Simulation Of Acoustic Waves Research Articles

SPH Simulation of Acoustic Waves: Effects of Frequency, Sound Pressure, and Particle Spacing

Acoustic problems consisting of multiphase systems or with deformable boundaries are difficult to describe using mesh-based methods, while the meshfree, Lagrangian smoothed particle hydrodynamics (SPH) method can handle such complicated problems. In this paper, after solving linearized acoustic equations with the standard SPH theory, the feasibility of the SPH method in simulating sound propagation in the time domain is validated. The effects of sound frequency, maximum sound pressure amplitude, and particle spacing on numerical error and time cost are then subsequently discussed based on the sound propagation simulation. The discussion based on a limited range of frequency and sound pressure demonstrates that the rising of sound frequency increases simulation error, and the increase is nonlinear, whereas the rising sound pressure has limited effects on the error. In addition, decreasing the particle spacing reduces the numerical error, while simultaneously increasing the CPU time. The trend of both changes is close to linear on a logarithmic scale.

A comparison of perfectly matched layers and infinite elements for exterior Helmholtz problems

Perfectly matched layers and infinite elements are commonly used for finite element simulations of acoustic waves on unbounded domains. Both involve a volumetric discretization around the periphery of an acoustic mesh, which itself surrounds a structure or domain of interest. Infinite elements have been a popular choice for these problems since the 1970s. Perfectly matched layers are a more recent technology that is gaining popularity due to ease of implementation and effectiveness as an absorbing boundary condition. In this study, we present massively parallel implementations of these two techniques, and compare their performance on a set of representative structural–acoustic problems on exterior domains. We examine the conditioning of the linear systems generated by the two techniques by examining the number of Krylov-iterations needed for convergence to a fixed solver tolerance. We also examine the effects of PML parameters, exterior boundary conditions, and quadrature rules on the accuracy of the solution. [Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL850000.]

Dispersion Analysis of Triangle‐Based Finite Element Method for Acoustic and Elastic Wave Simulations

AbstractAcoustic and elastic wave equations are discretized by finite element method with triangles and central difference scheme in space and time, respectively. The generalized eigenvalue problems are constructed to analyze the numerical dispersion of the finite element method. Three types of mass finite element method, which are consistent finite element method (CFEM), lumped finite element method (LFEM) and mixed finite element method (MFEM), are implemented to the numerical scheme, and the numerical dispersion is under a comprehensive study. Then, the MFEM is adopted to investigate the behavior of numerical anisotropy in terms of four typical triangle meshes. Comparing the numerical dispersion and anisotropy behavior when MFEM uses different interpolation orders, one can easily find that numerical error decreases as the interpolation order increases. Specifically, the numerical dispersion and anisotropy are negligible when third‐order interpolation is used. Finally, controlling the other impact factors, the dispersive properties of elastic wave propagation in elastic medium with various velocity ratios are analyzed, and the results of numerical dissipation are presented at the end of this paper.

Nonlinear evolution of ion acoustic solitary waves in space plasmas: Fluid and particle‐in‐cell simulations

AbstractSpacecraft observations revealed the presence of electrostatic solitary waves (ESWs) in various regions of the Earth's magnetosphere. Over the years, many researchers have attempted to model these observations in terms of electron/ion acoustic solitary waves by using nonlinear fluid theory/simulations. The ESW structures predicted by fluid models can be inadequate due to its inability in handling kinetic effects. To provide clear view on the application of the fluid and kinetic treatments in modeling the ESWs, we perform both fluid and particle‐in‐cell (PIC) simulations of ion acoustic solitary waves (IASWs) and estimate the quantitative differences in their characteristics like speed, amplitude, and width. We find that the number of trapped electrons in the wave potential is higher for the IASW, which are generated by large‐amplitude initial density perturbation (IDP). The present fluid and PIC simulation results are in close agreement for small amplitude IDPs, whereas for large IDPs they show discrepancy in the amplitude, width, and speed of the IASW, which is attributed to negligence of kinetic effects in the former approach. The speed of IASW in the fluid simulations increases with the increase of IASW amplitude, while the reverse tendency is seen in the PIC simulation. The present study suggests that the fluid treatment is appropriate when the magnitude of phase velocity of IASW is less than the ion acoustic (IA) speed obtained from their linear dispersion relation, whereas when it exceeds IA speed, it is necessary to include the kinetic effects in the model.

Finite Element Analysis of Y+41 LiNbO3 Based on SAW Resonators Including Perfectly Matched Layer

This paper describes the modelling and simulation of Surface acoustic waves (SAW) in piezoelectric thin film by using a finite element method (FEM) in combination with Perfectly Matched Layer (PML). Various important piezoelectric parameters of a resonator based on Y+41 Lithium Niobate (Y+41 LiNbO3), such as the surface velocity, the electromechanical coupling coefficient, the reflectivity and the displacement were computed. Harmonic modes of surface waves are also simulated, analyzed and compared to experimental results.

