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. Such an educated guess allows for quality enhancement with a smaller increase in computational costs as compared to more general overall refinements. The reflection-free simulation results are validated against experiments. The experimental data were post-processed with methods from the two-port theory to represent pure acoustic source power density for the acoustic modes, cleaned from test-domain-specific reflections. A detailed comparison between experiments and numerical simulations is carried out. As a result of this study, the most critical parameters for the numerical prediction of turbocharger noise are presented. The results can, furthermore, be used to improve the understanding of grid construction when predicting noise signature for compressor flows.