High-order Godunov schemes for global 3D MHD simulations of accretion disks. I. Testing the linear growth of the magneto-rotational instability

We assess the suitability of various numerical MHD algorithms for astrophysical accretion disk simulations with the PLUTO code. The well-studied linear growth of the magneto-rotational instability is used as the benchmark test for a comparison between the implementations within PLUTO and against the ZeusMP code. The results demonstrate the importance of using an upwind reconstruction of the electro-motive force (EMF) in the context of a constrained transport scheme, which is consistent with plane-parallel, grid-aligned flows. In contrast, constructing the EMF from the simple average of the Godunov fluxes leads to a numerical instability and the unphysical growth of the magnetic energy. We compare the results from 3D global calculations using different MHD methods against the analytical solution for the linear growth of the MRI, and discuss the effect of numerical dissipation. The comparison identifies a robust and accurate code configuration that is vital for realistic modeling of accretion disk processes.