Finite integration technique for coupled acoustic and elastic wave simulation and its application to noncontact ultrasonic testing

To better understand wave propagation and scattering phenomena in noncontact ultrasonic testing (UT), we have developed a time domain simulation tool to model wave propagation in air and solids. The tool is based on the finite integration technique (FIT) and an image-based modeling approach. The image-based FIT can treat the calculation of acoustic, elastic, and coupled waves in a unified grid form. In this paper, we first investigate the accuracy of the interface condition in FIT modeling by comparing numerical results with analytical solutions of transmission and reflection coefficients. Then we validate the FIT using measured signals in guided wave testing with air-coupled transducers. To simulate noncontact UT, a fine mesh is required in the FIT because the wavelength in air is much smaller than that in a solid. To solve the numerical problem with the finer mesh at high speed, we introduce a parallel computation technique with general-purpose computing on graphics processing units (GPUs). It is shown that the noncontact UT simulation can be executed within a reasonable time and with reasonable accuracy using multiple GPUs.

A reproducible framework for 3D acoustic forward modelling of hard rock geological models with Madagascar

SUMMARY A special challenge of hard rock exploration is to identify targets of interest within complex geological settings. Interpretation of the geology can be made from direct geological observations and knowledge of the area, and from 2D or 3D seismic surveys. These interpretations can be developed into 3D geological models that provide the basis for predictions as to likely targets for drilling and/or mining. To verify these predictions we need to simulate 3D seismic wave propagation in the proposed geological models and compare the simulation results to seismic survey data. To achieve this we convert geological surfaces created in an interpretation software package into discretised block models representing the different lithostratigraphic units, and segment these into discrete volumes to which appropriate density and seismic velocity values are assigned. This approach allows us to scale models appropriately for desired wave propagation parameters and to go from local to global geological models and vice versa. Then we use these digital models with forward modelling codes to undertake numerous 3D acoustic wave simulations. Simulations are performed with single shot and with exploding reflector (located on extracted geological surface) configurations.

Energy decay analysis in coupled volumes using an acoustic wave simulator

The acoustics in coupled volumes present various challenges. For example, the sound energy decay curve is double-sloped indicating that a single reverberation time cannot be assigned to coupled volumes. Such a behavior depends on various factors like the aperture sizes between the coupled volumes, absorption coefficients of each volume, etc. Recently, many studies using computer simulation have been performed to better understand the acoustic behavior of coupled volumes. None of these studies perform full 3D acoustic wave simulation on coupled volumes as they are regarded as computationally expensive and limited to very small spaces. We perform acoustic wave simulation using a relatively new wave solver called adaptive rectangular decomposition (ARD). ARD is more accurate than geometric acoustics techniques. It has been demonstrated to provide reliable simulation results through comparison with measurement data in indoor and outdoor scenes. Furthermore, it is practical and can handle large acoustic spaces on a single desktop. In this study, we analyze energy decay curves in coupled volumes using ARD. We perform numerical simulation for various coupled volume configurations such as varying aperture sizes, absorption coefficients, etc., and present their decay curves for analysis.

A comparison of perfectly matched layers and infinite elements for exterior Helmholtz problems

Perfectly matched layers and infinite elements are commonly used for finite element simulations of acoustic waves on unbounded domains. Both involve a volumetric discretization around the periphery of an acoustic mesh, which itself surrounds a structure or domain of interest. Infinite elements have been a popular choice for these problems since the 1970s. Perfectly matched layers are a more recent technology that is gaining popularity due to ease of implementation and effectiveness as an absorbing boundary condition. In this study, we present massively parallel implementations of these two techniques, and compare their performance on a set of representative structural-acoustic problems on exterior domains. We compare the ability of these methods to absorb acoustic waves on ellipsoidal domains with waves of relatively high oblique angles of incidence. We also examine the conditioning of the linear systems generated by the two techniques by examining the number of Krylov-iterations needed for convergence to a fixed solver tolerance. [Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL850000.]

Symplectic RKN Schemes for Seismic Scalar Wave Simulations

AbstractSeismic scalar wave equation is transformed into Hamiltonian system, and then a second‐order explicit Runge‐Kutta‐Nyström (RKN) scheme is proposed for high‐efficient acoustic wave simulations. The order conditions are obtained by the rooted tree theory. For order conditions with two free coefficients, one scheme with minimum error is obtained based on the optimal error truncation of the third‐order terms. We analyze the acoustic time advancing equation and choose coefficients to promote the stability upper bound, and then we develop an optimized scheme with strong stability. In the analysis of dispersion relation, the third optimized symplectic RKN scheme is constructed to substantially eliminate numerical dispersion. The theoretical properties of the three sets of symplectic RKN schemes have great advantages over other common schemes in terms of errors controlling, dispersion suppressing and stability promoting. Finally, we present numerical experiments to verify the theoretical analysis.

