Modified finite volume methods of Osher and Chakravarthy (MOC) and Sanders and Li (MSL) and a finite element method of Lin and Chin are investigated on several aeroacoustic problems. Higher order accuracy is obtained with the monotonic upwind-centered scheme for conservation laws approach. The tested problems include oblique shock reflection, linear wave convection, monopole radiation, vortex preservation, and blade-vortex interaction. Based on the order of accuracy, stability, grid nonuniformity, and dissipation property of each scheme, it is concluded that the MOC scheme is the most suitable scheme among the schemes tested for aeroacoustic computations. We also conclude that the MSL scheme needs to be improved on problems of convergence and small wiggles before it is used in computational aeroacoustics. In the blade-vortex interaction problem, two sound waves, transonic and compressibility waves, found in recent experiments are simulated. N recent years, considerable progress has been made in the numerical analysis of fluid dynamics. Usually, numerical methods which solve the Euler/Navier-Stokes equations for aerodynamic flows fall into three major classes: finite difference, finite volume, and finite element methods. Recently, successful methods have employed higher order upwind interpolations and limiter functions to obtain algorithms possessing higher resolution and higher stability bounds. The inherently dissipative nature of upwind schemes and limiter functions is beneficial at or near shock waves. Specifically, the implementation of limiter functions make schemes more stable for computing solutions with strong shock waves. In general, an upwind scheme with a limiter function is formally second- or thirdorder accurate but is locally first-order accurate in regions of high localized gradients (such as shocks) and in many cases at local extrema also. The loss of formal accuracy near shocks is not usually serious, but for aeroacoustic calculations the dissipation at extrema will be harmful. Upwind schemes may be classified into two classes: monotonic upwind-centered scheme for conservation laws (MUSCL) and nonMUSCL.1'4 The present work is focused on the MUSCL-based schemes. We have studied the performance of the following three basic schemes: 1) the finite element method of Lin and Chin (LC)5 and Lin et al.,6 2) the finite volume method of Osher and Chakravarthy (OC)7, and 3) the finite volume method of Sanders and Li (SL). 8'9 The popularity of the OC scheme for aeroacoustic computations is likely to increase since it is formally of third order and is stable in the computation of strong shock waves. The SL scheme is formally of fourth order and is a suitable method for the aeroacoustic computation of low-speed flows. An overall assessment of this scheme is available in Refs. 8 and 9. The LC scheme is formally of second order for both uniform and nonuniform meshes. This scheme has been extensively tested on both inviscid and viscous flows.5'6 It has been shown that the scheme is capable of computation of steady and unsteady flows. In this paper, we have modified the limiter functions in the OC and SL schemes to obtain two new schemes, the modified OC (MOC) and the modified SL (MSL) schemes. In this effort a detailed investigation is performed to evaluate the capability of those schemes. Several test problems are studied, including oblique shock reflection, linear wave convection, monopole radiation, vortex preservation, and blade-vortex interaction. Details