Volume 12, Issue 1
High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics

Junming Duan and Huazhong Tang

10.4208/aamm.OA-2019-0124

Adv. Appl. Math. Mech., 12 (2020), pp. 1-29.

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  • Abstract

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 are implemented to obtain the fully-discrete high-order entropy stable schemes.


  • History

Published online: 2019-12

  • AMS Subject Headings

65M10, 78A48

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