Aerial blast wave propagation is affected by numerous physical parameters such as the source energy, the topography, the ground nature, or the atmospheric conditions. Direct high performance computing simulations is a valuable tool, but remains extremely costly in complex environment which limits the number of simulations. It is best used locally or to build reference solutions useful for the evaluation of simplified fast running models. Indeed, as the blast wave propagates, its strength weakens and after some distance, linear acoustic theory may be valuable. Here, we present the results of a one-way coupling procedure between a nonlinear Euler direct simulation code for the near field, including the detonation phase, and a parabolic linear acoustic model for the far field. Both models take into account for topography and atmospheric conditions. We show that, compared to the full Euler simulations, the coupling procedure provides accurate results at a reduced computational cost for blast wave propagation in the vicinity of an actual pyrotechnic site. The quality of the signals is also improved in comparison with classical parabolic simulations started with an analytical solution.
Choosing the right number and type of elements in modern commercial finite element tools is a challenging task. It requires a broad knowledge about the theory behind or much experience by the user. Benchmark tests are a common method to prove the element performance against analytical solutions. However, these tests often analyze the performance only for single elements. When investigating the complete mesh of an arbitrary structure, the comparison of the element’s performance is quite challenging due to the lack of closed or fully converged solutions. The purpose of this paper is to show a high-precision comparison of eigenfrequencies of a real structure between experimental and numerical results in the context of an element performance check with respect to a converged solution. Additionally, the authors identify the practically relevant accuracy of simulation and experiment. Finally, the influence of accuracy with respect to the number of elements per standing structural bending wave is shown.
The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model. This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. Former investigations have shown that a pollution effect resulting from dispersion is unlikely for the boundary element method. However, numerical damping in the boundary element method can account for a pollution effect. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method. One of these consequences is that the number of waves within the domain may be controlling the discretization error in addition to the size and the order of the boundary elements. 'This will be demonstrated in computational examples discussing traveling waves in rectangular ducts. Different lengths, element types and mesh sizes are tested for the boundary element collocation method. In addition to the amplitude error which is due to numerical damping, a rather small phase error is observed. This may indicate numerical dispersion.
This study presents a simulation of interactions between sound and a surrounding pipe structure conveying fluid flows. A sound-attenuating structure using layered metamaterials of cylindrical shells is proposed and verified. Numerical simulations based on the finite difference method after considering steady fluid flow in the pipe were performed. The effective wave speed and density of the fluid required to determine acoustic characteristics were calculated from the transfer matrix method. This enabled estimation of noise reduction capability. The metastructure layers were lined parallel to the pipe walls to minimize flow resistance. The effective density was negative near the resonance frequency of the layers. The transmission loss predicted for a moving fluid medium was smaller than that for a stationary medium due to boundary layer formation. The proposed method can be used to design silencers to reduce the transmitted noise in pipe systems.
Reverse time migration (RTM), especially that for elastic waves, consumes massive computation resources which limit its wide applications in industry. We suggest to use the pseudospectral time-domain (PSTD) method in elastic wave RTM. RTM using PSTD can significantly reduce the computational requirements compared with RTM using the traditional finite difference time domain method (FDTD). In addition to the advantage of low sampling rate with high accuracy, the PSTD method also eliminates the periodicity (or wraparound) limitation caused by fast Fourier transform in the conventional pseudospectral method. To achieve accurate results, the PSTD method needs only about half the spatial sampling rate of the twelfth-order FDTD method. Thus, the PSTD method can save up to 87.5% storage memory and 90% computation time over the twelfth-order FDTD method. We implement RTM using PSTD for elastic wave equations and accelerate it by Open Multi-Processing technology. To keep the computational load balance in parallel computation, we design a new PML layout which merges the PML in both ends of an axis together. The efficiency and imaging quality of the proposed RTM is verified by imaging on 2D and 3D models.
