Black holes are believed to be one of the key ingredients of galaxy formation models, but it has been notoriously challenging to simulate them due to the very complex physics and large dynamical range of spatial scales involved. Here we address a significant shortcoming of a Bondi-Hoyle-like prescription commonly invoked to estimate black hole accretion in cosmological hydrodynamic simulations of galaxy formation, namely that the Bondi-Hoyle radius is frequently unresolved. We describe and implement a novel super-Lagrangian refinement scheme to increase, adaptively and 'on the fly', the mass and spatial resolution in targeted regions around the accreting black holes at limited computational cost. While our refinement scheme is generically applicable and flexible, for the purpose of this paper we select the smallest resolvable scales to match black holes' instantaneous Bondi radii, thus effectively resolving Bondi-Hoyle-like accretion in full galaxy formation simulations. This permits us to not only estimate gas properties close to the Bondi radius much more accurately, but also allows us to improve black hole accretion and feedback implementations. We thus devise a more generic feedback model where accretion and feedback depend on the geometry of the local gas distribution and where mass, energy and momentum loading are followed simultaneously. We present a series of tests of our refinement and feedback methods and apply them to models of isolated disc galaxies. Our simulations demonstrate that resolving gas properties in the vicinity of black holes is necessary to follow black hole accretion and feedback with a higher level of realism and that doing so allows us to incorporate important physical processes so far neglected in cosmological simulations.

21 pages, 15 figures, MNRAS accepted, figures and videos are available at http://www.ast.cam.ac.uk/~mc636/