Journal of Theoretical and Computational Acoustics

Modeling elastic waves in complex media, with varying physical properties, require very accurate algorithms and a great computational effort to avoid nonphysical effects. Among the numerical methods the spectral elements (SEM) have a high precision and ease in modeling such problems and the physical domains can be discretized using very coarse meshes with elements of constant properties. In many cases, models with very complex geometries and small heterogeneities, shorter than the minimum wavelength, require grid resolution down to the thinnest scales, resulting in an extremely large problem size and greatly reducing accuracy and computational efficiency. In this paper, a poly-grid method (PG-CSEM) is presented that can overcome this limitation. To accurately deal with continuous variations or even small-scale fluctuations in elastic properties, temporary auxiliary grids are introduced that prevent the need to use large meshes, while at the macroscopic level wave propagation is solved maintaining the SEM accuracy and computational efficiency as confirmed by the numerical results.

The seismic method on ice provides rich information and a feasible technical way for acoustic study in ice-covered water. This paper presents a method to determine the modes in ice–water bi-layer waveguides. We achieve the purpose by deducing the scaled boundary formulation for solid and fluid layers then coupling them with the coupling matrix. The wave numbers and mode shapes are compared with the results of the finite element method. It shows that the configuration for ice–water bi-layer waveguide is of high precision. In underwater acoustic applications, the depth of water is comparatively large relative to ice thickness, which addresses the additional difficulty of accuracy in high frequency. The study on convergence is carried out, and approximate formulas are addressed based on the calculated results, giving a quick insight into piratical application.

Backscattered wave acoustic tomography using wideband probing signals makes it possible to obtain three-dimensional (3D) images of scattering inhomogeneities. Signal processing based on the reverse time migration (RTM) method allows one to take into account the influence of background refractive obstacles of the medium to minimize distortions of reconstructed tomographic images. We propose a noniterative method of acoustic tomography in an immersion medium based on RTM approach supplemented with linear signal preprocessing to enhance resolution of reconstructing tomography images. The visualization of scattering objects is based on wave inversion from the measurement area considering the probing wave field specially distorted to perform regularized back convolution. The applicability of the proposed method for visualizing scattering objects in water is shown analytically, numerically and experimentally. The proposed method is resistant to noise according to regularization. The results obtained show the agreement between the numerical and analytical solution. Using the example of sounding with linear frequency modulation signals, it is demonstrated that the proposed method allows increasing the resolution of tomographic images in comparison with conventional RTM. The novelty of the proposed method is the preliminary filtration of the forward propagation wave in the course of solving the inverse problem. This approach improves the resolution of tomographic images and allows considering the influence of obstacles.

In this paper, a model of the heterogeneous anelastic seismic wave problem is proposed in three-dimensional (3D) cylindrical coordinates. We use the velocity-stress formula to describe the realistic attenuation properties of viscoelastic materials, derived from a rheological model of the generalized standard linear solid (GSLS). The equation system is completed by additional equations for the anelastic functions including the strain history of the material. We apply the staggered grid finite-difference (FD) method in 3D cylindrical coordinates to solve the equations. Moreover, to avoid the effect of gradual expansion of the grid size as the radius increases, we use a variable grid method to achieve compensation. In real drilling operations, the mud injected in the borehole is a fluid with viscous properties. The actual formation is also not elastic. In the synthetic data of acoustic logging while drilling (LWD), we find that the drill collar wave is not affected by the viscoelastic parameters of the formation. In contrast, the Stoneley wave is more sensitive to the viscosity of the drilling fluid. The phase and amplitude of the received waveform are affected by the drilling fluid as well as the formation viscoelasticity. Therefore, the development of the cylindrical variable-grid FD method provides a flexible and efficient numerical technique to solve 3D viscoelastic wave propagation problems, including realistic attenuation and complex geometry.

A frequency-domain formulation is proposed to compute the far-field noise generated by flows with periodically oscillating or rotating boundaries. The proposed formulation significantly enhances the efficiency of the frequency-domain method in handling the multi-frequency sources with nonrectilinear motion. The novelty of the proposed method is that the frequency- and time-dependent components of the Ffowcs Williams and Hawkings (FW-H) integral are separated by using the far-field asymptotic Green’s function. The separation of the frequency- and time-dependent components avoids the need for an expensive time integration in computing the multi-frequency noise generated by flows with periodically moving boundaries. They proposed only one Fourier transform computation in obtaining the noise at different frequencies. The efficiency of the proposed formulation is investigated by analyzing the required number of floating-point operations. Its validity is examined by computing the noise from rotating or oscillating permeable boundaries around composite monopoles and a flapping wing. The proposed formulation is applicable to the FW-H integral with periodically oscillating or rotating boundaries when the maximum velocity on the moving boundary is subsonic.

In this paper, a three-dimensional finite element method for solving the linearized potential equation (LPE) is implemented to predict the acoustic attenuation performance of mufflers in the presence of nonuniform flow. For accurate physical representations, the porous material is modeled as equivalent fluid with complex speed of sound and density while the background mean flow in fluid domain is captured by solving Reynolds-averaged Navier–Stokes equations. The treatment details for boundary integrals at different boundary conditions and expressions for transmission loss are presented. Good agreements of predicted and measured transmission loss of two reactive and a hybrid mufflers validated the present approach. Finally, the convective effect of nonuniform flow on the acoustic attenuation behavior of the hybrid muffler is examined numerically in detail.