Developments in computing infrastructure and methods over the last decade have enhanced the potential of numerical methods to reasonably predict the aerodynamic noise. The generation and propagation of the flow induced noise are aerodynamic phenomena. Although the fluid flow dynamics and the resultant acoustics are both governed by mass and momentum conservation equations, former is of convective and/or diffusive nature while the latter is propagative showing insignificant attenuation due to viscosity except for small viscothermal losses. Aeroacoustic modelling of systems with intricate geometries and complex flow is still not mature due to challenges in the accurate tractable representation of turbulent viscous flows. Therefore, state-of-the-art for computing flow-induced noise in small centrifugal compressors is reviewed and critical evaluation of various parameters in the numerical model is undertaken in this work. The impact of various turbulence formulations along with corresponding spatial and temporal resolutions on performance and acoustic predictions are quantified. The performance predictions are observed to be within 1.5% of the measured values irrespective of turbulence and timestep parameters. The noise generated by the impeller is observed to be reasonably correlated with the measurements and the absolute values of the sound pressure levels along with decay rates predicted by LES and SBES formulations are better than the similar predictions from DES and URANS formulations. The impact of timestep size is observed and is determinant of the frequency up to which spectra can be appropriately resolved. Furthermore, results emphasise the importance of high spatial resolution for scale resolving turbulence formulations to yield better results and the information can be used to select appropriate numerical configuration considering time and accuracy trade-offs.