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This paper develops the high-order accurate entropy stable finite differenceschemes for one- and two-dimensional special relativistic hydrodynamicequations. The schemes are built on the entropy conservative flux and theweighted essentially non-oscillatory (WENO) technique as well as explicitRunge-Kutta time discretization. The key is to technically construct theaffordable entropy conservative flux of the semi-discrete second-order accurateentropy conservative schemes satisfying the semi-discrete entropy equality forthe found convex entropy pair. As soon as the entropy conservative flux isderived, the dissipation term can be added to give the semi-discrete entropystable schemes satisfying the semi-discrete entropy inequality with the givenconvex entropy function. The WENO reconstruction for the scaled entropyvariables and the high-order explicit Runge-Kutta time discretization areimplemented to obtain the fully-discrete high-order schemes. Several numericaltests are conducted to validate the accuracy and the ability to capturediscontinuities of our entropy stable schemes.

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