A three-dimensional computational aeroacoustics (CAA) method combined with advanced parallel computing techniques is applied to the simulation of the acoustic response of flow-over cavities (Helmholtz resonator). Direct numerical simulation is conducted by solving a newly developed nonlinear disturbance equation [Morris et al., Comp. Phys. (in press)] which consists of linear and nonlinear fluctuation terms, spatially varying coefficients that depend on the mean-flow properties, and a mean-flow source term that is independent of the fluctuations. The mean-flow component is obtained from a numerical solution of the Reynolds-averaged Navier--Stokes equations with a turbulence model by taking advantage of traditional, robust CFD algorithms with good convergence characteristics. The capturing of time-accurate characteristics of the unsteady flow field and the the nondispersive and nondissipative characteristics of the acoustic field, is conducted by using CAA methodology for the perturbations about the mean flow. In order to reduce the computational time, the calculations are performed in parallel, using a domain decompostion strategy. This attempt at understanding and overcoming some obstacles that arise in direct simulation of CAA, opens new prospects for predicting the acoustics of aircraft engine liners.