Simulation Of Acoustic Waves Research Articles

Numerical simulation of impulse-induced surface acoustic waves for elastography purposes using k-Wave simulation toolbox

As elastography, an emerging medical imaging strategy, advances, surface acoustic waves have been utilized to examine superficial tissues quantitatively. So far, most studies are experimental, and a numerical method is needed to cost-effectively investigate surface acoustic wave generation and propagation for technical development and optimization purposes. This study aims to develop a reliable numerical method for simulating impulse-induced surface acoustic waves using the k-wave simulation toolbox. According to the physical process of surface acoustic wave based elastography, the proposed simulation method consists of two stages: compressional wave simulation and elastic wave simulation, which aim to generate acoustic radiation force impulse and elastic waves, respectively. The technical procedures were demonstrated by a wave simulation on a water–tissue model. Meanwhile, three acoustic radiation force modeling methods were adopted. The compressional wave simulation showed that the three force modeling methods could produce similar force distribution in space but largely different amplitudes. The elastic wave simulation confirmed the feasibility of numerically generating surface acoustic waves. The reliability of the simulated waves was verified by a quantitative comparison between the numerically acquired sound speeds and their theoretical expectations and by a qualitative comparison between the numerically generated waves and the experimental observations under similar conditions. In summary, this study confirms k-wave as an effective numerical method for simulating surface acoustic waves for elastography purposes. This study provides an immediate simulation platform for investigating Scholte waves, the surface acoustic wave at a liquid–solid interface, and also, a potential numerical framework to investigate other surface acoustic waves.

Enabling large-scale and high-precision fluid simulations on near-term quantum computers

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method “Iterative-QLS” that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than 0.2%, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum–classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.

Acoustic wave simulation in strongly heterogeneous models using a discontinuous Galerkin method

In recent years, the discontinuous Galerkin method (DGM) has been rapidly developed for the numerical simulation of seismic waves. For wavefield propagation between two adjacent elements, it is common practice to apply a numerical flux to the boundary of each element to propagate waves between adjacent elements. Several fluxes, including the center, penalty, local Lax-Friedrich (LLF), upwind, and Rankine-Hugoniot jump condition-based (RH condition) fluxes, are widely used in numerical seismic wave simulation. However, some fluxes do not account for media differences between adjacent elements. Although different fluxes have been successfully used in DGM for many velocity models, it is unclear whether they can produce sufficiently accurate or stable results for strongly heterogeneous models, such as checkerboard models commonly used in tomographic studies. We test different fluxes using the acoustic wave equation. We analyze the accuracy of the penalty, LLF, upwind, and RH-condition fluxes based on the results of the numerical simulations of the homogeneous and two-layer models. We conduct simulations using checkerboard models, and the results indicate that the LLF, penalty, and upwind fluxes may have instability problems in heterogeneous models with long-time simulations. We observe instability issues in the LLF, penalty, and upwind fluxes when the wave-impedance contrast is high at the media interface. However, the results of the RH-condition flux remain consistently stable. The series of numerical examples presented in this work provide insights into the characteristics and application of fluxes for seismic wave modeling.

A three-dimensional immersed boundary method for accurate simulation of acoustic wavefields with complex surface topography

Abstract Irregular topography of the free surface significantly affects seismic wavefield modelling, especially when employing finite-difference methods on rectangular grids. These methods represent the free surface as discrete points, resulting in a boundary that resembles a ‘staircase’. This approximation inaccurately represents surface topography, introducing errors in surface reflection traveltimes and generating artificial diffractions in wavefield simulation. We introduce a stable three-dimensional immersed boundary method (3DIBM) employing Cartesian coordinates to address these challenges. The 3DIBM enables the simulation of acoustic waves in media with complex topography through standard finite difference, extending the two-dimensional immersed boundary approach to compute spatial coordinates for ghost and mirror points in a three-dimensional space. Wavefield values at these points are obtained by three-dimensional spatial iterative symmetric interpolation, specifically through the Kaiser-windowed sinc method. By implicitly implementing the free surface boundary condition in three dimensions, this method effectively reduces artificial diffractions and enhances the accuracy of reflection traveltime. The effectiveness and accuracy of 3DIBM are validated through numerical tests and pre-stack depth migration imaging with simulated data, demonstrating its superiority as a modelling engine for migration imaging and waveform inversion in three-dimensional land seismic analysis.

Brillouin-based fiber loss measurement for PON using ERA-BOTDA with differential width pairs of frequency-swept pump pulses

We demonstrate Brillouin-based loss distribution measurement for passive optical networks with differential width pairs of frequency-swept pump pulses that can suppress the spatial resolution degradation, especially those created by large loss events typical of an 8-branch splitter. Based on the acoustic wave simulation of a frequency-swept pump pulse, we investigate the arrangement of the modulation frequency within the optical pulse. A preliminary experiment is conducted on a 5-dB loss event near an 8-branch splitter. The results show that the proposed technique can accurately measure loss events with a spatial resolution of better than 3 m.

