Simulation Of Acoustic Wave Propagation Research Articles

Numerical simulation of acoustic waves propagation by finite element method based on optimized matrices

Abstract Based on the wave equation, scholars worldwide have proposed various methods for numerical simulation of seismic wave propagation in underground and surface media. The finite element method offers a unique advantage in accurately depicting the undulating surfaces and steep palaeoburial hills with its triangular mesh. However, its computational efficiency cannot meet our needs while lots of memories are occupied. To address this, we optimized and improved the critical Mass matrix and Stiffness matrix of spatial discretization of the acoustic wave equation. We first fully utilized the flexibility of triangles to fit different undulating terrains, then reorganized the numbering of triangle mesh nodes and elements to reduce the bandwidth of the matrices, and then used optimized matrices for solving. The Crank-Nicolson scheme was adopted for time discretization, and the Perfectly Matched Layer condition was utilized to eliminate false waves reflected from the boundary. The numerical experiments with simple and significant fluctuation models proved that this method can accelerate computational efficiency while ensuring computational accuracy.

Numerical simulation of sound attenuation in an acoustically lined duct in high-temperature air flows

Noise reduction structures are important for the vibration and noise reduction design of aerospace engines. The design of noise-reducing structures often needs to be quickly evaluated via numerical simulations. Hence, the simulation results of the corresponding system are very important for guiding the design of noise-reducing structures. High temperature is one of the key environmental factors that need to be considered when evaluating the sound attenuation process via numerical methods. In this study, numerical simulations of acoustic wave propagation on an acoustic liner structure considering air temperature variations are carried out by using compressible Navier–Stokes equations and the ideal gas equation of state. The results showed that the effect of temperature on sound attenuation under grazing flow conditions is complex. Moreover, an increase in temperature will reduce the transmission loss of the acoustic liner in the grazing flow at high air speed.

Direct numerical simulation of acoustic wave propagation in ocean waveguides using a parallel finite volume solver

Numerical simulations based on the Finite Volume Method (FVM) solve the wave equation directly to provide highly accurate predictions of the sound field in ocean waveguides without model simplification and loss of generality. However, the huge computational complexity severely limits the application range of direct numerical solvers for underwater acoustic waves. In this paper, a highly scalable parallel algorithm for solving acoustic models using the cell-centred finite volume method was proposed, and a corresponding direct numerical solver was developed and validated. The paper has three main findings as follows. Firstly, the acoustic solver was implemented based on a generic framework for solving partial differential equations (PDEs), so that more complicated models such as fluid–sound coupling and sound–structure coupling could be easily extended. Secondly, the large spatial scales of underwater sound propagation can be efficiently calculated by parallel computing. Thirdly, our approach demonstrated high computational accuracy and the ability to support complex scenarios. We verify the accuracy and efficiency of the solver through experiments, and prove the solving ability of the solver in large-scale, complex structures and complex configurations.

A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media

This study presents a novel coupled meshless model for simulating acoustic wave propagation in heterogeneous media, based on the singular boundary method (SBM) and Kansa’s method (KS). In the proposed approach, the SBM was used to model the homogeneous part of the propagation domain, while KS was employed to model a heterogeneity. The interface compatibility conditions associated with velocities and pressures were imposed to couple the two methods. The proposed SBM–KS coupled approach combines the respective advantages of the SBM and KS. The SBM is especially suitable for solving external sound field problems, while KS is attractive for nonlinear problems in bounded non-homogeneous media. Moreover, the new methodology completely avoids grid generation and numerical integration compared with the finite element method and boundary element method. Numerical experiments verified the accuracy and effectiveness of the proposed scheme.

