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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
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一种新型的高分辨率通量差分裂格式
A novel high-resolution flux difference splitting scheme
投稿时间:2020-08-10  修订日期:2020-12-23
DOI:10.7511/jslx20200810001
中文关键词:  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
英文关键词:compressible flow  flux difference splitting scheme  Zha-Bilgen splitting method  boundary variation diminishing algorithm  high-resolution  robustness
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.
作者单位E-mail
胡立军 衡阳师范学院 数学与统计学院, 衡阳 421002 hulijun@lsec.cc.ac.cn 
赵昆磊 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  
袁海专 湘潭大学 数学与计算科学学院, 湘潭 411105  
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中文摘要:
      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。
英文摘要:
      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.
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