Two-dimensional Boundary Element Method Research Articles

Krauklis wave propagation within a complex fracture system: Modeling via a two-dimensional time-harmonic boundary element method.

Fluid-filled fractures involving kinks and branches result in complex interactions between Krauklis waves-highly dispersive and attenuating pressure waves within the fracture-and the body waves in the surrounding medium. For studying these interactions, we introduce an efficient 2D time-harmonic elastodynamic boundary element method. Instead of modeling the domain within a fracture as a finite-thickness fluid layer, this method employs zero-thickness, poroelastic Linear-Slip Interfaces to model the low-frequency, local fluid-solid interaction. Using this method, the scattering of Krauklis waves by a single kink along a straight fracture and the radiation of body waves generated by Krauklis waves within complex fracture systems are examined.

Optimization Analysis of the Shape and Position of a Submerged Breakwater for Improving Floating Body Stability

Submerged breakwaters can be installed underneath floating structures to reduce the external wave loads acting on the structure. The objective of this study was to establish an optimization analysis framework to determine the corresponding shape and position of the submerged breakwater that can minimize or maximize the external forces acting on the floating structure. A two-dimensional frequency-domain boundary element method (FD-BEM) based on the linear potential theory was developed to perform the hydrodynamic analysis. A metaheuristic algorithm, the advanced particle swarm optimization, was newly coupled to the FD-BEM to perform the optimization analysis. The optimization analysis process was performed by calling FD-BEM for each generation, performing a numerical analysis of the design variables of each particle, and updating the design variables using the collected results. The results of the optimization analysis showed that the height of the submerged breakwater has a significant effect on the surface piercing body and that there is a specific area and position with an optimal value. In this study, the optimal values of the shape and position of a single submerged breakwater were determined and analyzed so that the external force acting on a surface piercing body was minimum or maximum.

A two-dimensional boundary element method with generating absorbing boundary condition for floating bodies of arbitrary shape in the frequency domain

A two-dimensional (2D) boundary element method is developed for the rapid assessment of the hydrodynamic performance of floating structures in waves. The boundary element method is based on potential flow and has panels along all boundaries of the fluid domain – not only along the boundary of the floater – to make the extension to second order feasible. Panels along all boundaries requires the development of generating absorbing boundary conditions for use at radiation boundaries to send incident waves into the domain while absorbing waves originating from the floating body at the same boundary, at the same time. The model is verified by means of conservation of energy of a heaving wave energy converter, and by means of the propagation of second-order waves. The performance in terms of conservation of energy with 12 panels per wave length is good, the generating absorbing boundary condition works according to expectation and the second-order wave propagation corresponds to theory.

Numerical investigation of contact loads of unsynchronised, dry-running screw machines

Unsynchronised, dry-running screw machines have advantages compared to conventional oil-injected and synchronised, dry-running screw machines. Because of the absence of an additional timing gear and no injected lubricant, the effort for manufacturing and assembly can be reduced and lubricant residues in the process gas are avoided. In this design the female rotor torque resulting from the gas pressure is transferred directly to the male rotor by the contacting rotor surfaces. To investigate this contact, a two-dimensional boundary element method contact algorithm is developed to calculate the loads in terms of contact tractions and sliding velocities. The contact kinematics of the screw rotors and the non-constant curvature of the rotor surfaces are considered. The movement between the screw rotors is transformed into a relative coordinate system fixed on the male rotor. Furthermore, the influence of manufacturing tolerances to the occurring contact loads are investigated.

Impedance computation of cryogenic vacuum chambers using boundary element method

A two-dimensional boundary element method for calculating the impedance of infinitely long cryogenic vacuum chambers of general cross section is presented. The formulation is based on combining Kirchhoff's boundary integral representation of an electromagnetic field with the surface impedance boundary condition for the anomalous skin effect, which can occur in metals at cryogenic temperature. As a result, the electromagnetic field in the chamber is expressed as a superposition of the direct and indirect space charge fields and resistive-wall wakefield. This feature allows us to compute the corresponding three impedance contributions separately. This method does not assume a specific transverse charge density such as uniform and Gaussian distributions as well as the ultrarelativistic approximation. A technique for computing the impedances and the form factors in the method is also described. The presented method is applied to circular, rectangular, elliptical, and racetrack-type vacuum chambers. The geometric effect of the cryogenic vacuum chamber cross section on the resistive-wall impedance is shown. The effect of beam velocity is demonstrated for the racetrack-type cryogenic vacuum chamber.

