Aeroacoustic Computations Using a High-Order Shock-Capturing Scheme

For aeroacoustic computations in the supersonic regime, it is necessary to use a numerical scheme that can represent shock waves without generating spurious numerical oscillations. The centered schemes that are usually used with success in the subsonic case, combined with a selective filtering, will generally oscillate in the presence of discontinuities. A new class of shock-capturing schemes, the one-step monotonicity-preserving schemes, combine the high accuracy and the nonoscillating property. It is thus a good candidate for supersonic aeroacoustic applications. The good spectral properties of these schemes are illustrated in the scalar linear case. Results of aeroacoustic test problems for the Euler and Navier-Stokes equations are compared with a dispersion-relation-preserving scheme. The application to a supersonic cavity flow, which induces a complex pattern of moving shocks, shows that the one-step monotonicity-preserving schemes capture the moving discontinuities without spurious oscillations and preserve a high accuracy at the same time.