Stable perfectly-matched-layer boundary conditions for finite-difference time-domain simulation of acoustic waves in piezoelectric crystals

Perfectly-matched-layer (PML) boundary conditions are derived for finite-difference time-domain analysis of acoustic waves within piezoelectric crystals. The robustness and effectiveness of the derived boundary conditions are demonstrated by simulating acoustic wave propagation in the bismuth germanate material system—a system in which simple absorbing boundary conditions cause instabilities. An investigation into the stability and effectiveness of the PML is then presented in terms of the PML thickness and absorption profile. A range of optimised absorption profiles were determined by finding the maximum permissible absorption within the stability limit of the system. In the optimised case, the form of the absorption profile had little influence on the effectiveness of the PML. However, in the unoptimised case the linearly increasing absorption profile was found to be the most effective.

Absorption characteristics of a Stoneley wave in multilayered media and the logging method for estimating permeability

The aim of the study is to increase the reliability of estimation of the acoustic parameters of a layered permeable formation using new software, based on two-velocity continuum equations for 2D numerical simulation of acoustic waves propagating in a borehole. The key method is the method of finite differences as applied to solving equations of the continuum filtration theory. The dissipative characteristics of Stoneley waves have been identified for the case of their propagation in a layered formation. These aspects should be taken into account when using Stoneley waves to estimate the permeability of geologic media.

Precise simulation of surface acoustic wave devices using frequency-dependent coupling-of-modes parameters

Herein we extract all the frequency-dependent coupling-of-modes (COM) parameters, which will be used to the rapid simulation and optimal design of surface acoustic wave (SAW) devices. FEM/BEM is used to calculate the exact field distributions of forward and backward surface acoustic waves within a finite-length periodic grating at every frequency. The middle component of the grating, regarded as a periodic structure, is selected to be investigated which can satisfy the presupposition of the COM model. From these field distributions, the values of P-matrix elements of one cell are calculated. The COM parameters taken as functions of frequency are accurately obtained. Specifically, the frequency-dependent relationships of reflection coefficient and propagation velocity are obtained independently. Using the resultant COM parameters, a one-port resonator on the substrate of 128°YX-LiNbO3 is simulated and the admittance curve shows good agreement with the simulating results using FEM/BEM. These results verify the validity and accuracy of this method.

Numerical simulation of acoustic waves in air and poroelastic media using the partition of unity finite element method

Foams and fibrous materials are used in a large range of applications such as automotive or building acoustics. Their properties can be described with either a poroelastic model or an equivalent fluid model. These models, also used in geophysics, are now widely spread and are also available in some commercial finite element software applications. However, the discretization level required to achieve reasonable accuracy is not always acceptable in the mid-frequency range. In such case, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions seems appropriate to avoid this limitation. The PUFEM has been recently applied to rigid frame materials with and without coupling with an acoustic cavity. It has also been applied efficiently to poroelastic materials. The present work focuses on the coupling between a poroelastic material, i.e., described with Biot's equations, and an air cavity. Some practical examples are tested to demonstrate the efficiency of the PUFEM for solving noise control problems at medium frequency, but also to underline the precautions that must be taken when dealing with an air-porous interface.

Original coupled FEM/BIE numerical model for analyzing infinite periodic surface acoustic wave transducers

This paper proposes a new numerical coupled Finite Element Method/Boundary Integral Equations (FEM/BIE) technique which allows the 2D physical simulation of Surface Acoustic Waves (SAWs) transducers infinitely periodic in one direction. This new technique could be generalized to various periodic acoustic 2D simulations.This new method uses an original Variational Formulation (VF) which formally includes harmonic periodic boundary conditions, and, efficient boundary integral formulations allowing to account for the semi-infinite dielectric and piezoelectric spaces. In the case of the piezoelectric semi-space, the Green’s functions are efficiently computed using Fahmy–Adler’s method [8]. Only periodic boundary conditions are needed, which greatly simplifies the code implementation.This numerical model has been developed to analyze an Inter-Digital Transducer (IDT) with complex electrode shape (unburied, buried or raised electrodes). The use of buried electrodes in SAW transducer designs on quartz has important advantages when compared with unburied metal electrodes on the surface. One important property is the suppression of transverse waveguide modes in transducers. A second advantage is the ability to use thicker metal thereby reducing the resistive losses. Buried electrodes have also been shown to increase the quality factor of Surface Transverse Wave (STW) resonators [15]. This numerical model is a very useful tool for optimizing the electrode geometry. Analysis of raised electrodes is useful for predicting the effects of Reactive Ion Etch (RIE) on the SAW or STW electrical filter characteristics. RIE is commonly used as a frequency trimming technique for SAW or STW filters on Quartz.The first part of the paper presents the theory, and, the second part is devoted to numerical validations and numerical results.

