We assess the validity of a single step Godunov scheme for the solution of
the magneto-hydrodynamics equations in more than one dimension. The scheme is
second-order accurate and the temporal discretization is based on the
dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The
proposed scheme employs a cell-centered representation of the primary fluid
variables (including magnetic field) and conserves mass, momentum, magnetic
induction and energy. A variant of the scheme, which breaks momentum and energy
conservation, is also considered. Divergence errors are transported out of the
domain and damped using the mixed hyperbolic/parabolic divergence cleaning
technique by Dedner et al. (J. Comput. Phys., 175, 2002). The strength and
accuracy of the scheme are verified by a direct comparison with the eight-wave
formulation (also employing a cell-centered representation) and with the
popular constrained transport method, where magnetic field components retain a
staggered collocation inside the computational cell. Results obtained from two-
and three-dimensional test problems indicate that the newly proposed scheme is
robust, accurate and competitive with recent implementations of the constrained
transport method while being considerably easier to implement in existing hydro
codes.Comment: 31 Pages, 16 Figures Accepted for publication in Journal of
Computational Physic
