This Submission is for Special Issue on Underwater Acoustics: Perfectly Matched Layer Technique for Parabolic Equation Models in Ocean Acoustics

2017 ◽  
Vol 25 (01) ◽  
pp. 1650021 ◽  
Author(s):  
Chuan-Xiu Xu ◽  
Sheng-Chun Piao ◽  
Shi-E Yang ◽  
Hai-Gang Zhang ◽  
Li Li
Keyword(s):  
Parabolic Equation ◽  
Half Space ◽  
Numerical Solutions ◽  
Underwater Acoustics ◽  
Sound Field ◽  
Bottom Layer ◽  
Perfectly Matched Layer ◽  
Ocean Bottom ◽  
Field Calculation ◽  
Absorbing Layer

In ocean waveguides, the ocean bottom is usually approximated as a half-space. Thus, there exist no reflection waves at the half-space bottom and condition of radiation at infinity should be satisfied. In numerical solutions like parabolic equation methods, the depth domain has to be truncated, which can generate reflection waves from the truncated ocean bottom. To reduce the effect of reflection waves and to simulate an unbounded ocean bottom accurately, an artificial absorbing layer (ABL) was used. As was demonstrated, an ABL meets well the demand of accuracy in sound field calculation. However, both the sea-bottom layer and the artificial absorbing layer are needed to be set quite thick by using an ABL technique. Fortunately, a PML with several wavelengths can keep similar calculation accuracy with an ABL with dozens of wavelengths. In this paper, perfectly matched layer (PML) techniques for three parabolic equation (PE) models RAM, RAMS and a three-dimensional PE model in underwater acoustics are presented. A key technique of PML “complex coordinate stretching” is used to truncate unbounded domains and to simulate infinity radiation conditions instead of the ABL in those models. The numerical results illustrate that the PML technique is of higher efficiency than the ABL technique at truncating the infinity domain with minimal spurious reflections in PE models.

scholarly journals Improving the Performance of Mode-Based Sound Propagation Models by Using Perturbation Formulae for Eigenvalues and Eigenfunctions

2021 ◽  
Vol 9 (9) ◽  
pp. 934
Author(s):  
Alena Zakharenko ◽  
Mikhail Trofimov ◽  
Pavel Petrov
Keyword(s):  
Sound Propagation ◽  
Underwater Acoustics ◽  
Computational Cost ◽  
Normal Modes ◽  
Sound Field ◽  
Field Calculation ◽  
Combined Model ◽  
Eigenvalues And Eigenfunctions ◽  
Propagation Models ◽  
Area Of Interest

Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.

Limiting accuracy of two-dimensional parabolic equation solution using split-step Fourier transform method

2021 ◽  
Vol 64 (1) ◽  
pp. 43-49
Author(s):  
A.V. Mogilnikov ◽  
◽  
Yu.P. Akulinichev ◽  
Keyword(s):  
Fourier Transform ◽  
Parabolic Equation ◽  
Imaginary Component ◽  
Field Calculation ◽  
Mean Square ◽  
Rectangular Grid ◽  
Transfer Coefficients ◽  
Transform Method ◽  
Equation Solution ◽  
Absorbing Layer

Numerical solution of the wave parabolic equation on a rectangular grid is analyzed, when the method of discrete split-step Fourier transform (FT) is used to calculate the values of the field in an inhomogeneous medium at the next step in the range. The goal was to identify the limiting possibilities of the FT method itself, so studies were carried out for the case of radio wave propagation in free space. Two related problems were solved: what is the minimum value of the root-mean-square error (RMSE) of the field calculation and what should be the values of the transfer coefficients of the Fourier series harmonics and the values of the coefficients of the artificial absorbing layer (AL) both depending on the parameters of the computational scheme. It is shown that the dependence of the RMSE on the distance to the source always has the maximum. The forms of the optimal AL differ from those traditionally used primarily due to the presence of a significant imaginary component.

scholarly journals An Experimental Study of the Performance of a Crossed Rib Diffuser in Room Acoustic Control

2021 ◽  
Vol 11 (9) ◽  
pp. 3781
Author(s):  
Takumi Yoshida ◽  
Yasutaka Ueda ◽  
Norimasa Mori ◽  
Yumi Matano
Keyword(s):  
Sound Field ◽  
Wide Band ◽  
Scattering Coefficient ◽  
Scaled Model ◽  
One Dimensional ◽  
Broadband Absorption ◽  
Acoustic Control ◽  
Absorbing Layer ◽  
Speech Clarity ◽  
Reverberation Parameters

This paper presents a crossed rib diffuser (CRD) as an effective tool for room acoustic control. We performed an experimental investigation of its effectiveness using a specimen manufactured for this trial. The CRD is constructed by overlapping two one-dimensional (1D) periodic rib diffusers with different specifications so that they are crossed at non-right angles. The CRD achieves a higher scattering coefficient than 1D periodic rib diffusers in a wide band while maintaining the simple and friendly design of 1D periodic rib diffusers applicable to various architectural spaces. Moreover, inserting an absorbing layer between upper and lower ribs of the CRD, (CRD-A) yields a high broadband absorption coefficient. We first evaluated the random-incidence scattering coefficient of CRD using a 1/5 scaled model in comparison with those of 1D periodic diffusers assessed with a numerical method. Then, absorption coefficients for the CRD and the CRD-A were measured using a reverberation room. Subsequently, an experiment on a small meeting room with a 1D periodic rib diffuser, the CRD and the CRD-A was conducted to present performance of the CRD in room acoustic control. Impulse response measurements and evaluations of reverberation parameters (T20 and EDT) and speech clarity (D50) were conducted. Additionally, we present differences in structure of reflected sounds found for the flat wall, the CRD and the CRD-A visually using a four-channel sound field microphone.

