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The use of turbochargers with downsized internal combustion engines improves road vehicles’ energy efficiency but introduces additional sound sources of strong acoustic annoyance on the turbocharger’s compressor side. In the present study, direct noise computations (DNC) are carried out on a passenger vehicle turbocharger compressor. The work focuses on assessing the influence of grid parameters on the acoustic predictions, to further advance the maturity of the acoustic modelling of such machines with complex three-dimensional features. The effect of the boundary layer mesh structure, and of the spatial resolution of the mesh, on the simulated acoustic signatures is investigated on detached eddy simulations (DES). Refinements in the core mesh are applied in areas of major acoustic production, to generate cells with sizes proportional to the local Taylor microscale values.