Journal of Computational Acoustics

Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vortical disturbances and the scattering of vortical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vortical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.

The BEM has been used to compute the variations in the pressure field caused when a dilatational point load is placed inside a confined fluid channel. The channel was assumed to be filled with a homogeneous fluid and the presence of irregularities in its floor was considered. The width of the channel was fixed, and the influence of the walls was analyzed. This paper extends previous work by the authors^1,2 in which the fluid channel was considered to have infinite width. The Green's functions are defined in the frequency domain. They are obtained by superposing virtual acoustic sources, combined so as to generate the boundary conditions of both the free surface of the channel and the rigid surfaces of the floor and side walls. The responses in the time domain are obtained by means of Fourier transforms, making use of complex frequencies. The main features and spectral representation of the signals scattered by irregular floors are then described and used to elucidate some important aspects of wave acoustics, which may provide the basis for the development of non-destructive testing and imaging methods.

Dispersion-relation-preserving (DRP) spatial differentiation schemes are investigated for staggered non-uniform finite-volume grid type. It is shown that the staggering improves the numerical accuracy and stability whether the grid is uniform or non-uniform. The effect of the non-uniformity in the grid on the optimization procedure of the schemes is discussed. The spatial differentiation schemes are tested for the aeroacoustic problems of monopole and quadrupole radiation, showing the effectiveness of the non-uniform grid and the optimized high-order scheme.

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of five wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

This paper considers how the accuracy of range-dependent propagation modeling affects the results of matched-field inversion (MFI) for seabed geoacoustic parameters. In MFI, the forward problem of computing the acoustic fields associated with candidate geoacoustic models is solved a large number of times. Given significant mismatch due to measurement and theory errors, together with the computationally intensive nature of MFI, the appropriate tradeoff between modeling accuracy and computational speed is not obvious. This tradeoff is considered here in terms of the degradation in information content for the geoacoustic parameters that results from inaccurate propagation modeling. The information content is quantified using the marginal posterior probability distributions of the geoacoustic parameters, as computed from a fast Gibbs sampling approach to Bayesian inversion. A synthetic example of this analysis is presented in which the parabolic equation is used to model acoustic fields for a shallow-water, upslope environment, with different levels of modeling accuracy/speed controlled by the range and depth step sizes of the computational grid.

In this paper, a new technique for solving the two-dimensional inverse scattering problem for ultrasound inverse imaging is presented. Reconstruction of a two-dimensional object is accomplished using an iterative algorithm which combines the conjugate gradient (CG) method and a neural network (NN) approach. The neural network technique is used to exploit knowledge of the statistical characteristics of the object to enhance the performance of the conjugate gradient method. The results for simulations show that the CGNN algorithm is more accurate than the CG method and, in addition, convergence occurs more rapidly. For the CGNN algorithm, approximately 50% fewer iterations are needed to obtain the inverse solution for a signal-to-noise ratio (SNR) of 50 dB. For a smaller SNR of 35 dB, the CGNN method is not as accurate, but it still gives reasonable results.

Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov–Fokker–Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path integral theory.