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


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

Preview Full PDF BiBTex 152 333
  • 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

  • Cited by