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Processes, from accretion and feedback production close to the black hole (BH) event horizon out to galactic scales on which feedback acts, span a vast dynamic range that is currently unfeasible to capture entirely in simulations. However, recent developments in numerical techniques mean that we are closer than ever to spanning the gap.
I will present results from a range of simulations performed with the moving-mesh code AREPO that combine super-Lagrangian refinement (SLR, which improves resolution around the BH) with novel models for accretion and launching high-resolution jets and winds that afford new opportunities to study BH physics and how feedback behaves on a range of scales. This includes simulations of binary BHs in gas-rich circumbinary discs, which thanks to SLR capture gas streams and minidiscs that form around the individual BHs that contribute to torquing the binary. We additionally track BH spin evolution (thanks to our subgrid accretion disc model) and predict spin alignment timescales that have implications for recoil velocities and gravitational wave observations). As well as simulations of galaxies and clusters that include high-resolution jets injected close to the BH that propagate to large scales, unveiling in unprecedented detail how jets interact with and shape their host galaxies and the intracluster medium and implications for cosmology.