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 fluid dynamical flows in astrophysics including a self-consistent treatment of the effects of magnetic fields 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 field for MHD simulations. This formalism guarantees the numerically evolved field components will satisfy the divergence-free constraint at all times. We find, 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 o..