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Turbulent magnetic diffusivity plays an important role for accretion disksand the launching of disk winds. We have implemented magnetic diffusivity,respective resistivity in the general relativistic MHD code HARM. This paperdescribes the theoretical background of our implementation, its numericalrealization, our numerical tests and preliminary applications. The testsimulations of the new code rHARM are compared with an analytic solution of thediffusion equation and a classical shock tube problem. We have furtherinvestigated the evolution of the magneto-rotational instability (MRI) in toriaround black holes for a range of magnetic diffusivities. We find indicationfor a critical magnetic diffusivity (for our setup) beyond which no MRIdevelops in the linear regime and for which accretion of torus material to theblack hole is delayed. Preliminary simulations of magnetically diffusive thinaccretion disks around Schwarzschild black holes that are threaded by alarge-scale poloidal magnetic field show the launching of disk winds with massfluxes of about 50% of the accretion rate. The disk magnetic diffusivity allowsfor efficient disk accretion that replenishes the mass reservoir of the innerdisk area and thus allows for long-term simulations of wind launching for morethan 5000 time units.

rHARM: Accretion and Ejection in Resistive GR-MHD