**Xiaohan Cheng**

School of Science, Chang'an University, Xi'an 710064, China; xhcheng@chd.edu.cn

Received: 7 April 2019; Accepted: 17 May 2019; Published: 19 May 2019

**Abstract:** This paper develops a fourth order entropy stable scheme to approximate the entropy solution of one-dimensional hyperbolic conservation laws. The scheme is constructed by employing a high order entropy conservative flux of order four in conjunction with a suitable numerical diffusion operator that based on a fourth order non-oscillatory reconstruction which satisfies the sign property. The constructed scheme possesses two features: (1) it achieves fourth order accuracy in the smooth area while keeping high resolution with sharp discontinuity transitions in the nonsmooth area; (2) it is entropy stable. Some typical numerical experiments are performed to illustrate the capability of the new entropy stable scheme.

**Keywords:** conservation laws; entropy stable; entropy conservative; non-oscillatory reconstruction; sign property