Large-scale simulation of high-intensity focused ultrasound with Sierra/SD

High-frequency simulations of acoustic wave propagation are known to be computationally challenging, and the difficulty is compounded for large domains. For problems like high-intensity focused ultrasound (HIFU) with coupling between piezoelectric and acoustic media, both challenges are present. The larger domain sizes, higher-order elements, and greater levels of refinement necessary in such simulations result in millions of degrees of freedom, large system matrices, and substantial memory requirements, raising the need for parallel high-performance computing (HPC). Sierra/SD is a massively parallel HPC application developed for finite element method simulations in structural dynamics and acoustics. In this work, Sierra/SD is used to simulate an acoustic pulse from a piezoelectric transducer focused on an elastic scatterer in a fluid medium. Three-dimensional simulation results are presented for the acoustic field in the fluid and the stress field in the scatterer, and performance is compared between Sierra/SD and COMSOL Multiphysics for smaller geometries. Finally, to showcase the expanded analysis possibilities afforded by HPC for HIFU, an example is presented using a support vector machine to determine a decision boundary for maximum stress in the scatterer. [SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.]

Quantifying tongue tip visibility in ultrasound images of /r/ tongue shapes using numerical ultrasound simulations

Midsagittal ultrasound images provide important articulatory information about tongue shape by showing much of the tongue surface from the root to the tip. However, portions of the tongue tip are often obscured due to shadowing from the mandible bone and the sublingual airspace. Information about tongue tip position can be important for understanding tongue movement patterns, e.g., classification of a retroflex or bunched shape for the American English rhotic /r/. Here, numerical simulations of acoustic wave propagation in tissue were performed using the open-source k-Wave toolbox to recreate ultrasound images of the tongue for a range of retroflex and bunched tongue shapes segmented from magnetic resonance imaging (MRI). Extent of the tongue tip visibly missing from the simulated ultrasound images is quantified by comparison with the known tongue shape from MRI. The fraction of the tongue surface visible in ultrasound images is compared between tongue shapes that appear retroflex versus bunched in MRI. Implications for ultrasound biofeedback therapy are discussed, including possible ambiguity of retroflex versus bunched classification.

Acoustic wave propagation model in the surface layer area based on the Runge-Kutta method

Simulation of acoustic wave propagation in the surface layer area is carried out by taking a positive value acoustic velocity gradient so that in this simulation there will be a wave phenomenon trapped in the surface layer area. In this study, acoustic beam emission was conducted by varying the angle of incidence and length of the beam used, and the determination of the acoustic velocity gradient was carried out using the Runge-Kutta order of order 2. The results showed that at depths of 0 to 40 meters with an acoustic velocity of 1405 m/s, for a length of 1 meter and a gradient pattern of +2.5 obtained a minimum angle of incidence of 0.09 radians with a wave propagation of 250 meters. Comparison between analytical and computational results on wave propagation in the surface layer area is a 4.51% error.

Determination of the shadow zone area in the ocean computationally by simulating the propagation of acoustic rays

Simulation of acoustic wave propagation to determine the shadow zone area using computational methods has been carried out using negative value gradients. The study was conducted by varying the angle of incidence and variations in the length of the beam used. This research was conducted by comparing analytical results with computational results. The results of this study indicate that at a depth of 500 meters with a sound speed of 1493.1 m/s, a beam length of 1 meter, and a gradient pattern of -0.1, a maximum angle of 0.255 radians is obtained with the shadow zone area being at a depth of 0 to 800 meters and a distance of 5000 meters of wave source. The value of the difference or error in analytical data and computational data is 0.0817%.

Dynamic Simulation of Acoustic Wave Propagation and Attenuation in Low-Density Polyethylene by Recursive Convolution Finite-Difference Time-Domain Method

The dynamic simulation of pulsed electroacoustic (PEA) signals has been conducted by the recursive convolution finite-difference time-domain (RC-FDTD) method, in which acoustic attenuation in low-density polyethylene (LDPE) is calculated on the basis of viscoelastic theory. This method allows us to quantitatively analyze the distortion of the waveform in an LDPE film resulting from the acoustic attenuation. The RC-FDTD method can easily visualize the propagation, reflection, and attenuation of the acoustic waves in the LDPE film. Furthermore, the attenuated space charge profiles in the LDPE film are also calculated by the RC-FDTD method.

