Applied Mathematics and Mechanics (English Edition)
题名：Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism
作者：Xuesong LI, Xiaodong REN, Chunwei GU
单位：Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
摘要： The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism (MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed, and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust. More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.
关键词：Roe scheme   expansion shock   shock instability   momentum interpolation mechanism (MIM)   robust   curing method   
Cite this article as:
Li, X. S., Ren, X. D., and Gu, C. W. Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism. Applied Mathematics and Mechanics
(English Edition), 39(4), 455–466 (2018) https://doi.org/10.1007/s10483-017-2283-8
全文链接：http://www.amm.shu.edu.cn/EN/abstract/abstract15266.shtml