C.K. Tam, J.C. Webb

Acoustics problems are governed by the linearized Euler equations. According to wave propagation theory, the number of wave modes and their wave propagation characteristics are all encoded in the dispersion relations of the governing equations. Thus one is assured that the numerical solutions of a high order finite difference scheme will have the same number of wave modes (namely, the acoustic, vorticity and entropy waves), the same wave propagation characteristics (namely, nondispersive, nondissipative and isotropic) and the same wave speeds as those of the solutions of the Euler equations if both systems of equations have the same dispersion relations. Finite difference schemes which have the same dispersion relations as the original partial differential equations are referred to as Dispersion-Relation-Preserving (DRP) schemes. A way to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is proposed. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed. These conditions are derived from the asymptotic solutions of the governing equations. A sequence of numerical simulations has been carried out. These simulations are designed to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. The computed solutions agree very favorably with the exact solutions. The radiation boundary conditions perform satisfactorily causing little acoustic reflections. The outflow boundary conditions are found to be quite transparent to outgoing disturbances even when the disturbances are made up of a combination of acoustic, vorticity and entropy waves.

DGLR/AIAA 14th Aeroacoustics Conference, 1992

Conference Paper

englisch

21,0 x 29,7 cm, 9 Seiten

DGLR-Bericht, 1992, 1992-03, DGLR/AIAA 14th Aeroacoustics Conference - Proceedings; S.214-222; 1992; Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn

NA

aeroacoustics

Bibliothek

1992