Self-adjusting entropy-stable scheme for compressible Euler equations

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

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

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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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