Spatiotemporal Distributions of Acoustic Propagation in Skull During Ultrasound Neuromodulation.

There is widespread interest and concern about the evidence and hypothesis that the auditory system is involved in ultrasound neuromodulation. We have addressed this problem by performing acoustic shear wave simulations in mouse skull and behavioral experiments in deaf mice. The simulation results showed that shear waves propagating along the skull did not reach sufficient acoustic pressure in the auditory cortex to modulate neurons. Behavioral experiments were subsequently performed to awaken anesthetized mice with ultrasound targeting the motor cortex or ventral tegmental area (VTA). The experimental results showed that ultrasound stimulation (US) of the target areas significantly increased arousal scores even in deaf mice, whereas the loss of ultrasound gel abolished the effect. Immunofluorescence staining also showed that ultrasound can modulate neurons in the target area, whereas neurons in the auditory cortex required the involvement of the normal auditory system for activation. In summary, the shear waves propagating along the skull cannot reach the auditory cortex and induce neuronal activation. Ultrasound neuromodulation-induced arousal behavior needs direct action on functionally relevant stimulation targets in the absence of auditory system participation.

Application of differentiable programming to wave simulation

Wave simulations play a crucial role in a wide range of scientific and engineering applications, including seismic imaging, optical design, and acoustic modeling. Here we explore the advantages of differentiable programming in the context of acoustic wave simulation. Differentiable programming enables us to treat wave simulation as a differentiable function, allowing for the automatic computation of gradients with respect to any continuous input parameter. We demonstrate how this approach can be applied to various types of wave simulations, such as Pseudo-spectral time-domain solvers or iterative solvers. Implementing wave simulators via differentiable programming achieves several benefits. First, it enables efficient and accurate sensitivity analysis: This is particularly valuable for optimization and uncertainty quantification tasks. Second, it facilitates the incorporation of wave simulations into machine learning frameworks, enabling the integration of simulation-based models with data-driven approaches. Third, differentiable programming can accelerate the calibration and inversion of wave simulation models, making it easier to match simulated results to observed data. We present practical examples and discuss potential applications in fields such as geophysics and medical imaging. Our findings highlight the potential of this approach to advance the state-of-the-art in wave simulation techniques and their integration into larger computational pipelines.

A novel high accuracy finite-difference time-domain method

The finite-difference time-domain (FDTD) method is widely used for numerical simulations of electromagnetic waves and acoustic waves. It is known, however, that the Courant condition is restricted in higher dimensions and with higher order differences in space. Although it is possible to relax the Courant condition by utilizing the third-degree difference in space, there remains a large anisotropy in the numerical dispersion at large Courant numbers. This study aims to reduce the anisotropy in the numerical dispersion and relax the Courant condition simultaneously. A new third-degree difference operator including the Laplacian is introduced to the time-development equations of FDTD(2,4) with second- and fourth-order accuracies. The present numerical simulations have demonstrated that numerical oscillations due to the anisotropic dispersion relation are reduced with the new operator.Graphical

Machine learning-assisted inverse design of wide-bandgap acoustic topological devices

The topological simulation of acoustic waves has induced unconventional propagation characteristics, thereby offering extensive application potential in the field of acoustics. In this paper, we propose a machine learning-assisted method for the inverse design of acoustic wave topological edge states and demonstrate its practical applicability. Leveraging the predictions from a trained artificial neural network algorithm, the design of wide-bandwidth topological insulators is achieved, with simulation results indicating an approximately 2.8-fold enlargement of the single-cell topological bandgap. Further investigation into their wide-bandwidth topological transport properties is conducted. Additionally, two distinct functional acoustic routing devices are devised. Superior performance of the wide-bandwidth acoustic topological devices has been verified through simulation experiments. This approach provides an efficient and viable avenue for the design and optimization of acoustic devices, with the potential to enhance the management and control efficiency of acoustic signal propagation.

Mixed approximation of nonlinear acoustic equations: Well-posedness and a priori error analysis

Accurate simulation of nonlinear acoustic waves is essential for the continued development of a wide range of (high-intensity) focused ultrasound applications. In this article, we explore mixed finite element formulations of classical strongly damped quasilinear models of ultrasonic wave propagation, the Kuznetsov and Westervelt equations. Such formulations allow simultaneous retrieval of the acoustic particle velocity and either the pressure or acoustic velocity potential, thus characterizing the complete ultrasonic field at once. Using non-standard energy analysis and a fixed-point technique, we establish sufficient conditions for the well-posedness, stability, and optimal a priori errors in the energy norm for the semi-discrete equations. For the Westervelt equation, we also determine the conditions under which the error bounds can be made uniform with respect to the involved dissipation parameter. Additionally, we discuss convergence in the maximum error norm of the involved scalar quantities. Finally, computer experiments for Raviart–Thomas (RT) and Brezzi–Douglas–Marini (BDM) elements are performed to confirm the theoretical findings.

