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Chin. Phys. B, 2015, Vol. 24(2): 020202    DOI: 10.1088/1674-1056/24/2/020202
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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-Yuc, 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
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.
Keywords:  compressible Euler equations      entropy-stable scheme      switch function  
Received:  17 July 2014      Revised:  22 August 2014      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.70.Bf (Finite-difference methods)  
Fund: 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).
Corresponding Authors:  Nie Yu-Feng     E-mail:  yfnie@nwpu.edu.cn

Cite this article: 

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 2015 Chin. Phys. B 24 020202

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