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Open AccessArticle

A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws

School of Science, Chang’an University, Xi’an 710064, China
Entropy 2019, 21(5), 508; https://doi.org/10.3390/e21050508
Received: 7 April 2019 / Revised: 13 May 2019 / Accepted: 17 May 2019 / Published: 19 May 2019
(This article belongs to the Special Issue Entropy and Non-Equilibrium Statistical Mechanics)
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. View Full-Text
Keywords: conservation laws; entropy stable; entropy conservative; non-oscillatory reconstruction; sign property conservation laws; entropy stable; entropy conservative; non-oscillatory reconstruction; sign property
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Cheng, X. A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws. Entropy 2019, 21, 508.

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