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation.

A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman-Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow.

Sound and soliton wave propagation in homogeneous and heterogeneous mediums with the new two-derivative implicit–explicit Runge–Kutta–Nyström method

This paper derives a new family of implicit–explicit time-marching methods for PDEs with the second-order derivative in time. The present implicit method is based on the two-derivative Runge–Kutta–Nyström methods, which use a third-order time derivative of the solution. Although the current approach is implicit, it does not need to invert the coefficient matrix of the discretized system of equations. The stability properties are assessed using Fourier analysis for the model test problems by considering space–time discretizations together. The present methods are validated by comparing to some of the most widely used time-marching methods available in the literature. In addition, to assess the robustness and efficiency of the present methods, we have also performed numerical simulations of acoustic wave propagation in two- and three-layered heterogeneous media and sine-Gordon solitons for damped and undamped cases. Computed results match very well with the exact and numerical solutions noted in the literature.

Metamaterial Acoustics on the (2 + 1)D Einstein Cylinder

The Einstein cylinder is the first cosmological model for our universe in modern history. Its geometry not only describes a static universe—a universe being invariant under time reversal—but it is also the prototype for a maximally symmetric spacetime with constant positive curvature. As such, it is still of crucial importance in numerous areas of physics and engineering, offering a fruitful playground for simulations and new theories. Here, we focus on the implementation and simulation of acoustic wave propagation on the Einstein cylinder. Engineering such an extraordinary device is the territory of metamaterial science, and we will propose an appropriate tuning of the relevant acoustic parameters in such a way as to mimic the geometric properties of this spacetime in acoustic space. Moreover, for probing such a space, we derive the corresponding wave equation from a variational principle for the underlying curved spacetime manifold and examine some of its solutions. In particular, fully analytical results are obtained for concentric wave propagation. We present predictions for this case and thereby investigate the most significant features of this spacetime. Finally, we produce simulation results for a more sophisticated test model which can only be tackled numerically.

FEM simulations of acoustic wave propagation in the vicinity of the railroad structure

Noise is one of the major environmental concerns nowadays. The problem is especially significant around large urban agglomerations where high levels of noise can have a negative impact on physical or psychological well-being of citizens while a long-term exposure can be harmful to health. Residential areas are protected by the introduction of maximum allowable sound pressure levels according to appropriate norms. There are also similar regulations concerning natural areas under environmental protection. Different measures used in order to reduce levels of noise should be applied primarily to the source of the sound. This is the task mainly for the manufacturers of all kinds of machines as well as means of transport. However, noise levels can be also controlled by the introduction of appropriately designed or chosen elements or materials in civil engineering structures. The noise levels emitted by the rail traffic depend on the number, kind and speed of trains, night and day traffic organization as well as on the type of the railroad structure and its location (e.g. on an embankment, on a bridge or flyover). Railway noise mainly develops between wheels and rails and depends on the roughness of both these elements, rolling speed and dynamic characteristics of the railroad. The paper presents the mathematical formulation of a coupled acoustic-structure problem. Solving the problem with finite element method gives the possibility to predict sound pressure levels in the vicinity of a railway structure. A numerical model of a certain type of a railroad structure was built in order to simulate the acoustic wave propagation caused by a wheel-rail interaction. The harmonic analysis was carried out using the Abaqus software. The acoustic pressureobtained based on the harmonic analysis was evaluated in certain points of the acoustic medium for various excitation frequencies. The final results were presented in the form of one-third octave bands. In the article, a possible methodology for estimating noise levels from railway structures based on a numerical analysis was shown. In the future works, the numerical model will be validated by field test data and applied to evaluate different types of technological solutions (silencers) used to reduce railway noise levels. This paper is part of the project “Innovative solutions for the protection of people and building against noise from rail traffic”. The project is co-financed by the European Union from the European Regional Development Fund within the framework of the Smart Growth Operational Programme and by PKP PLK S.A. within the framework of a joint venture BRIK. Keywords: Finite Element Method; Acoustics; Railway Noise

Laboratory Physical Simulation of Acoustic Wave Propagation on the Shelf

In laboratory conditions, the vertical structure of short mode pulses was studied near the critical thicknesses of hydroacoustic waveguides of constant and variable depth with different bottom models.