Boundary element analysis of static plane problems in size-dependent consistent couple stress elasticity

Based on a consistent couple stress elasticity theory, a two-dimensional (2D) boundary element method (BEM) is developed to solve the boundary value problems in the couple stress elastic materials. The displacement boundary integral equations (BIEs) are applied to compute the mechanical quantities on the boundary. The integral representations for the generalized strains and stresses at internal points are also presented together with the explicit expressions for the high-order fundamental solutions. The collocation method is adopted for the spatial discretization of the BIEs. Some special numerical and semi-analytical techniques are provided for the evaluation of weakly and strongly singular integrals. The sinh transformation is used to deal with the nearly singular integrals for near-boundary internal points or boundary nodes in thin structures. An error-controlled integration scheme is adopted for computing the non-singular integrals to improve the accuracy. Three representative 2D boundary value problems in the consistent couple stress elasticity theory are studied by the developed BEM. The correctness and accuracy of the present BEM results are verified by comparison with the corresponding analytical results. Then, multiple flat elliptical holes in a plate are numerically studied to show the interaction effects on the stress concentration.

Viscothermal Effects in a Two-Dimensional Acoustic Black Hole: A Boundary Element Approach

The acoustic analog of the quantum black hole for airborne sound in two dimensions was denominated as an omnidirectional acoustic absorber by Climente et al. [see Appl. Phys. Lett., 100, 144103 (2012)], who characterized its absorbing properties without providing any theoretical support. The viscothermal losses of the underlying structure, which consists of an absorbing core and a surrounding gradient-index (GRIN) lens both made of periodic distributions of cylindrical rods, are here comprehensively studied by using the boundary element method (BEM) in two dimensions. It is shown that the numerical simulations in two dimensions reproduce fairly well the increase in absorption of the core when the GRIN lens is added and reveal that the discrepancy between measured and calculated values of absorbance is an artifact of the experimental setup. The possibility of independent calculation of viscous and thermal losses contributions in the two-dimensional (2D) BEM algorithm is employed for the comparison with a homogenization theory in which the cluster of cylinders is represented by a single fluidlike viscous cylinder with effective parameters. We conclude that viscous losses represent about 90% of the total energy dissipated in the core. The homogenization approach results are only 2% below the results calculated with 2D BEM, indicating that the effective parameters obtained by the homogenization are very accurate.

Two-Dimensional Boundary Element Method Using Interval B-Spine Wavelet

A two-dimensional (2D) boundary element method (BEM) is proposed by replacing traditional polynomial interpolation with one-dimensional (1D) scaling functions of B-spine wavelet on the interval (BSWI). Potential problem and elasticity problem are investigated by BSWI BEM. For these two problems, the boundary variables represented by coefficients of wavelets expansions are transformed from wavelet space to physical space through the nonsingular transformation matrices. To make the curve boundary able to be compatible well, the second-order scaling functions are applied to approximate geometric boundary. In addition, singular integral problems appearing in BSWI BEM are solved. Numerical examples verify that BSWI BEM has a desirable performance by comparing with conventional 2D BEM.

Scattered coupling between two wrinkled graphene nanoribbons analyzed by boundary element method

In this paper, we propose a two-dimensional (2D) boundary element method (BEM) to explore the coupling properties of two distorted graphene nanoribbons (GNRs) with wrinkles. From the calculation results, it is found that the resonant wavelengths are redshifted compared with a single GNR, and the scattering intensity is greatly increased, due to the coupling between the two GNRs. In the non-degenerate structure, the coupling resonance modes of the two GNRs are the superposition of the resonance modes of every single GNR, and the resonant wavelength and scattering intensity of different modes change differently with the gap between the two GNRs and their heights. When the coupling effect becomes stronger, some modes will split. We explain the results through the charge and current distribution of the GNRs. This work will help to understand the coupling mechanism of surface plasmon resonances of GNRs.

Reproducible validation and replication studies in nanoscale physics.

Credibility building activities in computational research include verification and validation, reproducibility and replication, and uncertainty quantification. Though orthogonal to each other, they are related. This paper presents validation and replication studies in electromagnetic excitations on nanoscale structures, where the quantity of interest is the wavelength at which resonance peaks occur. The study uses the open-source software PyGBe: a boundary element solver with treecode acceleration and GPU capability. We replicate a result by Rockstuhl et al. (2005, doi:10/dsxw9d) with a two-dimensional boundary element method on silicon carbide (SiC) particles, despite differences in our method. The second replication case from Ellis et al. (2016, doi:10/f83zcb) looks at aspect ratio effects on high-order modes of localized surface phonon-polariton nanostructures. The results partially replicate: the wavenumber position of some modes match, but for other modes they differ. With virtually no information about the original simulations, explaining the discrepancies is not possible. A comparison with experiments that measured polarized reflectance of SiC nano pillars provides a validation case. The wavenumber of the dominant mode and two more do match, but differences remain in other minor modes. Results in this paper were produced with strict reproducibility practices, and we share reproducibility packages for all, including input files, execution scripts, secondary data, post-processing code and plotting scripts, and the figures (deposited in Zenodo). In view of the many challenges faced, we propose that reproducible practices make replication and validation more feasible. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Numerical Study on Wave Radiation by a Barge with Large Amplitudes and Frequencies

