  We propose a constraint preserving discontinuous Galerkin method for ideal
compressible MHD in two dimensions and using Cartesian grids, which
automatically maintains the global divergence-free property. The approximation
of the magnetic field is achieved using Raviart-Thomas polynomials and the DG
scheme is based on evolving certain moments of these polynomials which
automatically guarantees divergence-free property. We also develop HLL-type
multi-dimensional Riemann solvers to estimate the electric field at vertices
which are consistent with the 1-D Riemann solvers. When limiters are used, the
divergence-free property may be lost and it is recovered by a divergence-free
reconstruction step. We show the performance of the method on a range of test
cases up to fourth order of accuracy.
