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一种健壮的低耗散通量分裂格式
引用本文:胡立军,袁礼,翟健.一种健壮的低耗散通量分裂格式[J].应用数学和力学,2019,40(2):150-166.
作者姓名:胡立军  袁礼  翟健
作者单位: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
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.

关 键 词:Euler方程    Zha-Bilgen分裂    HLL    R-ZB    低耗散    数值激波不稳定性
收稿时间:2018-04-25

A Robust and Low-Dissipation Flux Splitting Scheme
Institution:1College of Mathematics and Statistics, Hengyang Normal University, Hengyang, Hunan 421002, P.R.China;2Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R.China;3Dawning Information Industry Co., Ltd., Beijing 100193, P.R.China
Abstract: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 flaw of 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.
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