Showing papers in "Journal of Computational Acoustics in 2008"

The multiscale vtcr approach applied to acoustics problems

Abstract: An approach, called the "Variational Theory of Complex Rays," was proposed recently for calculating the vibrations of slightly damped elastic structures in the medium-frequency range. One key feature of this approach is the use of a new variational formulation of the vibration problem which allows the shape functions to be discontinuous across element boundaries, thus giving this strategy great flexibility and robustness. This method was fully developed for structural vibrations. In this paper, we apply it to acoustics problems. Examples of two-dimensional Helmholtz problems show that this method is very robust and accurate yet requires much less computational effort than the finite element method, which enables one to use it up to much higher frequencies.

Numerical computation of the sound radiation from a planar baffled vibrating surface

Abstract: The sound power radiated by a plane vibrating structure can be calculated by numerical integration of the Rayleigh integral or by means of finite and boundary element methods. However, these methods are usually time-consuming due to the numerical evaluation of surface integrals. This paper reviews and discusses an alternative numerical method (the lumped parameter model) to compute the sound radiation from planar structures which is based just on surface velocity information and a direct numerical evaluation of the radiation resistance matrix of the structure. As an example, the technique is applied to estimate the sound radiated from the structural axisymmetric modes of both clamped and simply-supported circular baffled plates.

An assessment of the performance of global optimization methods for geo-acoustic inversion

Abstract: Having available efficient global optimization methods is of high importance when going to a practical application of geo-acoustic inversion, where fast processing of the data is an essential requirement. A series of global optimization techniques are available and have been described in literature. In this paper three optimization techniques are considered, being a genetic algorithm (GA), differential evolution (DE), and the downhill simplex algorithm (DHS). The performance of these three methods is assessed using a test function, demonstrating superior performance of DE. Additionally, the DE optimal setting is determined. As a next step DE is applied for determining the geo-acoustic properties of the upper seabed sediments from simulated seabed reflection loss, indicating good DE performance also for real geo-acoustic inversion problems.

Coupled mode and finite element approximations of underwater sound propagation problems in general stratified environments

Abstract: We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms.

Dft modal analysis of spectral element methods for acoustic wave propagation

Abstract: Spectral element methods are now widely used for wave propagation simulations. They are appreciated for their high order of accuracy, but are still used on a heuristic basis. In this work we present the numerical dispersion of spectral elements, which allows us to assess their error limits and to devise efficient numerical simulations, particularly for 2D and 3D problems. We propose a novel approach based on a discrete Fourier transform of both the probing plane waves and the discrete wave operators. The underlying dispersion relation is estimated by the Rayleigh quotients of the plane waves with respect to the discrete operator. Together with the Kronecker product properties, this approach delivers numerical dispersion estimates for 1D operators as well as for 2D and 3D operators, and is well suited for spectral element methods, which use nonequidistant collocation points such as Gauss–Lobatto–Chebyshev and Gauss–Lobatto–Legendre points. We illustrate this methodology with dispersion and anisotropy graphs for spectral elements with polynomial degrees from 4 to 12. These graphs confirm the rule of thumb that spectral element methods reach a safe level of accuracy at about four grid points per wavelength.

A formulation of the fast multipole boundary element method (fmbem) for acoustic radiation and scattering from three-dimensional structures

Abstract: Compared to the traditional boundary element method (BEM), the single level fast multipole boundary element method (SLFMBEM) or the multilevel fast multipole boundary element method (MLFMBEM) reduces the computational complexity of a job from O(n2) to O(n3/2) or O(n log2n), respectively with n being the number of unknowns; this means a dramatical reduction in terms of CPU-time and storage requirement. Large scale problems, unsolvable with the traditional BEM, can be solved by using the FMBEM. In this paper, the traditional BEM, SLFMBEM, and MLFMBEM are formulated within the framework of the Burton–Miller Collocation BEM for acoustic radiation and scattering from 3D structures. Attention is especially paid to the practical aspects of the method in order to get a reliable and efficient computation code. The performance of the method is tested with practical examples, including one for computing the head-related transfer function (HRTF) between 1000 and 18 000 Hz.

Development of a three-point sixth-order helmholtz scheme

Abstract: A compact finite-difference scheme is presented in this paper for efficiently solving the variable Helmholtz equation. This scheme development involves relating the derivative terms, namely, uxx an...