A two-dimensional boundary element method is used to study the hydrodynamics of a single barge with prescribed motions of large amplitudes and high frequencies. The wave radiation problem is solved in the time domain based on the fully nonlinear potential flow theory. For numerical simulations, special treatments like plunging wave cutting and remeshing approaches are presented in detail. The numerical schemes are verified through comparing with analytical results. Both the generated outgoing wave amplitudes and hydrodynamic coefficients can be calculated with sufficient accuracy. Then, we focus on large heave, sway and roll motions to investigate the nonlinear effects on hydrodynamic forces, respectively. In particular, the heave motion with two frequencies is also simulated to study the interactions between results at different frequencies. It is interesting to see the sum and difference frequency components and the envelopes in time histories as a result. For forces caused by forced sway or roll motions, there are only even-order harmonics for vertical forces and only odd-order harmonics for horizontal forces. Finally, a single body with combined sway, heave and roll motion is studied to examine the interactions between motion modes.

Isogeometric boundary element analysis and shape optimization by PSO for 3D axi-symmetric high frequency Helmholtz acoustic problems

The boundary element method (BEM) has been widely used for approximating the solution of the Helmholtz acoustic equation due to its superiority for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM). Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. Isogeometric analysis (IGA) is coupled with BEM forming (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. In this work, we consider axi-symmetric domains, where the three-dimensional problem is simplified in BEM from a surface integral to a combination of two 1D integrals. The first is the line integral similar to a two-dimensional BEM problem. The second integral is performed over the angle of revolution. The discretization is applied only to the former integration. This leads to significant computational savings and, consequently, better treatment for higher frequencies over the full three-dimensional models. We first validate the capability of IGABEM for axi-symmetric problems to handle high frequencies and verify it by means of manufactured analytical solutions. Secondly, we show the performance of the proposed approach in shape optimization problems by using a particle swarm optimization (PSO) method. Coupling PSO with IGABEM in the optimization models benefits from the IGA feature of representing the three different models: shape design, analysis and optimization models using a single set of control points. The proposed method for the shape optimization of a horn is compared with reference solutions for BEM and FEM.

Numerical Analysis of Combined Wave Radiation and Diffraction on a Floating Barge

A two-dimensional boundary element method (BEM) based on the potential flow theory is adopted to study the combined wave radiation and diffraction by a single barge. The wave-body interaction problems are simulated using a mixed Euler-Lagrangian scheme, with fully nonlinear boundary conditions. The numerical schemes are verified through comparing with existing results, which show that both the wave runups on the barge and hydrodynamic forces can be calculated with sufficient accuracy. Cases of a single barge subjected to sway motion and regular waves are studied. The real contribution of this study is the outcomes of the spectral analysis conducted for test cases when wave radiation effects are considered in addition to pure wave diffraction. The cases of sway motion with the same frequency as incident wave are simulated first. It is found that sway motion will reduce the overall horizontal force when the frequency is lower than a critical frequency. After that, the higher the frequency, the bigger the horizontal force increasing effect. When the frequency of sway motion is lower than that of incident wave, in terms of the magnitude of the horizontal force, sway motion of the body will always make the resultant force larger than that of pure diffraction case.

Vibro-acoustic analysis of a rail transit continuous rigid frame box girder bridge based on a hybrid WFE-2D BE method

In this paper, a hybrid waveguide finite element (WFE) and two-dimensional boundary element (2D BE) method for the rapid calculation of bridge-borne noise is first proposed and then validated by the results of a vibration and noise field test conducted on a 3 × 40 m concrete continuous rigid-frame box-girder bridge in the Guangzhou Metro System. The advantages of the proposed method are discussed by comparison with a hybrid FE-3D BE model. Finally, the vibro-acoustic characteristics of the bridge are analysed. The results show that the dominant frequency range of the local vibration and radiated noise of the bridge is 63–200 Hz. The WFE model of the bridge has a higher efficiency and nearly the same accuracy compared with the traditional FE model. The 2D BE model of the bridge has a significant higher efficiency compared with the 3D BE model but loses a certain degree of accuracy. The sound fields of the region above the bridge, the region just below the bridge and the lower region beside the bridge are mainly affected by the sound radiated from top and flange slabs, flange and bottom slabs, web slab, respectively. It is beneficial for noise reduction to increase the bridge deck thickness or the bottom slab width.

