Computing transient CFD simulations of turbocharger compressors is computationally very demanding. It is of fundamental importance to resolve turbulent structures at the location of their generation and to establish a fine enough grid to allow propagation of the resolved structures. This results in high-resolution grids, existing of more than 20 million cells. By applying Lighthill's analogy, it is possible to only resolve turbulent structures at their location of generation and compute the pressure propagation by using an additional, not that demanding acoustic grid. This allows using coarser CFD grids in the inlet and outlet section. Furthermore, pressure propagation simulations based on Lighthill's inhomogeneous wave equation with the Finite Element Method are less affected by numeric dissipation compared to standard Finite Volume methods used in proprietary CFD solvers. For transferring Lighthill's source terms from the CFD to the acoustic grid, advanced interpolation algorithms are used. The simulation results are validated by measurements of a cold gas test rig.