A 2.5d traction boundary element method formulation applied to the study of wave propagation in a fluid layer hosting a thin rigid body

Abstract: This paper models three-dimensional wave propagation around two-dimensional rigid acoustic screens, with minimal thickness (approaching zero), and placed in a fluid layer. Rigid or free boundaries are prescribed for the flat fluid surfaces. The problem is computed using the Traction Boundary Element Method (TBEM), which is appropriate for modeling thin-body inclusions, overcoming the difficulty posed by the conventional direct Boundary Element Method (BEM). The problem is solved as a summation of two-dimensional problems for different wave numbers along the direction for which the geometry does not vary. The source in each problem is a spatially sinusoidal harmonic line load. The influence of the horizontal boundaries of the fluid medium on the final wave field is computed analytically using appropriate 2.5D Green's functions for each model developed. Thus, only the boundary of the rigid acoustic screen needs to be discretized by boundary elements. The computations are performed in the frequency domain and are subsequently inverse Fourier transformed to obtain time domain results. Complex frequencies are used to avoid aliasing phenomena in the time domain results.

Validating range-dependent, full-field models of the acoustic vector field in shallow water environments

Abstract: Numerical algorithms for computing acoustic particle velocity from a pressure propagation model are introduced. Implementation using both a parabolic equation and normal mode approach are considered. The parabolic equation model employed uses a split-step Fourier algorithm, although application of the technique is general to other parabolic equation models. Expressions for the normal mode equations are also presented, for both coupled and adiabatic mode models. Results for a Pekeris waveguide are presented for a point source, prompting a brief discussion of multipath influence on the estimation of the direction of energy flow. Approximate analytic solutions are used to validate the general results of both the models. Results for the range-dependent benchmark wedge are then presented, which show generally good agreement between the two types of models. The results from the two-way, coupled normal mode model provide potential benchmark solutions for the wedge and a means of confirming the accuracy of other models.

A fourth-order accurate scheme for solving one-dimensional highly nonlinear standing wave equation in different thermoviscous fluids

Abstract: Combination of a fourth-order Pade compact finite difference discretization in space and a fourth- order Runge-Kutta time stepping scheme is shown to yield an effective method for solving highly nonlinear standing waves in a thermoviscous medium. This accurate and fast-solver numerical scheme can predict the pressure, particle velocity, and density along the standing wave resonator filled with a thermoviscous fluid from linear to strongly nonlinear levels of the excitation amplitude. The stability analysis is performed to determine the stability region of the scheme. Beside the fourth- order accuracy in both time and space, another advantage of the given numerical scheme is that no additional attenuation is required to get numerical stability. As it is well known, the results show that the pressure and particle velocity waveforms for highly nonlinear waves are significantly different from that of the linear waves, in both time and space. For highly nonlinear waves, the results also indicate the presence of a wavefront that travels along the resonator with very high pressure and velocity gradients. Two gases, air and CO2, are considered. It is observed that the slopes of the traveling velocity and pressure gradients are higher for CO2 than those for air. For highly nonlinear waves, the results also indicate the higher asymmetry in pressure for CO2 than that for air.

Computational aspects of the discontinuous galerkin method for the wave equation

Abstract: The Discontinuous Galerkin (DG) method is a powerful tool for numerically simulating wave propagation problems. In this paper, the time-dependent wave equation is solved using the DG method for spatial discretization; and the Crank–Nicolson and fourth-order explicit, singly diagonally implicit Runge–Kutta methods, and, for reference, the explicit Runge–Kutta method, were used for time integration. These simulation methods were studied using two-dimensional numerical experiments. The aim of the experiments was to study the effect of the polynomial degree of the basis functions, grid density, and the Courant–Friedrichs–Lewy number on the accuracy of the approximation. The sensitivity of the methods to distorted finite elements was also examined. Results from the DG method were compared with those computed using a conventional finite element method. Three different model problems were considered. In the first experiment, wave propagation in a homogeneous medium was studied. In the second experiment, the scattering and propagation of waves in an inhomogeneous medium were investigated. The third experiment evaluated wave propagation in a more complicated domain involving multiple scattering waves. The results indicated that the DG method provides more accurate solutions than the conventional finite element method with a reduced computation time and a lower number of degrees of freedom.

