  This paper develops entropy stable (ES) adaptive moving mesh schemes for the
2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on
the ES finite volume approximation of the RHD equations in curvilinear
coordinates, the discrete geometric conservation laws, and the mesh adaptation
implemented by iteratively solving the Euler-Lagrange equations of the mesh
adaption functional in the computational domain with suitably chosen monitor
functions. First, a sufficient condition is proved for the two-point entropy
conservative (EC) flux, by mimicking the derivation of the continuous entropy
identity in curvilinear coordinates and using the discrete geometric
conservation laws given by the conservative metrics method. Based on such
sufficient condition, the EC fluxes for the RHD equations in curvilinear
coordinates are derived and the second-order accurate semi-discrete EC schemes
are developed to satisfy the entropy identity for the given convex entropy
pair. Next, the semi-discrete ES schemes satisfying the entropy inequality are
proposed by adding a suitable dissipation term to the EC scheme and utilizing
linear reconstruction with the minmod limiter in the scaled entropy variables
in order to suppress the numerical oscillations of the above EC scheme. Then,
the semi-discrete ES schemes are integrated in time by using the second-order
strong stability preserving explicit Runge-Kutta schemes. Finally, several
numerical results show that our 2D and 3D ES adaptive moving mesh schemes
effectively capture the localized structures, such as sharp transitions or
discontinuities, and are more efficient than their counterparts on uniform
mesh.
