ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I. The hydrodynamic algorithms and tests

In this, the first of a series of three papers, we begin a detailed description of ZEUS-2D, a numerical code for the simulation of fluid dynamical flows in astrophysics including a self-consistent treatment of the effects of magnetic fields 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 first 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 finite-differences implemented in a new covariant formalism which allows simulation in any orthogonal coordinate system. The effect of self-gravity on the flow dynamics is accounted for by an iterative solution of the sparse-banded matrix resulting from discretizing the Poisson equation in multidimensions. The results of an extensive series of HD test problems are presented.