Investigation of 3d acoustical effects using a multiprocessing parabolic equation based algorithm

Abstract: A parallelized algorithm based on an existing 3D wide-angle parabolic equation model is developed to perform numerical simulations of underwater acoustic propagation on a massively parallel computer. The parallelization method used is a suitable two-level procedure: A frequency decomposition and a spatial decomposition of the calculations, which are respectively dedicated to reduce CPU times for broadband and cw signal propagation. The high-performance of the parallelized algorithm is examined for the 3D extension of the classical ASA wedge benchmark. CPU times are reported and both speedup and efficiency are analyzed. An investigation of significant 3D effects at higher frequencies and at longer propagation ranges than in earlier works [F. Sturm, J. Acoust. Soc. Am.117(3) (2005) 1058–1079] is performed with reasonable CPU times by using the new parallel algorithm. Further, the feasability of the procedure applied to a realistic oceanic environment problem involving both real sound speed profiles and bathymetry data sets is also illustrated.

The matrix formulation of boundary integral modeling of elastic wave propagation in 2d multi-layered media with irregular interfaces

Abstract: A semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces is presented. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave fields between arbitrary shapes of layers can be computed using the indirect boundary element (BEM) method. Like any standard BEM methods, the primary task of the BEM-based propagation matrix method (thereafter called PM–BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial boundaries due to limited model space. To our knowledge, such implementation has not appeared in the literature. Several examples are presented in this paper to demonstrate the effectiveness of this proposed PM–BEM method for modeling elastic waves in media with complex structure.

A finite difference solution to the helmholtz equation in a radially symmetric waveguide: application to near-source scattering in ocean acoustics

Abstract: A finite difference (FD) method is developed and analyzed for the Helmholtz equation in a radially symmetric waveguide. The resulting algorithm can be used to solve for sound intensities in complex models that may include high material contrasts and arbitrary bathymetry. An analysis of the effect of grid discretization on the results indicates that numerical dispersion is significant within one-third of a wavelength from a point source and decreases beyond that. Numerical results are presented and compared to wide-angle parabolic equation (PE) solutions and analytic solutions, where available. Comparison with analytic results indicates that the FD method accurately solves for the acoustic wave field at all propagation angles and is more accurate than the PE method near the source. Results are also shown for models in which mode coupling occurs near the source.

Simulation of incident nonlinear sound beam and 3d scattering from complex targets

Abstract: This paper presents an integrated simulation method for investigating nonlinear sound beams and three-dimensional (3D) acoustic scattering from any combination of complicated objects. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the Khokhlov–Zabolotskaya–Kuznetsov equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

Acoustic attenuation characteristics of straight-through perforated tube silencers and resonators

Abstract: The one-dimensional analytical solutions are derived and three-dimensional substructure boundary element approaches are developed to predict and analyze the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators without mean flow, as well as to examine the effect of nonplanar waves in the silencers and resonators on the acoustic attenuation performance. Comparisons of transmission loss predictions with the experimental results for prototype straight-through perforated tube silencers demonstrated that the three-dimensional approach is needed for accurate acoustic attenuation performance prediction at higher frequencies, while the simple one-dimensional theory is sufficient at lower frequencies. The BEM is then used to investigate the effects of geometrical parameters on the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators in detail.

Generalized eigenproblem for acoustic wave propagation in periodically layered anisotropic media

Abstract: A stable matrix method is presented for studying acoustic wave propagation in thick periodically layered anisotropic media at high frequencies. The method enables Floquet waves to be determined reliably based on the solutions to a generalized eigenproblem involving scattering matrix. The method thus overcomes the numerical difficulty in the standard eigenproblem involving cell transfer matrix, which occurs when the unit cell is thick or the frequency is high. With its numerical stability and reliability, the method is useful for analysis of periodic media with wide range of thickness at high frequencies.

A modal analysis method to study fluid–structure coupling in hollow parts of a structure

Abstract: Complex structures often include hollow parts. These hollow parts constitute the skeleton of the structure and are largely responsible for its global behavior, hence the importance of analyzing them precisely. The method we propose in this paper is a modal method based on the modal analysis of elements of hollow parts. This method does not require nodal degrees of freedom on the boundaries between the elements: "modal" elements are created, and these elements can be assembled through modal mass and stiffness matrices in the same way as the finite element method. Thus, it is possible to choose the precision of the analysis by choosing the quantity of modes used in the modal analysis of the elements. We will study not only structural systems but also coupled fluid–structure systems, and our results will be compared with experimental tests.

