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一种新型的高分辨率通量差分裂格式
引用本文:胡立军,赵昆磊,袁海专.一种新型的高分辨率通量差分裂格式[J].计算力学学报,2021,38(6):810-818.
作者姓名:胡立军  赵昆磊  袁海专
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;湘潭大学数学与计算科学学院,湘潭411105
基金项目:国家自然科学基金(11871414);湖南省自然科学基金(2021JJ40009)资助项目.
摘    要:传统的Roe格式不满足熵条件并且在计算激波问题时会遭遇不同形式的不稳定现象,如慢行激波的波后振荡和红玉(carbuncle)现象.基于Zha-Bilgen对流-压力通量分裂方法,构造一种新型的通量差分裂格式.利用约旦标准型理论,通过添加广义特征向量构造通量差分裂方法来计算对流子系统.压力子系统具有一组完备的线性无关特征向量,因此可以构造传统的通量差分裂格式进行计算.为了提高接触间断的分辨率,利用界面变差下降(BVD)算法来重构对流通量耗散项中的密度差.激波稳定性分析表明,新格式可以有效地衰减数值误差,从而抑制不稳定现象的发生.一系列数值实验证明了本文构造的新型通量差分裂格式比Roe格式具有更高的分辨率和更好的鲁棒性.

关 键 词:可压缩流  通量差分裂格式  Zha-Bilgen分裂方法  界面变差下降算法  高分辨率  鲁棒性
收稿时间:2020/8/10 0:00:00
修稿时间:2020/12/23 0:00:00

A novel high-resolution flux difference splitting scheme
HU Li-jun,ZHAO Kun-lei,YUAN Hai-zhuan.A novel high-resolution flux difference splitting scheme[J].Chinese Journal of Computational Mechanics,2021,38(6):810-818.
Authors:HU Li-jun  ZHAO Kun-lei  YUAN Hai-zhuan
Institution:School of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, China;ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
Abstract:The conventional Roe scheme does not satisfy the entropy condition and encounters different forms of instability in calculation of shocks,such as the postshock oscillations in slowly moving shocks and the carbuncle phenomenon.Based on the Zha-Bilgen convection-pressure flux splitting method,a novel flux difference splitting scheme is proposed.Using the theory of Jordan form,a flux difference splitting method is constructed by adding generalized eigenvectors to calculate the convection subsystem.The pressure subsystem has a complete set of linearly independent eigenvectors,so it can be calculated by the conventional flux difference splitting scheme.In order to improve the resolution of contact discontinuities,the boundary variation diminishing (BVD) algorithm is implemented to reconstruct the density difference in the dissipation term of convection flux.The analysis of shock stability shows that the new scheme can effectively reduce numerical errors and thus suppress the instability.A series of numerical experiments demonstrate that the proposed flux difference splitting scheme has higher resolution and better robustness than the Roe scheme.
Keywords:compressible flow  flux difference splitting scheme  Zha-Bilgen splitting method  boundary variation diminishing algorithm  high-resolution  robustness
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