TY - JOUR
T1 - High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics
AU - Duan , Junming
AU - Tang , Huazhong
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 1
EP - 29
PY - 2019
DA - 2019/12
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0124
UR - https://global-sci.org/intro/article_detail/aamm/13417.html
KW - Entropy conservative scheme, entropy stable scheme,  high order accuracy, finite difference scheme, special relativistic hydrodynamics.
AB - <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>