  We report a new finite-difference scheme for two-dimensional
magnetohydrodynamics (MHD) simulations, with and without rotation, in
unstructured grids with quadrilateral cells. The new scheme is implemented
within the code VULCAN/2D, which already includes radiation-hydrodynamics in
various approximations and can be used with arbitrarily moving meshes (ALE).
The MHD scheme, which consists of cell-centered magnetic field variables,
preserves the nodal finite difference representation of $div(\bB)$ by
construction, and therefore any initially divergence-free field remains
divergence-free through the simulation. In this paper, we describe the new
scheme in detail and present comparisons of VULCAN/2D results with those of the
code ZEUS/2D for several one-dimensional and two-dimensional test problems. The
code now enables two-dimensional simulations of the collapse and explosion of
the rotating, magnetic cores of massive stars. Moreover, it can be used to
simulate the very wide variety of astrophysical problems for which multi-D
radiation-magnetohydrodynamics (RMHD) is relevant.