Reconstruction of Acoustic Radiation of a Vibrating Structure Located in a Half-Space Bounded by a Passive Surface with Finite Acoustic Impedance

2020 ◽  
Vol 28 (04) ◽  
pp. 2050019
Author(s):  
Daren Zhou ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
Yongxiong Xiao
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Free Space ◽  
Plane Surface ◽  
Spherical Wave ◽  
Boundary Surface ◽  
Sound Field ◽  
Wave Functions ◽  
Reconstruction Method ◽  
Direct Radiation

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

scholarly journals In Design of an Ocean Bottom Seismometer Sensor: Minimize Vibration Experienced by Underwater Low-Frequency Noise

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3446 ◽  
Author(s):  
Xiaohan Wang ◽  
Shangchun Piao ◽  
Yahui Lei ◽  
Nansong Li
Keyword(s):  
Seismic Waves ◽  
Low Frequency ◽  
Sound Field ◽  
Average Density ◽  
Vibration Velocity ◽  
Frequency Noise ◽  
Ocean Bottom ◽  
Ocean Bottom Seismometer ◽  
Underwater Noise ◽  
The Impact

Ocean Bottom Seismometers (OBS) placed on the seafloor surface are utilized for measuring the ocean bottom seismic waves. The vibration of OBS excited by underwater noise on its surface may interfere with its measured results of seismic waves. In this particular study, an OBS was placed on the seabed, while ray acoustic theory was used to deduce the sound field distribution around the OBS. Then using this information, the analytical expression for the OBS vibration velocity was obtained in order to find various factors affecting its amplitude. The finite element computing software COMSOL Multiphysics® (COMSOL) was used to obtain the vibration response model of the OBS which was exposed to underwater noise. The vibration velocity for the OBS calculated by COMSOL agreed with the theoretical result. Moreover, the vibration velocity of OBS with different densities, shapes, and characters were investigated as well. An OBS with hemispherical shape, consistent average density as that of the seafloor, and a physical structure of double tank has displayed minimum amplitude of vibration velocity. The proposed COMSOL model predicted the impact of underwater noise while detecting the ocean bottom seismic waves with the OBS. In addition, it provides significant help for the design and optimization of an appropriate OBS.

scholarly journals Rayleigh-type waves on a coated elastic half-space with a clamped surface

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190111 ◽  
Author(s):  
J. Kaplunov ◽  
D. Prikazchikov ◽  
L. Sultanova
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Substrate Surface ◽  
Numerical Data ◽  
Elastic Half Space ◽  
Asymptotic Results ◽  
Homogeneous Half Space ◽  
Upper Face ◽  
Localized Waves ◽  
Perturbed Equation

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

scholarly journals Dynamics of inhomogeneous elastic half-space under moving load

2019 ◽  
Vol 97 ◽  
pp. 05048
Author(s):  
Bakhtiyor Yuldashev ◽  
Sagdulla Abdukadirov
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Moving Load ◽  
Elastic Base ◽  
Elastic Half Space ◽  
Thin Elastic Plate ◽  
Wave Processes ◽  
Load Effect ◽  
Time Period ◽  
Resonant Processes

Wave processes in an elastic half-space covered with an elastic layer and (or) a thin elastic plate are considered in the paper. External load moves along the free surface. In the stationary statement, the waveguide properties of the system are determined. The multiple roots of the dispersion equations are revealed and the critical load velocities, leading to the initiation of resonant processes, are determined. In the case when the load moves with the velocity of the Rayleigh wave, additional resonances determined by the structure can be realized in the structure under consideration. It is revealed that Rayleigh resonance exists for long waves only. Numerical solutions are obtained that make it possible to trace the development of resonant excitations. The models of simple structures that have dispersive properties in the medium wave zone are analyzed, such as a thin plate on an elastic base; a model with an attached inertial medium. Analytical solutions have been obtained for these models. Computer simulations conducted simultaneously allow us to analyze the quantitative features of process throughout the entire time period of the load effect. The numerical and asymptotic solutions are compared.

Spin-Up From Rest of a Two-Layer Liquid in a Cylinder

1994 ◽  
Vol 116 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Kwan Yeop Kim ◽  
Jae Min Hyun
Keyword(s):  
Analytical Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Bottom Layer ◽  
Meridional Flow ◽  
Individual Layer ◽  
Ekman Number ◽  
Radial Profiles ◽  
The Individual

A numerical and analytical study is made of spin-up from rest of a two-layer liquid in a rapidly rotating cylinder. The overall system Ekman number is small. The density of the top layer is smaller than that of the bottom layer (ρ1/ρ2<1.0), but the ratio of the individual layer kinematic viscosities is arbitrary (v1/v2<1.0 or v1/v2>1.0). The highlights of the analytical model, which is based on amended formulations of the Wedemeyer-Gerber-Homicz flow configurations, are briefly recapitulated. Comprehensive numerical solutions are secured to the time-dependent Navier–Stokes equations. The numerical solutions are validated by comparing the maximum interface displacements with the available experimental data as well as the analytical model predictions. Descriptions are made of the prominent characteristics of the interface shape for the two regimes of v1/v2<1.0 and v1/v2 > 1.0. Details of the azimuthal and meridional flow structures are illustrated by exploiting the numerical solutions. The computed meridional flows are compatible with the basic assumptions embedded in the development of the analytical model. Sequential plots of the radial profiles of azimuthal velocities are presented. These show that the global spin-up process is substantially accomplished over (En−1/2Ω−1), where En denotes the value of the smaller Ekman number of the two layers. The numerical study gives credence to the reliability and accuracy of the simplified analytical model.

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