RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code

We have developed a new computer code, RAM, to solve the conservativeequations of special relativistic hydrodynamics (SRHD) using adaptive meshrefinement (AMR) on parallel computers. We have implemented acharacteristic-wise, finite difference, weighted essentially non-oscillatory(WENO) scheme using the full characteristic decomposition of the SRHD equationsto achieve fifth-order accuracy in space. For time integration we use themethod of lines with a third-order total variation diminishing (TVD)Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kuttatime integration schemes for comparison. The implementation of AMR andparallelization is based on the FLASH code. RAM is modular and includes thecapability to easily swap hydrodynamics solvers, reconstruction methods andphysics modules. In addition to WENO we have implemented a finite volume modulewith the piecewise parabolic method (PPM) for reconstruction and the modifiedMarquina approximate Riemann solver to work with TVD Runge-Kutta timeintegration. We examine the difficulty of accurately simulating shear flows innumerical relativistic hydrodynamics codes. We show that under-resolvedsimulations of simple test problems with transverse velocity components produceincorrect results and demonstrate the ability of RAM to correctly solve theseproblems. RAM has been tested in one, two and three dimensions and inCartesian, cylindrical and spherical coordinates. We have demonstratedfifth-order accuracy for WENO in one and two dimensions and performed detailedcomparison with other schemes for which we show significantly lower convergencerates. Extensive testing is presented demonstrating the ability of RAM toaddress challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures