College of Mathematics and Statistics,Hengyang Normal University, Hengyang ,Hunan 421002,P.R.China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences;Dawning Information Industry Co.,Ltd.,Beijing 100193,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,北京100190 [3]曙光信息产业(北京)有限公司,北京100193

出　　处：《应用数学和力学》2019年第2期150-166,共17页Applied Mathematics and Mechanics

摘　　要：随着计算流体力学的快速发展,设计精确、高效并且健壮的数值格式变得尤为重要.通过对3种流行的通量分裂方法(AUSM、Zha-Bilgen和Toro-Vázquez)的对流通量和压力通量进行特征分析,构造了一种简单、低耗散并且健壮的通量分裂格式(命名为R-ZB格式).采用Zha-Bilgen分裂方法将Euler方程的通量分裂成对流通量和压力通量,其中对流通量采用迎风方法来计算,压力通量采用低耗散的HLL格式来计算,从而克服了原始的HLL格式不能精确分辨接触间断的缺点.数值实验表明,该文给出的R-ZB格式不仅保留了原始Zha-Bilgen格式简单高效、能够精确分辨接触间断等优点,而且具有更好的健壮性,在计算二维问题时不会出现数值激波不稳定现象.With the rapid development of computational fluid dynamics,it is particularly important to design accurate,efficient and robust numerical schemes.Through the characteristics analyses of 3 popular flux splitting methods(AUSM,Zha-Bilgen and Toro-Vázquez),a simple,low-dissipation and robust flux splitting scheme(named as R-ZB) was constructed.The flux of Euler equations was split into a convection flux and a pressure flux with the Zha-Bilgen splitting procedure.The convection flux was computed with a simple upwinding scheme,and the pressure flux was evaluated with a low-dissipation HLL scheme to overcome the flawof failing to capture contact discontinuities.Numerical experiments show that,the proposed R-ZB scheme not only retains the merits of the original Zha-Bilgen scheme,such as simpleness,efficiency and capturing contact discontinuities accurately,etc.,but also has better robustness,which eliminates the numerical shock instabilities in the calculation of 2D problems.

关 键 词：EULER方程 Zha-Bilgen分裂 HLL R-ZB 低耗散 数值激波不稳定性 

分 类 号：O354[理学—流体力学] O241.82[理学—力学]