Predicted Absorption Performance of Cylindrical and Rectangular Permeable Membrane Space Sound Absorbers Using the Three-Dimensional Boundary Element Method

Three-dimensional, permeable membrane space sound absorbers have been proposed as practical and economical alternatives to three-dimensional, microperforated panel space sound absorbers. Previously, the sound absorption characteristics of a three-dimensional, permeable membrane space sound absorber were predicted using the two-dimensional boundary element method, but the prediction accuracy was impractical. Herein, a more accurate prediction method is proposed using the three-dimensional boundary element method. In the three-dimensional analysis, incident waves from the elevation angle direction and reflected waves from the floor are considered, using the mirror image. In addition, the dissipated energy ratio is calculated based on the sound absorption of a surface with a unit sound absorption power. To validate the three-dimensional numerical method, and to estimate the improvement in prediction accuracy, the results are compared with those of the measurements and two-dimensional analysis. For cylindrical and rectangular space sound absorbers, three-dimensional analysis provides a significantly improved prediction accuracy for any shape and membrane sample that is suitable for practical use.

Fully nonlinear analysis of second-order gap resonance between two floating barges

A two-dimensional boundary element method (BEM) based on the fully nonlinear potential flow theory is adopted to study second-order wave resonance in a gap formed by twin barges. Second-order resonance is related to second-order effects of wave elevations and hydrodynamic forces, which have components of the sum or difference frequency. Firstly, forced body motions (heave, sway, and roll mode) excited second-order resonance is studied with regard to different gap width and resonant mode. Then incident wave induced second-order resonance in the gap is simulated. It is found that second-order resonance is more easily provoked and significant when the gap width over draught ratio is large.

A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

In recent years, the boundary element method has shown to be an interesting alternative to the finite element method for modeling of viscous and thermal acoustic losses. Current implementations rely on finite-difference tangential pressure derivatives for the coupling of the fundamental equations, which can be a shortcoming of the method. This finite-difference coupling method is removed here and replaced by an extra set of tangential derivative boundary element equations. Increased stability and error reduction is demonstrated by numerical experiments.

공명형 방음벽 상단장치의 음향성능 평가 방안

Purpose : The purpose of this study is to investigate the acoustic performance evaluation method for resonance type noise reduction device installed on the top of noise barrier. Method: In order to evaluate the acoustic performance of the resonance type noise reduction device installed on the top of noise barrier, the measurement of insertion loss in the semi-anechoic chamber and transmission loss using the impedance tube were conducted. Acoustic mode analysis was also performed to evaluate the resonance frequency of a complicated shaped resonator. By using the two-dimensional boundary element method, the study on the deriving a problem in evaluating the acoustic performance at the rear stage of the resonance type device was conducted and an alternative solution of the problem was suggested, and the acoustic performance in the rear stage of resonance type device was evaluated when a number of resonators were mixed. Result : In order to solve the difficulty in analysis of the acoustic characteristics of resonance type noise reduction device, an effective evaluation method was proposed by using the two-dimensional boundary element method in present work. Also acoustic performance was analyzed at the receiver point of the noise reduction device in which many resonators present simultaneously.

Symmetrical or Non-Symmetrical Debonds at Fiber–Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

A recently proposed criterion is used to study the behavior of debonds produced at a fiber–matrix interface. The criterion is based on the Linear Elastic–(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber–epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

Theory of a Time Domain Boundary Element Development for the Dynamic Analysis of Coupled Multiphase Porous Media

This paper presents an advanced formulation of the time-domain two-dimensional (2D) boundary element method (BEM) for an elastic, homogeneous unsaturated soil subjected to dynamic loadings. Unlike the usual time-domain BEM, the present formulation applies a convolution quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of a suction-based mathematical model. In this formulation, the solid skeleton displacements [Formula: see text], water pressure [Formula: see text] and air pressure [Formula: see text] are presumed to be independent variables. The fundamental solutions in Laplace transformed-domain for such a dynamic [Formula: see text] theory have been obtained previously by authors. Then, the BE formulation in time is derived after regularization by partial integrations and time and spatial discretizations. Thereafter, the BE formulation is implemented in a 2D boundary element code (PORO-BEM) for the numerical solution. To verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is verified by comparison with the elastodynamics problem.