Only recently with the help of the constantly increasing computational power Direct Numerical Simulation of acoustic flows is possible, without the use of an acoustic analogy, which requires a priori knowledge about the kind of the sound sources in the flow field. In the present work a new 2 step methodology which decomposes the calculation of the flow and sound field for low Mach numbers shall be presented. According to this methodology the flow field is calculated using the incompressible Navier – Stokes equations, while the sound field is predicted using the compressible perturbed Euler equations, solving directly for the acoustic variables (perturbations). One 1-dimensional and one 2-dimensional isentropic problems were solved using this approach, while the ultimate goal is the use of a similar acoustic model for the study of sound generation and radiation in the human vocal tract.