Electron and ion kinetic effects on non-linearly driven electron plasma and ion acoustic waves

Fully non-linear kinetic simulations of electron plasma and ion acoustic waves (IAWs) have been carried out with a new multi-species, parallelized Vlasov code. The numerical implementation of the Vlasov model and the methods used to compute the wave frequency are described in detail. For the first time, the nonlinear frequency of IAWs, combining the contributions from electron and ion kinetic effects and from harmonic generation, has been calculated and compared to Vlasov results. Excellent agreement of theory with simulation results is shown at all amplitudes, harmonic generation being an essential component at large amplitudes. For IAWs, the positive frequency shift from trapped electrons is confirmed and is dominant for the effective electron-to-ion temperature ratio, Z Te/Ti ≳ 10 with Z as the charge state. Furthermore, numerical results demonstrate unambiguously the dependence [R. L. Dewar, Phys. Fluids 15, 712 (1972)] of the kinetic shifts on details of the distribution of the trapped particles, which depends in turn on the conditions under which the waves were generated. The trapped particle fractions and energy distributions are derived and, upon inclusion of harmonic effects, shown to agree with the simulation results, completing a consistent picture. Fluid models of the wave evolution are considered but prove unable to capture essential details of the kinetic simulations. Detrapping by collisions and sideloss is also discussed.

Numerical methods for direct and inverse problems in Acoustics and Photothermal Science

The aim of this paper is to survey the research activity of the author during the years prior to the XIII SEMA Young Researcher Award. In this paper we present an overall view of numerical techniques for the simulation of acoustic and thermal waves from two complete opposite points of view: the fields of direct and inverse problems.

Numerical simulation of surface acoustic wave actuated cell sorting

Abstract We consider the mathematical modeling and numerical simulation of high throughput sorting of two different types of biological cells (type I and type II) by a biomedical micro-electro-mechanical system (BioMEMS) whose operating behavior relies on surface acoustic wave (SAW) manipulated fluid flow in a microchannel. The BioMEMS consists of a separation channel with three inflow channels for injection of the carrier fluid and the cells, two outflow channels for separation, and an interdigital transducer (IDT) close to the lateral wall of the separation channel for generation of the SAWs. The cells can be distinguished by fluorescence. The inflow velocities are tuned so that without SAW actuation a cell of type I leaves the device through a designated outflow channel. However, if a cell of type II is detected, the IDT is switched on and the SAWs modify the fluid flow so that the cell leaves the separation channel through the other outflow boundary. The motion of a cell in the carrier fluid is modeled by the Finite Element Immersed Boundary method (FE-IB). Numerical results are presented that illustrate the feasibility of the surface acoustic wave actuated cell sorting approach.

Numerical studies on structure-preserving algorithms for surface acoustic wave simulations

We study the generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic inhomogeneity. The eigenvalues appear in the reciprocal pairs due to periodic boundary conditions in the modeling. By transforming the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP), the reciprocal relationship of the eigenvalues can be maintained. In this paper, we outline four recently developed structure-preserving algorithms, SA, SDA, TSHIRA and GTSHIRA, for solving the TPQEP. Numerical comparisons on the accuracy and the computational costs of these algorithm are presented. The eigenvalues close to unit circle on the complex plane are of interest in the area of filter and sensor designs. Our numerical results show that the Arnoldi-type structure-preserving algorithms TSHIRA and GTSHIRA with “re-symplectic” and “re-bi-isotropic” processes, respectively, are as accurate as the SA and SDA algorithms, and more efficient in finding these eigenvalues.

Numerical simulations of acoustic waves with the graphic acceleration GAMER code

Abstract We present results of numerical simulations of acoustic waves with the use of the Graphics Processing Unit (GPU) acceleration GAMER code which implements a second-order Godunov-type numerical scheme and adaptive mesh refinement (AMR). The AMR implementation is based on constructing a hierarchy of grid patches with an octree data structure. In this code a hybrid model is adopted, in which the time-consuming solvers are dealt with GPUs and the complex AMR data structure is manipulated by Central Processing Units (CPUs). The code is highly parallelized with the Hilbert space-filling curve method. These implementations allow us to resolve well desperate spatial scales that are associated with acoustic waves. We show that a localized velocity (gas pressure) pulse that is initially launched within a uniform and still medium triggers acoustic waves simultaneously with a vortex (an entropy mode). In a flowing medium, acoustic waves experience amplitude growth or decay, a scenario which depends on a location of the flow and relative direction of wave propagation. The amplitude growth results from instabilities which are associated with negative energy waves.