Applications of Artificial Wind Numerical Scheme for Relativistic Hydrodynamics in Astrophysics

Abstract

We apply a new way for the construction of efficient non-oscillation shock-capturing schemes, namely artificial wind (AW) scheme, for relativistic hydrodynamics (RHD) simulations in astrophysics. We also discuss physical foundations for computational RHD. An appropriate choice for a realistic equation of state of the matter at relativistic temperatures drastically facilitates the procedure for numerical integration of hydrodynamics equations. The time-consuming iteration approach to solve the coupling equation is avoided. We have developed a 2-D relativistic hydrodynamics code based on the AW scheme and the new RHD. Here we present two applications of the code in astrophysics, namely, numerical simulations of ultra-relativistic jet propagation andrelativistic Richtmyer-Meshkov instability. Due to numerical difficulties arising from strong relativistic shocks, motions with large value ofthe Lorentz f as well as due to the complicated structure ofthe relativistic equations, relativistic fluid simulations are traditionally believed to be much more difficult as compared with usual hydrodynamic simulations. Furthermore, the coupling equation between the primitive variables and the conservative ones through Lorentz factor γ is a quartic equation which should be solved at each cell several times ofiteration using Newton Raphson procedure to update the numerical solution for one time step. As a result, the relativistic codes are drastically time-consuming. Here, we apply a new way for the construction of efficient non-oscillation shockcapturing scheme, i.e., artificial wind (AW) scheme, for relativistic hydrodynamics simulation. The basic idea ofAW scheme is to solve the governing equations in different steadily moving frames of reference chosen in such a way that the flow is supersonic there, resulting in simple upwind formulas. The concept and principle of the AW scheme is given in an accompanying paper. 1) Recently, we proposed a new form of computational relativistic hydrodynamics (RHD). The key point is a special equation ofstate (EOS) f or the matter at relativistic temperature. 2) The new EOS is much more realistic, and can drastically facilitate the procedure for explicitly expressing the conservative variables via the primitive ones, and reversely, expressing the primitive variables via the conservative ones. In fact, in the new form of RHD, conservative variables are related to primitive variables through a simple second-order algebraic equation, the time-consuming iteration to solve the coupling equation is avoided. Here, we present two astrophysical applications. The first one is ultra-relativistic jet propagating through a homogeneous medium. The simulation has been run on