Journal of Computational Acoustics

It is shown by using a Dispersion-Relation-Preserving finite difference scheme that it is feasible to perform direct numerical simulation of acoustic wave propagation problems. The finite difference equations of the scheme have essentially the same Fourier-Laplace transforms and hence dispersion relations as the original linearized Euler equations over a broad range of wavenumbers (here referred to as long waves). Thus it is guaranteed that the acoustic waves, the entropy and the vorticity waves computed by the scheme are good approximations of those of the exact solutions of 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 of a computation scheme are, therefore, contaminants of the numerical solutions. The characteristics of these short waves are analyzed here by group velocity consideration and standard dispersive wave theory. Numerical results of direct simulations of these waves are reported. These waves can be generated by discontinuous initial conditions. 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.

In this paper, we show how wavelet analysis may be used to solve the parabolic approximate wave equation. The paper is naturally subdivided into three parts. The first entails a crash course in wavelet analysis with the aim of using it to solve partial differential equations. The second part develops the wavelet-Galerkin approximation for solving partial differential equations in variational form. Finally, the third section derives a range-depth adaptive wavelet approach, and, moreover, provides an algorithm for solving the propagation problem.

The problem of a time-harmonic acoustic wave scattering from a cylindrical object in shallow oceans is solved by an approximate boundary integral method. In the method we employ a Green's function of the Helmholtz equation with sound soft sea level and sound hard sea bottom conditions, and reformulate the problem into a boundary integral equation on the surface of the scattering object. The kernel of the integral equation is given by an infinite series, and is approximated by an appropriate truncation. The integral equation is then fully discretized by applying a quadrature rule. The method has an O(N⁻³) rate of convergence. Various numerical examples are presented.

A class of ocean acoustic propagation problems can be solved efficiently by the Parabolic Equation (PE) approximation method. The application of the PE method for the prediction of wave propagation introduces a new parameter, the reference wavenumber k₀. This requires selection of the most appropriate k₀, which is related to the reference sound speed c₀. The influence on the acoustic field by the choice of c₀ is rarely visible under weak range-dependent environments. Even if it is visible, the difference is small and is usually negligible since the present judicious choice of the c₀ seems to provide acceptable results. When the environment is not weakly range-dependent, the choice of c₀ will likely affect the computation of acoustic results. This paper examines a few different choices of c₀ and analyzes how these different choices can influence the acoustic results. An application is given where the farfield wave equation represents a realistic range-dependent environment. Different choices of c₀ were made for the computation of the acoustic field; as a consequence, different choices of c₀ produce different acoustic results. These numerical results are not in agreement with a known reference exact solution. The differences are not too small and may be considered non-negligible. So, there is a need to make an appropriate choice of c₀ in order to produce reasonable results. For the purpose of achieving satisfactory and acceptable acoustic results dealing with a PE-type equation, the requirements of the reference wavenumber will be discussed both mathematically and physically. Then, a number of computational choices of c₀ will be examined, especially the k₀-formula. An analysis as well as an assessment of the k₀-formula will be given.

We propose the modal spectrum of the PE field (MOSPEF) method for computing modal travel time under strong mode coupling environments. Instead of dealing with the coupled equations governing the complex modal amplitudes, the coupled modal amplitudes and phases are obtained from the spectral expansion of the full wave field given by the PE solution. Consequently, the method is very efficient and is free of problems at critical coupling points. Numerical simulations for computing modal travel time perturbations caused by a mesoscale eddy are conducted. A case which illustrates the failure of the adiabatic mode theory is also presented, the result of which raises an important issue for ocean acoustic tomography schemes.

The transient problem of finite cracks with vanishing thickness in an anti-plane strain solid is investigated by finite element method. The infinitesimally thin crack with traction free on both faces of the crack is simulated by the energy-sharing-node technique. The following cases are considered: (a) One finite line crack in a whole space subjected to (i) a concentrated line source and (ii) an inclined incident SH plane wave. (b) Two cracks in a whole space subjected to an inclined incident SH plane wave. Emphasis has been laid on the quantitative evaluation of the dynamic disturbances for the problem in the interference stage, which is generally difficult to be obtained by analytical approaches. The synthetic seismograms for displacements along the crack surfaces, which cover a period up to an instant of time during which the second order scattering from crack tips can be observed, are presented. Snapshots of the scattered displacement field for each case are also displayed so that the generations of the scatterings and the processes of the wave propagations can be clearly visualized. The two-dimensional wave propagation for transient acoustic problem and electromagnetic problem with the same nature of boundaries can be analogously obtained.

Following a recent experiment in which ambient noise (acoustic daylight) was used as the sole source of acoustic illumination for detecting objects in the ocean, a full wave-theoretic analysis is presented in this article of the visibility of a pressure-release spherical target when illuminated by ambient noise showing various degrees of anisotropy. The basis of the analysis is a new, accurate approximation for the Green's function representing the field around the sphere. From this expression, an analysis of the acoustic contrast is developed, as observed at the output of an endfire line array, which constitutes the acoustic lens. Our essential conclusion is that, even in isotropic noise, which presents one of the least favourable conditions for incoherent imaging, the visibility of the sphere (i.e. the ratio of intensities with the sphere present and absent) is approximately 4 dB. This is consistent with our early experimental observations, and is adequate to form the basis of an acoustic daylight imaging system.

It is shown that some of the properties of spurious waves that occur in computational fluid dynamics calculations (in particular in the inviscid case, when time stepping is conservative) are largely independent of how numerical time stepping is implemented. They depend primarily on the manner in which the spatial part of the equations is approximated. The properties that are shown to be invariant are the location of the turning points of the rays followed by sinusoidal components of those spurious waves, and, when they are generated by initial data, the asymptotic distribution of their energy.