A Simulation Study of Ultra-relativistic Jets. II. Structures and Dynamics of FR-II Jets

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 fifth-order accurate WENO-JS, WENO-Z, and WENO-ZA, and different time-integration methods, such as the fourth-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 regimes. In addition, it incorporates a high-order accurate averaging of fluxes along the transverse directions to enhance the accuracy of multidimensional 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. 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