Journal of Computational Acoustics

We investigate the problem of wave propagation in a porous medium, in the framework of Biot's theory, computing the numerical solution of the differential equations by a grid method. The problems posed by the stiffness of the equations are circumvented by using a partition (or splitting) time integrator which allows for an efficient explicit solution as in the case of nonstiff differential equations. The resulting algorithm possesses fourth-order accuracy in time and "infinite" (spectral) accuracy in space. Alternatively, a second-order algorithm, based on a Crank–Nicolson method, provides similar stability properties, although lower accuracy. The simulations correctly reproduce the wave forms of the fast and slow compressional waves and their relative amplitudes. Moreover, we observe the static slow mode, particularly strong when the source is a bulk perturbation or a fluid volume injection. The numerical results are confirmed by the analytical solution.

A number of questions have emerged in the field of Computational Aeroacoustics (CAA) over the capability of applying conventional Computational Fluid Dynamics (CFD) methodologies to capture the physical attributes of acoustic fields. One of the more fundamental questions is the capability of direct simulation techniques versus perturbation techniques to capture the acoustic phenomena. This issue is the topic of this research; wherein one such methodology, an explicit four stage Runge–Kutta finite volume scheme, has been utilized for acoustic simulations using both direct simulation and perturbation approaches. The two-dimensional unsteady Euler equations are solved directly for the direct simulation methodology, while in the perturbation method the steady mean flow Euler equations are subtracted from the fully unsteady Euler equations, and the remaining perturbed equations are then solved for the acoustic flow quantities. These methodologies have been compared by applying them to a standard acoustic problem, the acoustic field of a point monopole. Emphasis has been placed on the ability of the methodology to capture the physics of the problem. The effects of dissipation, grid spacing, and amplitude have been addressed and compared for both methodologies. While both methods gave comparable results for most of the cases, the direct simulation methodology was found to have difficulties resolving small amplitude acoustic waves.

A new technique in the frequency domain is presented for the characterization of a surface-breaking crack in plates. The strip element method has been used to calculate the responses of the displacement field in the plate subjected to a time harmonic line load on the upper surface of the plate. In the present technique, the crack can be located from the distribution of the displacement field, which is found to be discontinuous at the crack position. It is found that there are additional oscillations in the curve of the absolute values of the displacement in between the load and the crack. The crack length can be determined from the mean value of the peak of the additional oscillations. It is also found that the mean value of the peak is dependent on the crack length and less dependent on the distance from the load to the crack. Approximate polynomial formula of degree three for predicting the length of surface-breaking crack in isotropic homogeneous plates is also proposed. Numerical examples are given to demonstrate the present technique.

A tracking algorithm may be used to reduce the ambiguity of the positions of a moving underwater acoustic source. The objective of this paper is to evaluate two efficient target tracking algorithms suitable for use with Matched-Field Processing (MFP). The detection after tracking algorithms described here are applicable to targets moving linearly at constant speed and depth that produce low Signal-to-Noise Ratio (SNR) signals at the receivers. The input to the tracker consists of the positions of the largest Bartlett statistics or peaks on the MFP ambiguity surfaces. Even at very low SNRs, these largest peaks usually include the match at or near the source position sufficiently often that the detection performance of our efficient tracker rivals that of an exhaustive tracker. In this paper efficient algorithms are developed and evaluated based on examining either the sum of the uniformly weighted Bartlett array outputs or the sum of the Bartlett array outputs weighted by predicted received signal strength. This sum is evaluated along a set of linear tracks that connect the largest peaks. Detection performance is shown to be better for the signal-strength weighted tracker. The performance difference is largest for tracks along a constant bearing from the array.

Several nonreflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each nonreflecting boundary condition. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate than the local ones considered. Results also show that this condition is more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other nonreflecting conditions.