Self-adjusting entropy-stable scheme for compressible Euler equations**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).

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.