  In an attempt to investigate the structures of ultra-relativistic jets
injected into the intracluster medium (ICM) and the associated flow dynamics,
such as shocks, velocity shear, and turbulence, we have developed a new special
relativistic hydrodynamic (RHD) code in the Cartesian coordinates, based on the
weighted essentially non-oscillatory (WENO) scheme. It is a finite difference
scheme of high spatial accuracy, which has been widely employed for solving
hyperbolic systems of conservation equations. The code is equipped with
different WENO versions, such as the 5th-order accurate WENO-JS (Jiang & Shu
1996), WENO-Z, and WENO-ZA, and different time integration methods, such as the
4th-order accurate Runge-Kutta (RK4) and strong stability preserving RK
(SSPRK), as well as the implementation of the equations of state (EOSs) that
closely approximate the EOS of the single-component perfect gas in relativistic
regime. In addition, it incorporates a high-order accurate averaging of fluxes
along the transverse directions to enhance the accuracy of multi-dimensional
problems, and a modification of eigenvalues for the acoustic modes to
effectively control the carbuncle instability. Through extensive numerical
tests, we assess the accuracy and robustness of the code, and choose WENO-Z,
SSPRK, and the EOS suggested in Ryu et al. (2006) as the fiducial setup for
simulations of ultra-relativistic jets. The results of our study of
ultra-relativistic jets using the code is reported in an accompanying paper
(Seo et al. 2021, Paper II).
