Considering the computational efficiency along with the high-fidelity to the underlying physical principles, significant advances have been achieved in aeroacoustics simulations. This, however, appears to have remained somewhat limited to the modeled periodic noise generation and propagation by assuming linear waves in uniform flow. Toward this goal, some useful applications have been computed with low-dispersion schemes, by solving the linearized Euler and Navier–Stokes equations. In addition to the benchmark cases reported in the CAA Workshops, these included a supersonic jet noise simulation. On the other hand, there are numerous aeroacoustics applications, such as subsonic jet noise and cavity noise, where the linear wave and uniform flow assumptions would be too compromising. Consequently, the linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear equations. It has been tested for a number of simple initial-value and periodic-source problems. Presently, a cavity noise problem and its suppression are being computed with this computational model. [Work partially supported by NASA Langley Research Center.]