A Study of the Short Wave Components in Computational Acoustics

Abstract

The feasibility of performing direct numerical simulations of acoustic wave propagation problems has recently been demonstrated by a number of investigators. It is easy to show that the computed acoustic wave solutions are good approximations of those of the exact solutions of the linearized Euler equations as long as the wavenumbers are in the long wave range. Computed waves with higher wavenumber, or the short waves, generally have totally different propagation characteristics. There are no counterparts of such waves in the exact solutions. The short waves are contaminants of the numerical solutions. The characteristics of these short waves are analyzed here by group velocity consideration. Numerical results of direct simulations of these waves are reported. To purge the short waves so as to improve the quality of the numerical solution, it is suggested that artificial selective damping terms be added to the finite difference scheme. It is shown how the coefficients of such damping terms may be chosen so that damping is confined primarily to the high wavenumber range. This is important for then only the short waves are damped leaving the long waves basically unaffected. The effectiveness of the artificial selective damping terms is demonstrated by direct numerical simulations involving acoustic wave pulses with discontinuous wave fronts.

This work was supported by the NASA Lewis Research Center Grant NAG 3–1267 and in part by the Office of Naval Research Grant No. N00014–89-J-1836 and the Florida State University through time granted on its Cray — YMP Supercomputer.