Sea-surface wind agitation can be considered the dominant noise sources whose intensity relies on local wind speed during typhoon period. Noise source levels in previous researches may be unappreciated for all oceanic regions and should be corrected for modeling typhoon-generated ambient noise fields in deep ocean. This work describes the inversion of wind-driven noise source level based on a noise field model and experimental measurements, and the verification of the inverted noise source levels with experimental results during typhoon period. A method based on ray approach is presented for modeling underwater ambient noise fields generated by typhoons in deep ocean. Besides, acoustic field reciprocity is utilized to decrease the calculation amount in modeling ambient noise field. What is more, the depth dependence and the vertical directionality of noise field based on the modeling method and the Holland typhoon model are evaluated and analyzed in deep ocean. Furthermore, typhoons named "Soulik" in 2013 and "Nida" in 2016 passed by the receivers deployed in the western Pacific (WP) and the South China Sea (SCS). Variations in sound speed profile, bathymetry, and the related oceanic meteorological parameters are analyzed and taken into consideration for modeling noise field. Boundary constraint simulated annealing (SA) method is utilized to invert the three parameters of noise source levels and to minimize the objective function value. The prediction results with the inverted noise source levels exhibit good agreement with the measured experiment data and are compared with predicted results with other noise sources levels derived in previous researches.
Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this paper, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. This provides an additional advantage of PML over the infinite element approach.
The perfectly matched layer (PML) absorbing boundary condition has been proven to absorb body waves and surface waves very efficiently at non-grazing incidence. However, the traditional PML would generate large spurious reflections at grazing incidence, for example, when the sources are located near the truncating boundary and the receivers are at a large offset. In this paper, a new PML implementation is presented for the boundary truncation in three-dimensional spectral element time domain (SETD) for solving acoustic wave equations. This method utilizes pseudospectral time-domain (PSTD) method to solve first-order auxiliary differential equations (ADEs), which is more straightforward than that in the classical FEM framework.
Yangtze finless porpoises (Neophocaena asiaeorientalis) are known to use the narrowband signals for echolocation. In this study, a finite-element model was configured based on computed tomography imaging technique and tissue physical properties measurement to simulate biosonar signal emission and transmission processes through animal's head. The roles of the main structures in the head such as the air sacs, melon, bony structures, connective tissue, blubber, mandibular fat on the biosonar beam formation were investigated, and the relative importance of these structures was compared. The biosonar beam properties of this neonate porpoise were compared with those of adult ones. The method in this paper suggested an effective way for investigating the acoustic processes in the heads of the neonate odontocetes.
An analytical model is developed to investigate the sound transmission loss from orthogonally rib-stiffened plate structure under diffuse acoustic field excitation. The validity and feasibility of the model are verified by comparing the present theoretical predictions with the numerical results published previously. The influences of structure geometrical parameters on sound transmission loss are subsequently presented. The optimization algorithm is used to search for the optimal structural parameters with the objective to maximize the sound transmission loss over a frequency band. Furthermore, the sensitivity of structural parameters on the overall vibration and acoustic performance of the stiffened plates structure is also analyzed.
Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses are applied to an acoustic metamaterial. Metamaterials are structures formed by smaller, usually periodic, units showing remarkable physical properties when observed as a whole. Acoustic losses are relevant in metamaterials in the millimeter scale. In addition, their geometry is intricate and challenging for numerical implementation. The results are compared with existing measurements.
