A divergence-free upwind code for multidimensional magnetohydrodynamic flows

A description is given for preserving del . B = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, total variation diminishing (TVD) schem e and Strang type operator splitting for multidimensionality. The method is based on the staggered mesh technique to constrain the transport of magnet ic held: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is ca lculated by interpolating the values from grid interfaces. The advective fl uxes on grid edges for the magnetic held evolution are calculated from the upwind fluxes at grid interfaces. Then the magnetic held can be maintained with del . B = 0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analyt ic solutions or with numerical solutions from a code using an explicit dive rgence-cleaning method. Also, the robustness is shown through tests involvi ng realistic astrophysical problems.