Finite element simulation of Rayleigh surface acoustic wave in (100) AlN/(100) ZnO/diamond layered structure

Finite element simulation of Rayleigh surface acoustic wave in (100) AlN/(100) ZnO/diamond layered structure

Numerical Simulation of Acoustic Wave Generated by DC Corona Discharge Based on the Shock Wave Theory

The audible noise generated by corona discharge has the N-type characteristic at the initial generation stage, and it is a typical shock wave. This shock wave usually only exists around the corona source with a tiny range, making it difficult to obtain its characteristics through experimental measurements. An electrosound-combined simulation of the corona discharge based on the shock wave theory was conducted, and the development process involving the corona discharge, shock wave, and sound wave was simulated. First, the corona was numerically simulated based on the 2D pin–plate axisymmetric hydrodynamic model. It was found that the plasma was mainly distributed near the axis of the corona field where the electric field changed violently, and the maximum value of the electric field appeared at the head of the discharge channel. Then, the plasma energy was equivalent to the explosive energy, and a plasma explosion shock model was established. It was found that the shock wave pressure had obvious positive and negative pressure zones, and the propagation velocity decays to the sound velocity gradually. Finally, the shock wave pressure derived by the explosion model was used as the acoustic source, and the acoustic wave propagation process was simulated. The simulated sound pressure waveform had the same characteristics as the relevant experimental measurement results, proving that the developed method possessed strong applicability and gave rise to a new angle for the simulation of corona-generated audible noise.

A WebGPU-based acoustic wave simulator for ultrasound NDT

Ultrasound NDT is a standard industrial technique for health monitoring and flaw identification in several structures, such as subsea oil pipelines. Its primary purpose is to form a representative image of the internal structure of the inspected object, which provides, in many cases, early warning of structure discontinuities, making it possible to reduce repair costs and mitigate risks. One of the imaging methods that has been receiving increasing attention in the ultrasound and seismology communities is the Full Waveform Inversion (FWI), which estimates the velocity model for the inspection area by confronting the acquired information obtained by the NDT system with theoretical simulated data. Since FWI algorithms rely on successive ultrasonic wave simulations, it is essential to ensure that each simulation is optimized and contributes little to the total running time. Acoustic wave simulations can be optimized using a graphical processing unit (GPU), which provides hardware acceleration through parallelism, where each point of the simulated area can be computed simultaneously. Among all available GPU APIs, WebGPU is the next-generation standard graphics Web API that exposes modern computer graphics capabilities by giving the user low-level, general-purpose access to the GPUs. This API is designed to efficiently map to native GPU APIs, which enables applications to run on different GPUs, making implementations more scalable and interchangeable. Motivated by this flexibility, we explore the acceleration capabilities of the WebGPU API by implementing a WebGPU-based acoustic wave simulator for ultrasound NDT.

A modified symplectic discontinuous Galerkin method for acoustic and elastic wave simulations

Numerically solving seismic wave equations is vital to large-scale forward modeling and full waveform inversion. In this paper, a new modified symplectic discontinuous Galerkin (MSDG) method is proposed to solve the acoustic and elastic equations. The MSDG method employs a symmetric interior penalty Galerkin formulation as the space discretization. The time discretization is based on a modified symplectic partitioned Runge–Kutta scheme with minimized phase error. Thus, the MSDG method has the advantages of high accuracy, being flexible to deal with complex geometric boundaries and internal structures, and stable for long time simulations. The numerical stability conditions, dispersion and dissipation are investigated in detail for the MSDG method. To validate the method, we carry out several numerical examples for solving the acoustic and elastic wave equations in various media. The numerical results show that the MSDG method can effectively suppress the numerical dispersion and is suitable for wavefield simulations.

Time-domain simulation of acoustic wave scattering and internal propagation from a gas bubble of various shapes.

Acoustic scattering and resonances of gas bubbles are computed using a time-domain simulation based on numerical solutions of the conservation laws. The time histories of scattered pressure and fluid velocity, outside and inside the bubble, are obtained simultaneously from an immersed-boundary method allowing for the investigation of exterior and interior fields for non-spherical geometries. The acoustic resonances of the bubble are investigated for various bubble sizes, shapes, and inner gas parameters and compared in limiting cases to the partial wave scattering solutions for spherical bubbles. The dynamics of the gas motion and its associated contribution to resonance response has received little attention in previous analytical and numerical formulations. In this study, the acoustic propagation and motion inside the interior gas is investigated with respect to the monopole resonance with the combined time-domain simulation and immersed-boundary method. For the non-spherical prolate and oblate shapes, the scattering and resonance behaviors are compared with the approximate analytical results based on the shape factor method. The simulation method can be extended to less-understood shapes relevant to underwater and physical acoustics, such as "pancake-shaped" or "cigar-shaped" bubbles, as well as to spatial and time-dependent forcing.

