Boundary Element Method Model Research Articles

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling.

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

BEM Modeling for Stress Sensitivity of Nonlocal Thermo-Elasto-Plastic Damage Problems

The main objective of this paper is to propose a new boundary element method (BEM) modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The numerical solution of the heat conduction equation subjected to a non-local condition is described using a boundary element model. The total amount of heat energy contained inside the solid under consideration is specified by the non-local condition. The procedure of solving the heat equation will reveal an unknown control function that governs the temperature on a specific region of the solid’s boundary. The initial stress BEM for structures with strain-softening damage is employed in a boundary element program with iterations in each load increment to develop a plasticity model with yield limit deterioration. To avoid the difficulties associated with the numerical calculation of singular integrals, the regularization technique is applicable to integral operators. To validate the physical correctness and efficiency of the suggested formulation, a numerical case is solved.

On the application of acoustic liners for the reduction of jet-flap installation noise

In this work, an experimental and numerical analysis of the feasibility of using acoustic liners to reduce the acoustic far-field radiation of a subsonic jet near a flat plate is presented. The Boundary Element Method (BEM) with a wavepacket model of the jet noise and considering an acoustic impedance boundary condition was used to calculate the far-field noise for different conditions. A parametric optimization was performed in order to find an optimum impedance in terms of the Overall Sound Pressure Level reduction. Semi-empirical models of acoustic liners were then used to design a liner with an impedance as close as possible to the optimum impedance. The liners were built using additive manufacturing and tested in terms of their acoustic impedance and the resulting noise reduction when applied to a region of the flat plate. The BEM simulations, considering the impedance, showed good agreement with experimental data. Overall, by means of the BEM model, optimization and liner semi-empirical models, it was possible to design an acoustic liner which significantly reduced the installation noise at the far-field, with the overall noise reduction between 2 dB to 4 dB depending on observation angle.

Electrostatic interactions between rough dielectric particles.

From colloid suspension to particle aggregation in protoplanetary formation, electrostatic attraction and repulsion between particles is a key mechanism behind the aggregation and clustering of particles. Although most studies have focused on canonical spherical particles, it remains unclear how nonspherical and rough dielectric particles interact and whether the complicated interplay between roughness and charge distribution affects their force couplings. Here a boundary-element method model was leveraged to study electrostatic interactions between charged dielectric particles with modular, axisymmetric surface features. Charge accumulation at convex surface asperities decreases the strength of electrostatic interactions between particles, and the sensitivity of the electrostatic force to the particle surface roughness and orientation is especially apparent at small particle separations. Surface interactions between the particle near-contact regions were isolated to determine the degree that near-contact interactions dictate the relationship between the net electrostatic force and the particle roughness and orientation. A correction factor ΔF is introduced to recover higher order dielectric effects from a low order analytical model. Finally, implications of surface charge asymmetries produced for different particle orientations and surface roughnesses on the long-standing problem of triboelectrification are discussed.

Hydrodynamic forces in higher modes of a thin cantilever beam resonator

The hydrodynamic force in a thin uniform beam cantilever is essential quantity for designing a resonator. We obtained the hydrodynamic drag forces in a uniform cantilever vibrating at the first four transverse modes using a semi-analytical boundary element method (BEM) and finite element method (FEM) in ANSYS. The present three-dimensional (3D) BEM inertial and damping forces are compared with FEM over a frequency range with less than 9.5% deviation until frequency parameter of 100; thereafter, it deviates numerically due to neglecting the non-linear convective forces. Considering the hydrodynamic damping force, the quality factor is estimated for the first four transverse modes of a uniform cantilever beam. As a result, the present 3D BEM model behaves well at the first bending mode compared to FEM. We also study the effect of the aspect ratio (ratio of width to length) of the beam for all four modes. However, the first mode quality factor sufficiently correlates with the numerical value for all aspect ratios. For uniform beams operating with higher modes, the influence of nonlinear and resonance frequency by the numerical model is more pronounced at smaller lengths. Hence, the 3D BEM approach can estimate the hydrodynamic forces on cantilever-based resonators, for example, atomic force microscopy and biosensors.

