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Whilst in galaxy-size simulations, supermassive black holes (SMBH) areentirely handled by sub-grid algorithms, computational power now allows theaccretion radius of such objects to be resolved in smaller scale simulations.In this paper, we investigate the impact of resolution on two commonly usedSMBH sub-grid algorithms; the Bondi-Hoyle-Lyttleton (BHL) formula for accretiononto a point mass, and the related estimate of the drag force exerted onto apoint mass by a gaseous medium. We find that when the accretion region aroundthe black hole scales with resolution, and the BHL formula is evaluated usinglocal mass-averaged quantities, the accretion algorithm smoothly transitionsfrom the analytic BHL formula (at low resolution) to a supply limited accretion(SLA) scheme (at high resolution). However, when a similar procedure isemployed to estimate the drag force it can lead to significant errors in itsmagnitude, and/or apply this force in the wrong direction in highly resolvedsimulations. At high Mach numbers and for small accretors, we also findevidence of the advective-acoustic instability operating in the adiabatic case,and of an instability developing around the wake's stagnation point in thequasi-isothermal case. Moreover, at very high resolution, and Mach numbersabove $\mathcal{M}_\infty \geq 3$, the flow behind the accretion bow shockbecomes entirely dominated by these instabilities. As a result, accretion ratesonto the black hole drop by about an order of magnitude in the adiabatic case,compared to the analytic BHL formula.

Bondi or not Bondi: the impact of resolution on accretion and drag force modelling for Supermassive Black Holes