A neumann to dirichlet map for the bottom boundary of a stratified sub-bottom region in parabolic approximation

Abstract: The acoustic propagation problem is modeled via the parabolic approximation. The physical domain consists of the water column with a horizontal water–bottom interface and the bottom region consists of N-strata with horizontal interfaces. The computational domain is restricted to the water column, while the stratified bottom region is modeled by a nonlocal boundary condition applied along the water–bottom interface, and having the form of a Neumann to Dirichlet map (NtD). The discrete analog of the NtD has been implemented in a finite difference scheme for the general wide angle PE model, and successfully tested for several benchmark problems. The stratification of the media can be either physical, e.g. sediment formulation in the bottom, or artificial/computational, e.g. forced by sparse distribution of environmental data measurements in the water column. It should be emphasized that the sound speed may vary from layer to layer, but is constant within each layer. The proposed NtD map can be used in geoacoustic inversion via the optimal control adjoint method.

Acoustic performance of nonreflecting boundary conditions for a range of incident angles

Abstract: A detailed study on the accuracy and reflection behavior of nonreflection boundary conditions is presented. To this end, a selection of five distinct nonreflecting boundary conditions is evaluated and the mechanisms which dominate the reflection properties of boundary conditions are identified based on a rigorous quantification of reflection levels. It is shown that the reflection behavior is significantly affected by the incident angle. The relation between the boundary condition effectiveness and the incident angle is investigated and the reflection rates as a function of the incident angle are quantified. Furthermore, the obtained results are used to predict the reflections from boundary conditions in general applications. It is shown that these predictions are reliable for different test cases.

Two-way coupled-mode solutions in the complex horizontal wavenumber plane

Abstract: A coupled-mode formalism based on complex Airy layer mode solutions is presented. It is an extension into the complex horizontal wavenumber plane of the companion article [Stotts, J. Acoust. Soc. Am.111 (2002) 1623–1643], referred to here as the real horizontal wavenumber version, which accounted for general ocean environments but was restricted to normal modes on the real horizontal wavenumber axis. A formulation of the expressions for both trapped and continuum complex coupling coefficients is developed to dramatically reduce computer storage requirements and to make the calculation more practical. The motivation of this work is to demonstrate the numerical implementation of the derivations and to apply the method to an example benchmark. Differences from the real horizontal wavenumber formalism are highlighted. The coupled equations are solved using the Lanczos method [Knobles, J. Acoust. Soc. Am.96 (1994) 1741–1747]. Comparisons of the coupled-mode solution to a parabolic equation solution for the ONR shelf break benchmark validate the results.

The coupled natural boundary-finite element method for solving the acoustic scattering problem in a 3d oceanic waveguide

Abstract: This study is concerned with the problem of acoustic scattering by a three-dimensional obstacle in a shallow water waveguide. A method coupling of the finite-element and natural boundary-element is analyzed and presented for solving the acoustic scattering problem numerically based on the Galerkin variational principle and the DtN mapping theory. The proposed method has the advantage of avoiding the absorbing boundary condition of the conventional finite-element method. Numerical examples are given of successful computational results for several 3D obstacles of various shapes.

Near-axial interference effects in long-range ocean acoustic pulse propagation

Abstract: In many long-range ocean propagation experiments the source and receiver are placed close to the depth of the waveguide axis. In this case, rays emerging from the source at sufficiently small angles intersect the sound-channel axis many times and form in its vicinity a large number of caustics with caustics cusps located repeatedly along the axis. In neighborhoods of cusped caustics there exists a very complicated interference pattern. Neighborhoods of interference grow with range and at long ranges they overlap. As a result, a complex interference wave (axial wave), that propagates along the waveguide axis, appears. The goal of this paper is to obtain the representation for the axial wave in the time domain and calculate its magnitude for a realistic model of a three-dimensional range-independent medium. Numerical computations are done for the average profile from the Acoustic Engineering Test (AET) experiment. The pulse center frequency of 75 Hz with 30-Hz bandwidth is used that corresponds to broadband acoustic signals which were transmitted during November 1994 in the eastern North Pacific Ocean as a part of the AET. The propagation range is 3250 km. The sound source is located on the waveguide axis, and the receiver is placed close to the depth of the axis. Through numerical simulation the dependencies of the magnitude of the axial wave on depth of the receiver and propagation range are studied.