2D frequency-domain finite-difference acoustic wave modeling using optimized perfectly matched layers

Seismic forward modeling is fundamental in sensitivity analysis and full-waveform inversions. In finite-difference acoustic wavefield simulation, the absorption boundary, especially the perfectly matched layer (PML), is widely used, but the setting of PML parameters is empirical. An optimized complex frequency-shift PML (CFS-PML) for the modeling of acoustic fields has been developed. It refines the selection of parameters for improving the artificial attenuation. The improved CFS-PML boundary condition is applied to a 2D frequency-domain acoustic wave simulation using an optimal 17-point finite-difference scheme. Numerical results are compared with a conventional nine-point scheme in terms of computational time and physical memory consumption. These tests indicate that our CFS-PML absorption boundary can effectively improve numerical accuracy without increasing the computational burden remarkably.

A high-order stabilized finite-element model for the Linearized Navier-Stokes equations

A numerical approach based on high-order stabilized finite elements is proposed to solve thermo-acoustic and visco-acoustic problems accounting for non-uniform mean flow effects. The approach is based on the Linearized Navier-Stokes equations written in conservative form in the frequency domain. An adaptive polynomial Finite-Element Method (FEM) using hierarchic shape functions is applied for accuracy and ease-of-use. A new enrichment strategy, inspired by the extended Finite Element Method (X-FEM), is developed to resolve the finer scales near the walls at a reasonable computational cost. It relies on a re-orthogonalization procedure proposed to preserve both the continuity of the solution and the conditioning properties of the discrete model. The performance of the method is first evaluated by performing two-dimensional simulations of acoustic waves affected by visco-thermal wall losses and mean flow effects while propagating in a duct. Numerical results are in good agreement with the analytical solution. The applicability of this new methodology is then demonstrated by computing the sound absorption of an acoustic liner installed in an impedance tube in the presence of a grazing flow in 2D. Numerical predictions of the sound pressure levels in the tube are compared to experimental data from the literature.

Finite element simulation and experimental study of laser-generated surface acoustic waves on determining mechanical properties of thin film

The laser-generated surface acoustic wave (LSAW) nondestructive testing (NDT) technique is a promising method to characterize the mechanical properties of thin films. In this study, based on the thermoelastic mechanism, a finite element method (FEM) is put forward to simulate the LSAW in the film/substrate structure, and the effect of the temporal and spatial distribution of the Gaussian pulse laser on the Rayleigh-type SAW signals is revealed. For the SiO2 and low dielectric constant (low-k) dense Black Diamond™ (SiOC:H, BD) films with the thickness of 500 and 1000 nm, the typical displacement waveforms of SAW at a series of probing points along the propagation direction are obtained. By analyzing the full width at half maximum (FWHM) of the signal, the optimal NDT experimental conditions for laser are determined with the minimum possible pulse rising time and the linewidth less than 10 μm. Based on the FEM simulation result, the LSAW NDT experiment is carried out and the dispersion curve of SAW is calculated to characterize Young's modulus of the SiO2 and low-k samples. It is found that the experimental results are in good agreement with the simulation results. This study verifies the validity of FEM simulation of LSAW in layered structures containing thin film and that the laser parameters determined by FEM fit perfectly in characterizing the mechanical properties of thin films.

Nonlinear spectral analysis of ion acoustic solitons arising from a streaming charged object using the numerical inverse scattering transform

Observations of nonlinear coherent plasma phenomena in spacecraft and terrestrial experiments often rely on visual identification of solitary modes because nonlinear coherent modes are broadband in a Fourier transform based analysis. We implement an alternative spectral decomposition known as the inverse scattering transform and demonstrate its ability to successfully isolate nonlinear modes on the homogeneous and forced Korteweg–De Vries equation which models these nonlinear modes. We also demonstrate for the first time that this decomposition is useful when forcing is applied. This is because the stable modes generated by localized forcing are similar to the homogeneous solutions where the inverse scattering transform is a rigorous decomposition. This spectral technique is then applied to simulations of ion acoustic waves generated by a 10 mm spherical debris object interacting with the ionospheric plasma orbiting at 2000 km altitude. The algorithm is found to successfully detect the resultant solitons. This demonstrates the feasibility of using this spectral technique as a real time analysis tool for screening spacecraft data for nonlinear solitary modes.

A mesh-free finite-difference scheme for frequency-domain acoustic wave simulation with topography

A mesh-free finite-difference scheme for frequency-domain acoustic wave simulation with topography