# High-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamics

## TL;DR

This paper introduces high-order accurate entropy stable finite difference schemes for 1D and 2D special relativistic hydrodynamics, ensuring numerical stability and accuracy for complex fluid simulations.

## Contribution

It presents a novel construction of entropy conservative fluxes combined with WENO and Runge-Kutta methods for relativistic hydrodynamics, improving stability and accuracy.

## Key findings

- Schemes achieve high-order accuracy in tests.
- Methods effectively capture discontinuities.
- Numerical validation confirms stability and precision.

## 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 schemes. Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.