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We employ the PLUTO code for computational astrophysics to assess and comparethe validity of different numerical algorithms on simulations of themagneto-rotational instability in 3D accretion disks. In particular we stresson the importance of using a consistent upwind reconstruction of theelectro-motive force (EMF) when using the constrained transport (CT) method toavoid the onset of numerical instabilities. We show that the electro-motiveforce (EMF) reconstruction in the classical constrained transport (CT) methodfor Godunov schemes drives a numerical instability. The well-studied lineargrowth of magneto-rotational instability (MRI) is used as a benchmark for aninter-code comparison of PLUTO and ZeusMP. We reproduce the analytical resultsfor linear MRI growth in 3D global MHD simulations and present a robust andaccurate Godunov code which can be used for 3D accretion disk simulations incurvilinear coordinate systems.

A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability