Boundary Element Method Calculations Research Articles

Impact of the contact-patch gap on sound radiation from a tyre

Depending on location, vibrations on a rolling tyre may vary significantly in the noise they produce. Calculation of their amplification is thus central to tyre-noise prediction. However, the appropriate representation of sound propagation through the contact-patch region remains uncertain. More fundamentally, it is not even known whether this aspect is important. Here, this question is investigated via Boundary Element Method calculations for an idealised geometry, in which the irregular gap in the contact patch is represented by a constant-height channel between the road and the flattened-off portion of a cylinder. Compared to calculations with no gap, the results show attenuation of the high amplification levels in the horn-like region where the tyre nears the road, and introduction of source amplification within the gap. These features are evident for a gap as small as 1% of the cylinder radius (approximately 3 mm for a representative tyre). On this basis, it appears that the contact-patch region must indeed be modelled, and that parts of the tyre other than the horn may be significant contributors to the radiated noise.

Three-Temperature Boundary Element Modeling of Ultrasound Wave Propagation in Anisotropic Viscoelastic Porous Media

The main goal of this work is to develop a novel boundary element method (BEM) model for analyzing ultrasonic wave propagation in three-temperature anisotropic viscoelastic porous media. Due to the problems of the strong nonlinearity of ultrasonic wave propagation in three-temperature porous media, the analytical or numerical solutions to the problems under consideration are always challenging, necessitating the development of new computational techniques. As a result, we use a new BEM model to solve such problems. A time-stepping procedure based on the linear multistep method is obtained after solving the discretized boundary integral equation with the quadrature rule. The calculation of a double integral is required to obtain fundamental solutions, but this increases the total BEM computation time. Our proposed BEM technique is used to solve the current problem and improve the formulation efficiency. The numerical results are graphed to demonstrate the effects of viscosity and anisotropy on the nonlinear ultrasonic stress waves in three-temperature porous media. The validity, accuracy, and efficiency of the proposed methodology are demonstrated by comparing the obtained results to a corresponding solution obtained from the finite difference method (FDM).

Numerical analysis and experimental measurement on segmented ring transducer acoustic fields

In order to overcome the shortcomings of the two traditional methods of finite element method (FEM) and direct coupling of mechanical FEM and acoustic boundary element method (BEM) in the comprehensive simulation of acoustic characteristics of non-two-dimensional axisymmetrical transducers, the acoustic FEM and acoustic BEM coupling method is adopted in this study to model, calculate and analyze the three-dimensional (3D) model of the segmented ring transducer. Firstly, the basic theory of FEM, BEM and FEM-BEM coupling calculation of the transducer is introduced. Secondly, a 1/8 3D model of the segmented ring transducer is built to simulate the underwater electro-acoustic characteristics of the transducer. Finally, a transducer prototype is manufactured according to the numerical model, and the electro-acoustic performance of the transducer is measured in the anechoic tank. The numerical results of transmission voltage response (TVR), admittance and radiation directivity curves are in good agreement with the experimentally measured results, which indicate that the proposed method is correct and effective. Therefore, the method could be used to comprehensively calculate the acoustic characteristics of the segmented ring transducer. In addition, the method could be used not only to study the acoustic problems of other transducers or transducers arrays with complex structures that are non-two-dimensional axisymmetrical, but also to comprehensively analyze and predict the near-field and far-field acoustic characteristics of any transducers including two-dimensional (2D) axisymmetrical transducers.

Synthesis of magnetic nanoparticles by laser ablation of strontium ferrite under water and their characterization by optically detected magnetophoresis supported by BEM calculations

Optically detected magnetophoresis, using Boundary Element Method calculations, is exploited for characterizing the magnetic properties of low amounts of nanoparticles.

A method to calculate acoustic radiation modes based on spheroidal wave functions.

Acoustic radiation modes (ARMs) have been widely used in noise control engineering. For an arbitrarily shaped radiator, ARMs are usually obtained by using the boundary element method (BEM). For high frequencies and large structures, the BEM calculation is usually time consuming. An alternative method was recently developed in which the ARMs are obtained by using generalized singular value decomposition and spherical harmonic functions. In this paper, spheroidal harmonic functions are used instead of spherical harmonic functions. The proposed method is potentially more efficient for ARM calculations for structures with one dimension significantly larger than the other two.

AstroSeis: A 3D Boundary Element Modeling Code for Seismic Wavefields in Irregular Asteroids and Bodies

Abstract We developed a 3D elastic boundary element method computer code, called AstroSeis, to model seismic wavefields in a body with an arbitrary shape, such as an asteroid. Besides the AstroSeis can handle arbitrary surface topography, it can deal with a liquid core in an asteroid model. Both the solid and liquid domains are homogenous in our current code. For seismic sources, we can use single forces or moment tensors. The AstroSeis is implemented in the frequency domain, and the frequency-dependent Q can be readily incorporated. The code is in MATLAB (see Data and Resources), and it is straightforward to set up the model to run the code. The frequency-domain calculation is advantageous to study the long-term elastic response of a celestial body due to a cyclic force, such as the tidal force, with no numerical dispersion issue suffered by many other methods requiring volume meshing. Our AstroSeis has been benchmarked with other methods such as normal-mode summation and the direct solution method. This open-source AstroSeis will be a useful tool to study the interior and surface processes of asteroids.

Free-Surface Effects on the Performance of Flapping-Foil Thruster for Augmenting Ship Propulsion in Waves

Flapping foils located beneath or to the side of the hull of the ship can be used as unsteady thrusters, augmenting ship propulsion in waves. The basic setup is composed of a horizontal wing, which undergoes an induced vertical motion due to the ship’s responses in waves, while the self-pitching motion of the wing is controlled. Flapping foil thrusters can achieve high level of thrust as indicated by measurements and numerical simulations. Due to the relatively small submergence of the above biomimetic ship thrusters, the free-surface effects become significant. In the present work, the effect of the free surface on the performance of flapping foil thruster is assessed by means of two in-house developed computational models. On one hand, a cost-effective time-domain boundary element method (BEM) solver exploiting parallel programming techniques and general purpose programming on graphics processing units (GPGPU) is employed, while on the other hand a higher fidelity RANSE finite volume solver implemented for high performance computing (HPC) is used, and comparative results are presented. BEM and RANSE calculations present quite similar trends with respect to mean submergence depth, presenting 12%, 28%, and 18% of differences concerning the mean values of lift, thrust, and moment coefficients, respectively. The latter differences become very small after enhancement of the BEM model to include viscous corrections. Useful information and data are derived supporting the design of the considered biomimetic thrusters, for moderate submergence depths and conditions characterized by minor flow separation effects.

Investigating of LSPR spectra on a hybrid Fe3O4-Au within core-shell structure

In this study, we have investigated the tunability of localized surface plasmon resonance (LSPR) spectra of the magneto-plasmonic system composed of Au-coated Fe3O4 (Fe3O4@Au) by public optical simulation, MNPBEM based on boundary element method calculation. The magneto-plasmonic system is modeled nanorod core-shell structure with three different core’s aspect ratio: 2.3, 4.3, and 6.3. The nanoparticle was immersed in water (1.33+0i). Then, we applied the electromagnetic field in parallel and perpendicular to the long axis of nanorod. Interestingly, the peak of LSPR spectra Fe3O4@Au shows blue-shifted at gold thickness toward around ∼50 nm and as the gold-shell keep growing, a red-shifted can be occurred on greater than ∼50 nm of thick gold-shell. The peak of LSPR spectra shows to shift to lower wavelength or blue-shift and produce narrow width spectra. Based on the result, we believe our observation can be utilized for tuning LSPR spectra from visible range to near-infrared such as photocatalysis application and biosensing with well-controlled of thicknesses.

Fundamental solutions in 3D elastodynamics for the BEM: A review

In this work, we attempt to collect all available fundamental solutions in 3D elastodynamics that would be suitable for use in Boundary Element Method (BEM) formulations. Given that research on transient and steady state cases involving the elastic, homogeneous and isotropic continuum commenced in the 1950′s, it is practically impossible to reference all work done since then, so we apologize a priori for any omissions on our part. When we use the term fundamental solution, what comes to mind is the elastic full space under a point load in space and time and with the radiation condition arising because the medium has no boundaries, i.e. it extends to infinity. However, this is far from being the end: If the full space becomes a half-space, then boundary conditions enter the picture and now we are talking about Green's functions. These are more desirable for BEM formulations because it now becomes unnecessary to discretize the free surface. In general, the more particular features of the problem at hand are included in the Green's function, the less discretization is necessary in the BEM formulation. What we aim for in this review is to present and briefly discuss the basic fundamental solutions and more specialized Green's functions in a 3D elastic continuum, in either the frequency or the time domain, for the following type of materials: (1) Isotropic and homogeneous; (2) isotropic and inhomogeneous; (3) anisotropic and homogeneous; (4) anisotropic and inhomogeneous. We also look at poroelastic materials with all above possible combinations. We note at this point that the continuously inhomogeneous (e.g., functionally graded) material is understood as one having its material parameters as functions of position. There is, of course, the category of layered media, considered here as discretely inhomogeneous materials. One final note of caution has to do with the numerical implementation of these solutions: Some are very difficult to program, despite the fact that they come in closed form, because they may involve integrals, or there may be turning points in the solution where the form available depends on the frequency, or because of round-off errors in computing special functions. In closing, there is a trade-off between easy to implement fundamental solutions that require substantial spatial discretization effort and advanced ones based on Green's functions that are difficult to implement but require minimal discretization effort. This points out the relevance of speeding up BEM computations, a subject that is treated in the Appendix.

Site-selective CO disproportionation mediated by localized surface plasmon resonance excited by electron beam.

Recent reports of hot-electron-induced dissociation of small molecules, such as hydrogen, demonstrate the potential application of plasmonic nanostructures for harvesting light to initiate catalytic reactions. Theories have assumed that plasmonic catalysis is mediated by the energy transfer from nanoparticles to adsorbed molecules during the dephasing of localized surface plasmon (LSP) modes optically excited on plasmonic nanoparticles. However, LSP-induced chemical processes have not been resolved at a sub-nanoparticle scale to identify the active sites responsible for the energy transfer. Here, we exploit the LSP resonance excited by electron beam on gold nanoparticles to drive CO disproportionation at room temperature in an environmental scanning transmission electron microscope. Using in situ electron energy-loss spectroscopy with a combination of density functional theory and electromagnetic boundary element method calculations, we show at the subparticle level that the active sites on gold nanoparticles are where preferred gas adsorption sites and the locations of maximum LSP electric field amplitude (resonance antinodes) superimpose. Our findings provide insight into plasmonic catalysis and will be valuable in designing plasmonic antennas for low-temperature catalytic processes.

On the kinematic criterion for the inception of breaking in surface gravity waves: Fully nonlinear numerical simulations and experimental verification

The evolution of unidirectional wave trains containing a wave that gradually becomes steep is evaluated experimentally and numerically using the Boundary Element Method (BEM). The boundary conditions for the nonlinear numerical simulations corresponded to the actual movements of the wavemaker paddle as recorded in the physical experiments, allowing direct comparison between the measured in experiments’ characteristics of the wave train and the numerical predictions. The high level of qualitative and quantitative agreement between the measurements and simulations validated the kinematic criterion for the inception of breaking and the location of the spilling breaker, on the basis of the BEM computations and associated experiments. The breaking inception is associated with the fluid particle at the crest of the steep wave that has been accelerated to match and surpass the crest velocity. The previously observed significant slow-down of the crest while approaching breaking is verified numerically; both narrow-/broad-banded wave trains are considered. Finally, the relative importance of linear and nonlinear contributions is analyzed.

Active Control in an Anechoic Room: Theory and First Simulations

Noise control and source design require the measurement of sound radiation at low frequencies. Anechoic rooms, which are designed for this purpose, allow echo-free measurements at medium or high frequency but passive wall treatment is less effective at low frequency and in practice no facility provides anechoicity below 50Hz. This paper discusses the applicability of an active control algorithm which has been previously introduced to minimize the echoes from a scattering object to the cancellation of the low frequency wall echoes in an anechoic room including wall-embedded secondary sources. At first the paper discusses, in the general case then for a free half-space as a model case, the algorithm key which consists in estimating the scattered acoustic pressure from total pressure measurements. Boundary Element Method computations are secondly used to simulate estimation and active control of error signals accounting for the low-frequency scattered pressure in an anechoic room. The simulations show that control with a few dozen microphones and noise sources allows a large reduction of the noise scattered from the walls at low-frequency.

Diffraction formulation for the sound radiation of a loudspeaker on a rigid convex edged shape enclosure

We present a method for calculating the sound radiation of a loudspeaker on a box-shape enclosure. This method is based on the iterative Asheim-Svensson formulation [Asheim et al. J. Acoust. Soc. Am., 2013]. In this geometrical acoustical model, the radiated sound is given by the addition of the direct sound of a baffled piston and the sound scattered by the edges of the loudspeaker enclosure. The latter are expressed in the form of multiple-order edge diffraction components. This method becomes particularly attractive at high frequencies since the maximum order required to get a correct estimation decreases with frequency. Altogether, the method becomes less costly than the Boundary Element Method (BEM) beyond a given frequency. The convergence of the method can be estimated by considering the distance traveled by the creeping wave on the enclosure instead of considering the successive orders of diffraction by each edge. An iterative formulation follows which is well-suited to slender objects such as a sound bar. Comparisons with measurements and results of a BEM calculation will be presented. [Work supported by the ANR-13-CORD-0008 EDISON 3D grant from the French National Agency of Research.]

A Comparison of the BEM and RANS Calculations for the hydrodynamic performance of the PODS

In the present study, the hydrodynamic performance of the Podded Drive System (PODS) using Reynolds-Averaged Navier Stokes (RANS) method and Boundary Element Method (BEM) is reported. The BEM is based on potential inviscid flow problem while RANS are for the viscous flow problem. Hydrodynamic characteristics of the single propeller are determined by both methods and the results are compared and discussed. Then, it is extended to the PODS at the zero yaw angle. Validation is made through the comparison of both numerical results against experimental test data for the PODS propulsive characteristics coefficients. The results show that there is a good agreement between the experimental data and numerical results, particularly in the viscous calculations.

