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

In this, the second of a series of three papers, we continue 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. In this paper, we give a detailed description of the magnetohydrodynamical (MHD) algorithms in ZEUS-2D. The recently developed constrained transport (CT) algorithm is implemented for the numerical evolution of the components of the magnetic eld for MHD simulations. This formalism guarantees the numerically evolved eld components will satisfy the divergence-free constraint at all times. We nd, however, that the method used to compute the electromotive forces must be chosen carefully to propagate accurately all modes of MHD wave families (in particular shear Alfv en waves). A new method of computing the electromotive force is developed using the method of characteristics (MOC). It is demonstrated through the results of an extensive series of MHD test problems that the resulting hybrid MOC-CT method provides for the accurate evolution of all modes of MHD wave families. Subject headings: hydrodynamics hydromagnetics numerical methods radiative transfer 1 Also Department of Astronomy, University of Illinois at Urbana-Champaign AAS WGAS macros v2.0