Ram: a Relativistic Adaptive Mesh Refinement Hydrodynamics Code

We have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite difference, weighted essentially non-oscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth order accuracy in space. For time integration we use the method of lines with a third order total variation diminishing (TVD) Runge-Kutta scheme. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods and physics modules. In addition to WENO we have implemented a finite volume module with the piecewise parabolic method for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. We examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. We show that under-resolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical coordinates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics. Subject headings: hydrodynamics – methods: numerical – relativity