A partially dimensionally-split approach to numerical MHD

We modify an existing magnetohydrodynamics algorithm to make it more compatible with a dimensionally-split (DS) framework. It is based on the standard reconstruct-solve-average strategy (using a Riemann solver), and relies on constrained transport to ensure that the mag-netic field remains divergence-free ( ∇ · B = 0). The DS approach, combined with the use of a single, cell-centred grid (for both the fluid quantities and the magnetic field), means that the algorithm can be easily added to existing DS hydrodynamics codes. This makes it particularly useful for mature astrophysical codes, which often model more complicated physical effects on top of an underlying DS hydrodynamics engine, and therefore cannot be restructured eas-ily. Several test problems have been included to demonstrate the accuracy of the algorithm, and illustrative source code has been made freely available online. Key words: MHD – methods: numerical – magnetic fields