The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier-Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.