Apart from consolidated rocks, the effect of relaxation on acoustic propagation in unconsolidated sands cannot be neglected. In this paper, we study the influence of relaxation frequency on the propagation of acoustic waves. We compute the frequency-dependent velocities and attenuation of P1-wave, P2-wave, and S-wave at different bulk or shear relaxation frequency for plane wave. In addition, we derive the integral solutions of acoustic field equations in cylindrical coordinate system to simulate acoustic logging. The reflected acoustic waveforms in a borehole are calculated at different bulk or shear relaxation frequency. Calculation results show that the increase of bulk relaxation frequency will cause the velocity of P1-wave to decrease slightly, and the velocity of P2-wave to decrease substantially. The change of bulk relaxation frequency has no effect on the velocity of S-wave. The increase of bulk relaxation frequency will cause the attenuation of P1-wave or P2-wave to decrease or increase in different wave frequency range. The change of bulk relaxation frequency has no effect on the attenuation of S-wave. The increase of shear relaxation frequency will cause the velocity of P1-wave to increase slightly, and the velocity of P2-wave or S-wave to decrease substantially. The increase of the shear relaxation frequency will cause the attenuation of P1-wave, P2-wave or S-wave to decrease. For acoustic field in a borehole surrounded by unconsolidated sands, the effect of bulk or shear relaxation frequency on the velocity of reflected waves in a borehole is negligible at the dimension of the distance from a logging source. The increase of bulk or shear relaxation frequency will cause the amplitude of the reflected waveforms from the borehole wall to increase.
Traditionally, ocean acoustic propagation models assume the sea surface can be treated as an idealized pressure release boundary. For flat surfaces, this can easily be accomplished through a variety of modeling techniques. Rough surfaces, however, introduce additional complexities in numerical models which assume a pressure release condition. An alternative approach is to model the physical water/air interface in a manner analogous to the water/sediment interface of the bottom. However, the ocean surface boundary introduces a much larger interface discontinuity than the bottom interface. In this work, a previously developed hybrid split-step Fourier/finite-difference approach is implemented at the water/air interface. Results are compared with standard SSF smoothing approaches. Normal mode and finite element models are utilized to provide benchmark solutions. Tradeoffs between accuracy and stability are discussed, as well as the model's ability to accurately compute transmission across the water/air interface.
A method for denoising underwater acoustic signals used in applications of acoustical oceanography is presented. The method has been introduced for imaging denoising and has been modified to be applied with acoustic signals. The method keeps the energy significant part of the raw signal and reduces the effects of noise by comparing overlapping signal windows and keeping components which resemble true signal energy. It is shown by means of characteristic experiments in connection with a statistical signal characterization scheme based on wavelet transform, that using the statistical features of the wavelet sub-band coefficients of the denoised signal, tomography or geoacoustic inversions lead to a reliable estimation of the parameters of a marine environment.
This paper presents a review of basic concepts of the boundary element method (BEM) for solving 3D half-space problems in a homogeneous medium and in frequency domain. The usual BEM for exterior problems can be extended easily for half-space problems only if the infinite plane is either rigid or soft, since the necessary tailored Green's function is available. The difficulties arise when the infinite plane has finite impedance. Numerous expressions for the Green's function have been found which need to be computed numerically. The practical implementation of some of these formulas shows that their application depends on the type of impedance of the plane. In this work, several formulas in frequency domain are discussed. Some of them have been implemented in a BEM formulation and results of their application in specific numerical examples are summarized. As a complement, two formulas of the Green's function in time domain are presented. These formulas have been computed numerically and after the application of the Fourier Transformation compared with the frequency domain formulas and with a FEM calculation.
The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to determine the location of the original explosion, given limited spatial observations. We test the effectiveness of this scheme under conditions including dissipation, dispersion, etc. We use finite differences and implement absorbing boundary conditions to simulate an unbounded region.
For flow noise simulations, the nonreflecting boundary condition (NRBC) is significant to confine the computational domain to a small domain. Lattice Boltzmann method (LBM) has advantages for noise because of its low dissipation, but is limited to the uniform grid. In this paper, an absorbing boundary condition (ABC) based on perfectly matched layer (PML) technique is introduced to LBM. Then PML stability is analyzed and a new strategy is developed to achieve robustness. Invoking the decoupling time integration, the underlying equation for streaming is solved with the nodal discontinuous Galerkin method. Benchmark acoustic problems were used to demonstrate the PML absorption. Moreover, PML parameters, long time behavior and inhomogeneous pseudo mean flow are discussed. The methodology appears to work very well and would be hoped for practical flow noise computation.