Acoustic streaming effect on flow and heat transfer in porous tissue during exposure to focused ultrasound

High-intensity focused ultrasound (HIFU) is a minimally invasive technique of regional treatment in which ultrasound waves are focused on targeted tissue. Nevertheless, the precise localization of the target area of HIFU ablation remains challenging. This study investigated acoustic pressure, fluid flow, and heat transfer in porous tissue during exposure to HIFU. The effects of the heat transfer model, tissue permeability, and exposure time on fluid flow and temperature distribution in the tissue were numerically investigated. Additionally, the heating-region shape and heating position were studied. The acoustic pressure, fluid flow, and temperature distributions in the porous tissue during exposure to HIFU were calculated using the numerical simulation of acoustic wave propagation and heat transfer models. The heat transfer models used were formulated based on the conventional bioheat model and porous media theory. With the porous media model, the temperature distributions were observed to be different from those of the conventional bioheat model; this was caused by the acoustic streaming effect. Permeability affected the flow pattern and temperature distribution in the tissue. In particular, tissue permeability also has a significant effect on the position of the target area and lesion shape within the tissue.

Simulations and human cadaver head studies to identify optimal acoustic receiver locations for minimally invasive photoacoustic-guided neurosurgery

Real-time intraoperative guidance during minimally invasive neurosurgical procedures (e.g., endonasal transsphenoidal surgery) is often limited to endoscopy and CT-guided image navigation, which can be suboptimal at locating underlying blood vessels and nerves. Accidental damage to these critical structures can have severe surgical complications, including patient blindness and death. Photoacoustic image guidance was previously proposed as a method to prevent accidental injury. While the proposed technique remains promising, the original light delivery and sound reception components of this technology require alterations to make the technique suitable for patient use. This paper presents simulation and experimental studies performed with both an intact human skull (which was cleaned from tissue attachments) and a complete human cadaver head (with contents and surrounding tissue intact) in order to investigate optimal locations for ultrasound probe placement during photoacoustic imaging and to test the feasibility of a modified light delivery design. Volumetric x-ray CT images of the human skull were used to create k-Wave simulations of acoustic wave propagation within this cranial environment. Photoacoustic imaging of the internal carotid artery (ICA) was performed with this same skull. Optical fibers emitting 750 nm light were inserted into the nasal cavity for ICA illumination. The ultrasound probe was placed on three optimal regions identified by simulations: (1) nasal cavity, (2) ocular region, and (3) 1 mm-thick temporal bone (which received 9.2%, 4.7%, and 3.8% of the initial photoacoustic pressure, respectively, in simulations). For these three probe locations, the contrast of the ICA in comparative experimental photoacoustic images was 27 dB, 19 dB, and 12 dB, respectively, with delay-and-sum (DAS) beamforming and laser pulse energies of 3 mJ, 5 mJ, and 4.2 mJ, respectively. Short-lag spatial coherence (SLSC) beamforming improved the contrast of these DAS images by up to 15 dB, enabled visualization of multiple cross-sectional ICA views in a single image, and enabled the use of lower laser energies. Combined simulation and experimental results with the emptied skull and >1 mm-thick temporal bone indicated that the ocular and nasal regions were more optimal probe locations than the temporal ultrasound probe location. Results from both the same skull filled with ovine brains and eyes and the human cadaver head validate the ocular region as an optimal acoustic window for our current system setup, producing high-contrast (i.e., up to 35 dB) DAS and SLSC photoacoustic images within the laser safety limits of a novel, compact light delivery system design that is independent of surgical tools (i.e., a fiber bundle with 6.8 mm outer diameter, 2 mm-diameter optical aperture, and an air gap spacing between the sphenoid bone and fiber tips). These results are promising toward identifying, quantifying, and overcoming major system design barriers to proceed with future patient testing.

