Self-adjusting entropy-stable scheme for compressible Euler equations

doi:10.1088/1674-1056/24/2/020202

›› 2015, Vol. 24 ›› Issue (2): 20202-020202.doi: 10.1088/1674-1056/24/2/020202

Self-adjusting entropy-stable scheme for compressible Euler equations

程晓晗^a, 聂玉峰^a, 封建湖^b, Luo Xiao-Yu^c, 蔡力^a

a School of Science, Northwestern Polytechnical University, Xi'an 710129, China;
b School of Science, Chang'an University, Xi'an 710064, China;
c School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

收稿日期:2014-07-17 修回日期:2014-08-22 出版日期:2015-02-05 发布日期:2015-02-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11171043, 11101333, and 11471261 ) and the Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX201426).

Self-adjusting entropy-stable scheme for compressible Euler equations

Cheng Xiao-Han (程晓晗)^a, Nie Yu-Feng (聂玉峰)^a, Feng Jian-Hu (封建湖)^b, Luo Xiao-Yu^c, Cai Li (蔡力)^a

a School of Science, Northwestern Polytechnical University, Xi'an 710129, China;
b School of Science, Chang'an University, Xi'an 710064, China;
c School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

Received:2014-07-17 Revised:2014-08-22 Online:2015-02-05 Published:2015-02-05
Contact: Nie Yu-Feng E-mail:yfnie@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11171043, 11101333, and 11471261 ) and the Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX201426).

摘要/Abstract

摘要： In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy.

关键词: compressible Euler equations, entropy-stable scheme, switch function

Abstract: In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy.

Key words: compressible Euler equations, entropy-stable scheme, switch function

中图分类号: (Partial differential equations)

02.30.Jr

02.70.Bf (Finite-difference methods)

程晓晗, 聂玉峰, 封建湖, Luo Xiao-Yu, 蔡力. Self-adjusting entropy-stable scheme for compressible Euler equations[J]. , 2015, 24(2): 20202-020202.

Cheng Xiao-Han (程晓晗), Nie Yu-Feng (聂玉峰), Feng Jian-Hu (封建湖), Luo Xiao-Yu, Cai Li (蔡力). Self-adjusting entropy-stable scheme for compressible Euler equations[J]. Chin. Phys. B, 2015, 24(2): 20202-020202.

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Self-adjusting entropy-stable scheme for compressible Euler equations

Self-adjusting entropy-stable scheme for compressible Euler equations

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