@Article{AAMM-12-1,
author = {Duan , Junming and Tang , Huazhong},
title = {High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2019},
volume = {12},
number = {1},
pages = {1--29},
abstract = {<p style="text-align: justify;">This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory (WENO) technique as well as explicit Runge-Kutta time discretization. The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair. As soon as the entropy conservative flux is derived, the dissipation term can be added to give the semi-discrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function. The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization&nbsp;are implemented to obtain the fully-discrete high-order entropy stable schemes. Several numerical tests
are conducted to validate the accuracy and the ability to capture discontinuities of our
entropy stable schemes.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0124},
url = {http://global-sci.org/intro/article_detail/aamm/13417.html}
}