ZEUS-2D: A Radiation Magnetohydrodynamics Code for Astrophysical Flows in Two Space Dimensions: I. The Hydrodynamic Algorithms and Tests

In this, the rst of a series of three papers, we begin a detailed description of ZEUS-2D, a numerical code for the simulation of uid dynamical ows in astrophysics including a self-consistent treatment of the e ects of magnetic elds and radiation transfer. The algorithms in ZEUS-2D divide naturally into three areas: 1) hydrodynamics (HD), 2) magnetohydrodynamics (MHD), and 3) radiation hydrodynamics (RHD). In this rst paper, we give a detailed description of the HD algorithms which form the foundation for the more complex MHD and RHD algorithms. We use simple, well developed Eulerian HD algorithms based on the method of nite-di erences implemented in a new covariant formalism which allows simulation in any orthogonal coordinate system. The e ect of self gravity on the ow dynamics is accounted for by an iterative solution of the sparse banded matrix resulting from discretizing the Poisson equation in multi-dimensions. The results of an extensive series of HD test problems are presented. Subject headings: hydrodynamics hydromagnetics numerical methods radiative transfer 1 Also Department of Astronomy, University of Illinois at Urbana-Champaign AAS WGAS macros v2.0