ELECTRIC POTENTIAL AND FIELD CALCULATION OF CHARGED BEM TRIANGLES AND RECTANGLES BY GAUSSIAN CUBATURE

It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for the case of electric potential and field computation of charged triangles and rectangles applied in the boundary element method (BEM). Analytical potential and field formulas are rather complicated (even in the simplest case of constant charge densities), they have usually large computation times, and at field points far from the elements they suffer from large rounding errors. On the other hand, Gaussian cubature, which is an efficient numerical integration method, yields simple and fast potential and field formulas that are very accurate far from the elements. The simplicity of the method is demonstrated by the physical picture: the triangles and rectangles with their continuous charge distributions are replaced by discrete point charges, whose simple potential and field formulas explain the higher accuracy and speed of this method. We implemented the Gaussian cubature method for the purpose of BEM computations both with CPU and GPU, and we compare its performance with two different analytical integration methods. The ten different Gaussian cubature formulas presented in our paper can be used for arbitrary high-precision and fast integrations over triangles and rectangles.

An analytical solution versus half space BEM formulation for acoustic radiation and scattering from a rigid sphere

A half space problem in acoustics is described by introducing an infinite plane boundary that reflects the wave coming into the plane. A numerical solution using Boundary Element Method (BEM) has been known which is formulated using a modified Green's function in the Helmholtz Integral Formulation, which eliminates the discretization over the infinite plane. Hence, the discretization are confined to the body or obstacle in question only. This feature constitutes the main advantage of the BEM formulation for half space problems. However, no general analytical solution is available to verify the BEM results for half space problems. This paper is aimed to propose an analytical solution for the BEM to compare with, hence to verify the BEM calculation. This analytical approach is currently developed for a half space problem involving radiation and scattering of acoustic waves from a rigid sphere. The image of sphere as well as the image of the field point are defined with respect to the infinite plane. Then, an ad hoc solution is assumed involving a constant and the distance from the center of the sphere to the field point and the distance from the center of the image of the sphere to the field point. The constant is determined by imposing the boundary conditions. Test cases were run with several configuration involving the location of field points and the sphere. Comparison of the analytical solution with BEM calculations shows a good agreement between the two results..

BEM computation of 3D Stokes flow including moving front

Liquid composite molding (LCM) includes all composite-manufacturing methods, where the liquid state resin is forced into the dry preformed reinforcement. In this study, numerical simulation of the resin infusion is presented based on a coupled approach involving Boundary Element Method (BEM) and Level Set Method. The method developed can handle stationary and transient flows by solving the Stokes equations. The numerical results on a square packed set of fibers show excellent agreement with the analytical model. The comparison between experimental and simulation results of flow front patterns revealed a fair accordance.

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.

Active earth pressure due to soil mass partially subjected to water seepage

A method for determination of the active earth pressure exerted by a cohesionless backfill, subjected to water seepage from a high water table, on a retaining structure is presented. The method comprises a numerical procedure based on the boundary element method (BEM) for the seepage analysis and a trial wedge method for the limit equilibrium analysis. The numerical results of the seepage analysis are presented as normalized charts that can be used in the trial wedge method without recourse to the BEM computer code. The main benefits of the proposed analysis are the simplicity of use and the small amount of data necessary. For the seepage analysis, only the phreatic line exit point height at the retaining structure face is required. Numerical results obtained for a proposed example of a retaining wall show the influence of the water seepage on the active earth pressure. The analysis method also can deal with cases of soil anisotropy with respect to the permeability.

Diffusion-controlled growth rate of stepped interfaces.

For many materials, the structure of crystalline surfaces or solid-solid interphase boundaries is characterized by an array of mobile steps separated by immobile terraces. Despite the prevalence of step-terraced interfaces a theoretical description of the growth rate has not been completely solved. In this work the boundary element method (BEM) has been utilized to numerically compute the concentration profile in a fluid phase in contact with an infinite array of equally spaced surface steps and, under the assumption that step motion is controlled by diffusion through the fluid phase, the growth rate is computed. It is also assumed that a boundary layer exists between the growing surface and a point in the liquid where complete convective mixing occurs. The BEM results are presented for varying step spacing, supersaturation, and boundary layer width. BEM calculations were also used to study the phenomenon of step bunching during crystal growth, and it is found that, in the absence of elastic strain energy, a sufficiently large perturbation in the position of a step from its regular spacing will lead to a step bunching instability. Finally, an approximate analytic solution using a matched asymptotic expansion technique is presented for the case of a stagnant liquid or equivalently a solid-solid stepped interface.