Vortex-generated sound in flow about spinning cylinders

Abstract: This study provides a computational insight into unsteady far-field and surface pressure developed by vortex interaction with multiple rigid bodies in lift conditions. Flows around a spinning cylinder and two cylinders in tandem were taken as simple but yet representative prototypes of flows around multi-element lifting devices. The unsteady Euler equations are solved in terms of propagating disturbances originating from deforming vortices in the mean flow developed in the neighborhood of cylinders. Numerical errors associated with the discretization and boundary conditions were kept small employing a high-order scheme with accurate nonreflecting boundary conditions. To model the interaction of vortices with rigid bodies using moderate amount of computational resources, we apply a single-grid approach and implement the bipolar coordinate transformation where applicable. We address here the amplification of sound by the mean flow with nonzero circulation, strong influence of vortex profile on the generated sound waves, and different degree of amplification of sound in lifting flows for localized and nonlocal vortices. We find that the flow about a cylinder not only amplifies the sound strength but it also shifts the sound directivity. Vortices deforming within the flow about cylinders placed in tandem and in the traverse layouts were examined.

Hybrid algorithm of the depth solver for wavenumber integration technique in an ocean waveguide with a porous bottom

Abstract: A new hybrid algorithm of the depth solver for the wavenumber integration technique is derived. The global matrix method is adopted as the depth solver in the ocean, where there are sources and receivers present, and the reflectivity scheme is used for calculating the wave field of the porous ocean bottom. In order to hybridize both depth solvers, a novel technique has been developed where a virtual fluid layer with zero thickness is inserted between the ocean and the porous ocean bottom. This technique makes the hybrid algorithm simple to implement and compatible with any other depth solvers for the ocean bottom. Numerical simulation shows the proposed algorithm to work well.

Measurement and simulation for wind noises in the ocean environments with nonlinear internal waves

Abstract: This study obtains wind noise variations by experimental data and simulated results to describe meteorological and oceanic effects. The ambient noise data were measured by a vertical line array in the 2001 ASIAEX South China Sea experiment. An acoustic propagation model is used in noise modeling for calculating the sound pressure of noises at receiving sites, including the effects of ocean environmental changes, bottom interactions, and noise fluctuations at different depths. Both range-independent and range-dependent sound speed profiles are generated with in-situ water temperature data. Results show fluctuating noise levels with variations in ocean environments. But the fluctuations are small such that only weak correlation exists in the acoustic noise data and ocean data. Results also indicate that using range-independent sound speed profiles can simulate noise field in range-dependent ocean environments with nonlinear internal waves for shallow regions with flat bottoms.

Underwater acoustic sensing of sea surface waves

Abstract: Rough surface scattering theory is applied to the problem of estimating gravity-capillary wavenumber spectra from measurements of sea surface backscatter at high acoustic frequencies. Ensemble averaged scattering cross sections predicted by small-slope expansions are evaluated to examine the inversion of acoustic data assuming Bragg scatter. The ratio of the full fourth-order small-slope and Bragg predictions is found to exhibit a minimum value of ~ 2dB at moderate angles of incidence. At such angles, the corrections to perturbation theory depend weakly on acoustic frequency and environmental conditions. This latter finding indicates that only a modest effort is required to monitor sea surface conditions to estimate the correction. Corrections to Bragg predictions increase rapidly with increasing incidence angle and at high angles, the fourth-order contributions of the small-slope and extended small-slope expansions differ. This finding casts some doubt on the applicability of small-slope approximations t...

Relationship between the axial wave, and first normal modes for ducted, propagation in a waveguide

Abstract: For ducted propagation in a waveguide when the source and receiver are placed close to the depth of the waveguide axis, there exist cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics, the interference of the wave fields that correspond to near-axial rays occurs. This results in the formation of a coherent structure (the axial wave) that propagates along the waveguide axis like a wave. In this paper, for the two-dimensional reference point source problem with the parabolic index of refraction squared the axial wave is represented in the form of a sum of the first normal modes and a remainder field. The mathematical framework is provided by two different representations of the acoustic field. The first one was obtained by Grigorieva et al.1 It includes a sum of ray summands and the axial wave. The second representation including ray summands, a sum of the first normal modes, and a remainder field is derived in the present paper. For the remainder a simple formula including a special function is obtained. Numerical simulations are carried out for parameters corresponding to long-range ocean acoustic propagation experiments.