Journal of Theoretical and Computational Acoustics

The complex nature of the ocean environment requires advanced computational acoustic models to gain insights into the dominating physical factors controlling the underwater sound propagation and scattering in the ocean. In this study, we explore the “ab-initio” approach to solve wave equations with numerical algorithms that can be implemented in distributed memory parallel computers. The goal is to improve the calculation speed so long-range global scale hydroacoustic wave propagation can be studied more efficiently and effectively. Two major algorithms: the finite difference time domain (FDTD) method and the Parabolic Equation (PE) method are investigated. Two PE-based numerical models are considered. One is the Split-Step-Fourier Parabolic Equation (SSFPE) model using split-step Fourier schemes in three-dimensional (3D) environments. The second PE model is a multi-frequency implementation of the Range-dependent Acoustic Model (RAM) that computes two-dimensional (2D) sound pressure fields.

One of the primary challenges in global-scale hydroacoustic propagation modeling with the “ab-initio” approach is the demand for significant computational resources on both memories and computational speeds. To address this, we employed parallel computing techniques using directive-based programming languages, such as OpenACC and XscalableACC, to leverage the power of multiple Graphics Processing Unit (GPU) systems and Central Processing Unit (CPU) cluster computers. Our performance evaluation revealed substantial speedup gains. For the FDTD method, we achieved approximately 3.5-fold and 4-fold speedups with four GPUs and four CPU cluster nodes, respectively. With the 3D SSFPE model, we obtained a speedup of 3.7-fold using four CPU cluster nodes. A significant result was observed with the 2D broadband multi-frequency RAM model, where we achieved a 110-fold speedup compared to one core original implementation.

These results demonstrate the promising potential of massively parallel computers for ocean acoustic propagation modeling and highlight the significant performance benefits of utilizing parallel computing techniques. Our findings emphasize the importance of efficient computational strategies.

In a translation-invariant environment, the three-dimensional sound field can be determined through spatial Fourier transform by superimposing two-dimensional sound fields. This technique is commonly referred to as the 2.5D method, due to the dimensional reduction that takes place.

If the sound source is not stationary but moves along the axis of invariance, the calculation of the sound field generally becomes more complex. However, if a harmonically radiating point source moves uniformly at a constant speed along the invariance axis, the opposite is true, and the calculation is significantly simplified.

Motivated by the form of the Green’s function in the free field, the so-called separation of variables, or product approach, reduces the problem to a purely two-dimensional one, the general solution of which is referred to in this work as the Product-Doppler formula. Constructing a Fourier integral over the wavenumber domain along the invariance axis is no longer necessary.

It is shown that the Product-Doppler formula can be used to solve both interior and exterior problems. The sound field generated by a moving source inside a cylindrical tunnel, and the sound generated by an exterior moving source and scattered from an absorbing cylinder are analyzed.

The complex problem of sound diffraction caused by a source moving along the edge of a wedge or a screen is studied in detail. A comparison with results from the literature shows strong agreement.

A waveguide consisting of an isospeed water layer overlying a halfspace with a sound speed gradient is considered. The dependence of horizontal wavenumbers of normal modes in such a waveguide on the sound frequency, water depth and geoacoustic parameters of the bottom are investigated. It is shown that these dependencies are described by ordinary differential equations that can be solved numerically at very low computational cost providing a substantial increase in the efficiency of broadband modelling of sound propagation. The explicit formulae for the derivatives of horizontal wavenumbers with respect to the bottom parameters can be also used in dispersion-based geoacoustic inversion methods. This approach can be extended to the case of a waveguide consisting of several layers of Airy-type media. We also propose a new and concise proof that the spectrum of the Sturm-Liouville problem from which the modes are found for this waveguide is purely discrete.

To circumvent the difficulties in computing sound at moving observers for the prompting Cooperative Autonomous Underwater Vehicles, we propose a frequency-domain formulation for computing sound with Ffowcs Williams-Hawkings equation. The proposed formulation avoids the expensive integration at each moment over the frequency domain when the acoustic pressure is computed at moving observers, because we novelly decompose the far-field asymptotics of the Green’s function into time- and frequency-dependent components. The proposed formulation is applicable to computation of sound at moving observers with both rectilinear and non-rectilinear motions in subsonic flows. We validate the proposed formulation by computing sound generated from moving acoustic monopole and dipole in freestream flows. The oscillating and rectilinear motions of a far-field observer along various paths are specially considered. The results demonstrate that the proposed formulation provides reliable predictions for sound received by moving observers.

Cavitation phenomena are accompanied by harsh cavitation noise. Studying cavitation noise is an effective method to monitor cavitation conditions. In order to study the characteristics of cavitation noise, a Venturi test bench experiment platform is built, the cavitation flow field and cavitation noise of Venturi test bench are simulated. The frequency domain analysis of cavitation noise is carried out, and the relationship between cavitation region, flow rate and sound pressure level of cavitation noise is verified by comparison between simulation and experiment. Because the cavitation noise is easily polluted by ambient noise, wavelet transform is used to analyze the cavitation noise and background noise, and the characteristics of cavitation noise are studied by comparing the difference between them.

In this paper, vibroacoustic analysis of an L-shaped acoustic cavity comprising of rigid and laminated composite thin and flexible walls with opening has been performed by coupling multi-domain boundary element (BE) method with finite element (FE) method, where the cavity is divided into several domains with intermediate interface layers and the continuity conditions have been established at the interface. Finite element structural analysis of the interacting enclosure has been conducted to extract the mobility relationship between pressure and velocity at the interacting walls and apply that to the pressure-velocity multi-domain BE formulation of the interior acoustic cavity. Absorbent layers have been applied at multiple walls to investigate their effects on sound pressure levels at the boundary and inside the domain. Radiation impedance and admittance relationship have been implemented to model the opening and the absorbent layers at the boundary respectively. An in-house software incorporating the aforementioned features has been developed to solve practical vibroacoustic engineering problems of irregular-shaped cavities. The present program has been verified with analytical and experimental data available in the literature to ensure accuracy. It has been demonstrated that the shape of the acoustic domain along with the presence of opening alters the modal characteristics of the structure causing considerable modifications in the sound pressure level (SPL) pattern. Examples reveal that one can restrict the acoustic output at the resonant frequencies by suitably adding absorbents.

To avoid computing a double integral when simulating the acoustic field diffracted by a finite-sized hard reflector, its surface is discretized into many elements, and then each element is treated as a point-like reflector. The total acoustic field diffracted by the finite-sized hard reflector is calculated by adding the acoustic fields diffracted by each element. The efficiency of this approach over numerically computing the double integral boundary equation has been shown within an isogeometric analysis framework.