Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

doi:10.1007/s10483-017-2283-8

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (4): 455-466.doi: https://doi.org/10.1007/s10483-017-2283-8

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Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

Xuesong LI, Xiaodong REN, Chunwei GU

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

收稿日期:2017-02-19 修回日期:2017-05-20 出版日期:2018-04-01 发布日期:2018-04-01
通讯作者: Xuesong LI, E-mail:xs-li@mail.tsinghua.edu.cn E-mail:xs-li@mail.tsinghua.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 51736008 and 51276092)

Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

Xuesong LI, Xiaodong REN, Chunwei GU

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

Received:2017-02-19 Revised:2017-05-20 Online:2018-04-01 Published:2018-04-01
Contact: Xuesong LI E-mail:xs-li@mail.tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 51736008 and 51276092)

摘要/Abstract

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, three-dimensional problem, perturbation method, variationalprinciple. laminated plate, nonlinearity, robust, momentum interpolation mechanism (MIM), curing method, expansion shock, shock instability

Abstract:

Key words: three-dimensional problem, perturbation method, variationalprinciple. laminated plate, nonlinearity, momentum interpolation mechanism (MIM), robust, shock instability, curing method, Roe scheme, expansion shock

中图分类号:

76Lxx
76M12

Xuesong LI, Xiaodong REN, Chunwei GU. Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(4): 455-466.

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Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

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