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Recent advances in black hole astrophysics, particularly the first visualevidence of a supermassive black hole at the center of the galaxy M87 by theEvent Horizon Telescope (EHT), and the detection of an orbiting "hot spot"nearby the event horizon of Sgr A* in the Galactic center by the GravityCollaboration, require the development of novel numerical methods to understandthe underlying plasma microphysics. Non-thermal emission related to such hotspots is conjectured to originate from plasmoids that form due to magneticreconnection in thin current layers in the innermost accretion zone.Resistivity plays a crucial role in current sheet formation, magneticreconnection, and plasmoid growth in black hole accretion disks and jets. Weincluded resistivity in the three-dimensional general-relativisticmagnetohydrodynamics (GRMHD) code BHAC and present the implementation of anImplicit-Explicit scheme to treat the stiff resistive source terms of the GRMHDequations. The algorithm is tested in combination with adaptive mesh refinementto resolve the resistive scales and a constrained transport method to keep themagnetic field solenoidal. Several novel methods for primitive variablerecovery, a key part in relativistic magnetohydrodynamics codes, are presentedand compared for accuracy, robustness, and efficiency. We propose a newinversion strategy that allows for resistive-GRMHD simulations of lowgas-to-magnetic pressure ratio and highly magnetized regimes as applicable forblack hole accretion disks, jets, and neutron star magnetospheres. We apply thenew scheme to study the effect of resistivity on accreting black holes,accounting for dissipative effects as reconnection.

General relativistic resistive magnetohydrodynamics with robust primitive variable recovery for accretion disk simulations