Wrapround Multiple Reflectors over the Seafloor in the Gas Hydrate Area: A Possible Indicator of Methane Plume

Seismic wraparound multiples which are produced by the previous shot and trapped between the sea surface and flat seabed in the two-dimensional marine seismic reflection data have the potential to provide information about oceanographic phenomena because their repetition in the water column could enhance the detectability of the disturbance of seismic wave propagation. By focusing on the disturbance of wraparound multiples, we inferred the possible presence of methane gas bubbles emitting from the seafloor over several kilometers within a submarine canyon with a flat seabed. We observed the significant disturbance of wraparound multiples in both pre-stacked gathers and common mid-point stacked sections, which may be caused by methane bubbles. The existence of a bottom simulating reflection, a fault, and Calyptogena colonies provides indirect evidence of methane gas bubble seeps, while the existence of a cold seep is direct evidence of them in the study area. Finally, we conducted preliminary numerical simulations of acoustic wave propagation to investigate the cause of disturbances of wraparound multiples. Our preliminary numerical simulations imply that the disturbance of wraparound multiples might be associated with the internal scattering caused by an aggregation of gas bubble seeps in the water column.

Unsupervised clustering method to convert high-resolution magnetic resonance volumes to three-dimensional acoustic models for full-wave ultrasound simulations

Simulations of acoustic wave propagation, including both the forward and the backward propagations of the wave (also known as full-wave simulations), are increasingly utilized in ultrasound imaging due to their ability to more accurately model important acoustic phenomena. Realistic anatomic models, particularly those of the abdominal wall, are needed to take full advantage of the capabilities of these simulation tools. We describe a method for converting fat-water-separated magnetic resonance imaging (MRI) volumes to anatomical models for ultrasound simulations. These acoustic models are used to map acoustic imaging parameters, such as speed of sound and density, to grid points in an ultrasound simulation. The tissues of these models are segmented from the MRI volumes into five primary classes of tissue in the human abdominal wall (skin, fat, muscle, connective tissue, and nontissue). This segmentation is achieved using an unsupervised machine learning algorithm, fuzzy c-means clustering (FCM), on a multiscale feature representation of the MRI volumes. We describe an automated method for utilizing FCM weights to produce a model that achieves agreement with manual segmentation. Two-dimensional (2-D) and three-dimensional (3-D) full-wave nonlinear ultrasound simulations are conducted, demonstrating the utility of realistic 3-D abdominal wall models over previously available 2-D abdominal wall models.

Numerical Simulation of Acoustic Waves Propagation in an “Atmosphere–Forestland–Ground” System

Under study is the problem of numerical simulation of acoustic waves propagation in a two-dimensional inhomogeneous medium represented by the “atmosphere–forestland–ground” model. A specific feature of the simulation is the introduction into the basic equations of acoustics of a linear damping function that characterizes the energy loss of the acoustic wave with respect to afforestation. The problem is considered of interaction between the acoustic waves incident at a given angle from the atmosphere to the “forestland–ground” boundary and the seismic waves arising in the ground. The issue of the forestland influence on the levels of acoustic and seismic waves is investigated. In particular, the impact of the friction coefficient on the attenuation rate of acoustic oscillations in the forestland is estimated. The algorithm and software are developed and implemented for calculating the acoustic pressure levels in various media, by using the wave equation for the atmosphere, Euler’s gas dynamics equations for the forestland, and the elasticity equation for the ground. The results of numerical experiments are presented as instantaneous images of the wave field.

Numerical simulation of acoustic waves propagation in an atmosphere-forestland-ground system

Numerical simulation of acoustic waves propagation in an atmosphere-forestland-ground system