Journal of Theoretical and Computational Acoustics

A model is presented for the scattered acoustic field above a bulky rigid cuboid shape in a rigid plane insonified by an acoustic field. The Kobayashi Potential method and the image sources method were used in order to derive the scattered acoustic field in a modal form. The incident source was then decomposed into plane waves. The total scattered field was determined by summing all the elementary scattered fields. This model was compared to finite element modeling and experimental results for three bulky cuboid shapes in an infinite rigid screen and a rectangular corner insonified by a spherical source. A good agreement between numerical and experimental results was obtained supporting the validity of the model.

To calculate the acoustic problems of relative uniform motion between the acoustic source and the fluid, we propose a boundary element method (BEM) strategy that can calculate various forms of relative uniform motion in subsonic conditions in a unified framework and is simple to implement. The acceleration algorithm for the BEM, like the fast multipole method (FMM), in the relative motionless state between the source and the fluid can be directly used without major modifications to the program. We propose a two-step transformation method to unify the wave equations of different relative motion forms into the classical form. In the first step, we transform the wave equations for various forms of relative motion into the equation where the convective terms are present only in the source part. Then, in the second step, we propose an acoustic-analogy Lorentz (a-a Lorentz) transformation to apply Lorentz covariance further to eliminate the convection term and establish the wave equation with classical form in a-a Lorentz space. We implement the boundary integration in the transformed a-a Lorentz space and derive a transformation method to transform discretized geometry and boundary conditions in the original space to the a-a Lorentz space. The problem that the boundary conditions are difficult to apply when solving the boundary integral equation (BIE) after the time-space coordinate transformation is solved. Numerical validations for the proposed method are performed by comparing with analytical results over a wide range of relative velocities. The results show that the proposed method can efficiently compute such problems with high accuracy and concise formulation.

Realistic acoustic problems often involve interactions between arbitrary-shaped moving objects at the interface with a fluid domain. The present work aims at developing numerical methods to take into account moving boundaries for acoustic problems, with a high order of convergence. The reference problem considered in this work is the solution of the non-linear Euler equations by a finite-difference time-domain method, describing the formation of one-dimensional waves created by a moving piston. The most suitable class of methods to solve this type of problem in the case of complex moving boundaries is the ghost-point method for sharp interface with 4th order reconstruction. In order to accurately formulate the immersed boundaries with ghost points, the boundary conditions are formulated in terms of characteristic waves of the non-linear equations. The proposed approach is also extended to represent moving boundaries with a prescribed acoustic impedance. This is achieved by coupling a time-domain acoustic impedance model to the immersed boundary technique. The method is also applied to a two-dimensional example, where an acoustic pulse is reflected by a moving wall.

When modeling sound waves in fluids it can be important to include the viscous and thermal losses originating from the fluids’ interaction with boundaries. In the audible frequency range, the thickness of the boundary layers is between a micrometer and a millimeter. As such the viscous and thermal losses are important when simulating the properties of small acoustical devices such as e.g. hearing aids or transducers. However, the inclusion of viscous and thermal losses is a computationally demanding task as it requires a fine discretization of the boundary layer in order to fully capture the complicated physical phenomena happening on the microscale. Recently, there has been developments to ease the computational demands using both the Finite Element Method and the Boundary Element Method, by approximating the losses using the Boundary Layer Impedance (BLI) boundary condition. In this paper, we extend previous developments for multi-frequency analysis using the Reduced Order Series Expansion Boundary Element Method to handle the BLI condition. This model follows a two-step procedure: Using a series expansion to decrease the assembly time of the BEM matrices and a projection to reduce the overall memory consumption of the model. Results from two acoustic interior problems show that the model decreases the total computational time by around 96% while using less than 15% of the memory. For both test setups the limiting factor of the accuracy was the reduction and not the series expansion.

Broadband signals interacting with deep ocean fine-grained sediment are crucial in shaping the acoustic field of the geometric shadow zone. These signals travel through both the seabed reflected path and the refracted path. In this article, a sequential inversion scheme is employed to estimate the geoacoustic parameters in abyssal clay sediments. This inversion is based on seabed reflection loss data at different frequencies, as well as travel time difference data between refractions and reflections obtained from the South China Sea Experiment in 2018. Depth-dependent profiles of geoacoustic parameters are formulated using Bernstein polynomials. The polynomial coefficients and their posterior probability density functions are efficiently estimated using the adaptive simplex simulated annealing method and an approximate variational inference technique known as Variational Bayesian Monte Carlo. This technique demonstrates superior efficiency and comparable accuracy to Markov Chain Monte Carlo sampling. The inversion results indicate that the abyssal clay sediments in this area exhibit a positive sound speed gradient and relatively low attenuation, both with high probabilities. The deduced seabed model accurately predicts the transmission loss, aligning well with the experimental data.

Frequency-difference source localization (FDSL) is a relatively new method for locating sources emitting acoustic or electromagnetic waves from recorded data. Estimates of location are produced by matching a nonlinear function of the received data with the same nonlinear function of modeled data. This so-called matched-field approach depends on the accuracy of the modeled field. FDSL exhibits less sensitivity to model errors in some cases of interest. Fluctuations of the speed of sound in the ocean are affected by a wide variety of phenomena and internal gravity waves is one where their spectrum is usually well known. There is no analytical theory for predicting how these fluctuations of sound speed affect the accuracy of FDSL, leaving a numerical evaluation as the alternative for the focus of this paper. Experimental application of FDSL was previously made for an acoustic source of 100 Hz bandwidth surrounding 250 Hz for a 129 km section in the Philippine Sea with data recorded on a long vertical array [Geroski and Dowling, Long-range frequency-difference source localization in the Philippine Sea, J. Acoust. Soc. Am. 146 (2019) 4727–4739.]. The role of internal waves is quantified with a realistic FDSL simulation using models based on the parabolic and ray approximations of the linear acoustic wave equation. The modeled vertical variation of FDSL error is similar to observed while the modeled horizontal error is too small. The complicated software model is automatic but is computationally intensive, with our version needing about 1.5 mo to compute on a PC with 16 cpu cores.