A novel damage identification algorithm by combining the boundary element method and a series connection neural network

A novel damage identification approach based on a model-driven and a data-driven combined algorithm is developed. By using this approach with only boundary strains, the existence, location, classification as well as the extent of the damage in a plate can be predicted at once with high accuracy and efficiency. To accumulate the data, the boundary element method (BEM) is applied as a model-driven in modeling plates with one or multiple damages in the forms of circular or elliptical holes or cracks and for solving the boundary strains of the defective plates. The dimensionality reduction and semi-analytical characteristics of BEM not only can compress the feature data also can improve the accuracy of the database for the data-driven algorithm. The boundary strains are obtained directly from BEM models, which are also easily collected through the use of strain gauges mounted on the surfaces of structures being monitored in real applications. A series connection neural network algorithm is established to accomplish the novel damage identification assignments with deep learning. The number of the existing damages is firstly detected by a classification neural network model, then the extracted features are transmitted to the corresponding regression neural network model to prognosis the location, classification as well as the extent of each flaw. A high accuracy of about 99.86 % is achieved by the present combined neural network algorithm, which is promising in applications of actual structural health monitoring.

BEM modelling of a hydrodynamic lifting surface working in ground proximity

Present paper aims to assess the performance and limits of boundary element method for the reliable simulation of ground effect phenomena on hydrodynamic lifting surfaces. Benefitting from the ground effect, especially in extreme ground proximity, suggests a promising concept for lifting bodies. On the other hand, the more pronounced the ground effect, the more complicated flow physics it exhibits, making the problem harder to handle numerically. In this study, a potential-based boundary element method (BEM) is applied to the flow past a 3D rectangular wing within a wide range of ground clearances corresponding to out of ground effect (OGE), in ground effect (GE) and extreme ground effect (EGE) conditions. Both positive and negative angles of attack are tested to examine the lift and downforce producing cases. The potential flow around the airfoil is computed using the mixed constant-strength source and constant-strength dipole based panel method. The results show that BEM successfully predicts the lift force variation for a wing working in ground proximity (GE). However, approaching the bounds of extreme ground effect is seen to introduce a progressive decrease of the fidelity of the method. A similar tendency is observed in the downforce generating conditions, which is also an important scenario for ground vehicle aerodynamics. BEM remarkably overestimates the magnitude of the downforce when the ground clearance reaches up to the EGE conditions, still, it produces quite satisfactory results for the rest of the tested configurations. The pressure distributions are also provided to examine the flow field in the aforementioned cases. Overall, the results lead us to conclude that BEM stands as a robust and reliable prediction tool for ground effect on 3D wings but the extreme ground effect condition represents the limit of its accuracy range.

Wave energy capturing of an offshore stationary platform equipped with three oscillating wave column devices

This paper deals with the hydrodynamic properties of an offshore stationary multi-functional platform consisting of triple oscillating water column (OWC) wave energy converters (WECs). The three OWCs are arranged on the vertices of an equilateral triangle, and one of them is forced to face the incident wave, and is labeled as the seaward OWC. Based on the potential flow theory, a second-order time-domain higher order boundary element method (HOBEM) model was established to investigate the wave energy capturing of this triple-OWCs-platform. It is found that there exists a quarter-cycle phase lag between the surface elevation and the air pressure measured in the chamber of the OWCs. In addition, the wave energy capturing capability of the seaward OWC is found to be improved significantly when the incident wave approaches the platform with an angle of 0 and π/3. Its maximum efficiency can reach up to 97.4% with the optimized device spacing. The averaged efficiency of the three OWCs at the resonant frequency is found to be enhanced when the device spacing is four times larger than the diameter of the OWCs.

Efficient BEM Modeling of the Heat Transfer in the Turbine Blades of Aero-Parts

The modeling of the turbine blades in aero-parts presents difficulties in conventional domain solution techniques, especially when internal cooling air passages and a thermal barrier coating (TBC) are applied. This paper presents a very efficient 3D modeling of the anisotropic heat conduction in turbine blades with the boundary element method (BEM), where both the TBC and cooling air passages are considered. The BEM is very ideal for this modeling, since only boundary meshes are required for it; however, a serious problem of nearly singular integration will arise in modeling with coarse meshes. In this article, an efficient modeling and computational algorithm using the BEM is applied for the simulation of heat conduction in the turbine blades of aero-parts. The present work proposes a simplified BEM model to replace multiple thin coating layers on the top of the blade. In the end, the veracity of the implemented BEM code as well as its computational efficiency are illustrated with a few examples, showing that the settled temperature on the substrate can be reduced by 20% by employing a TBC. As compared to the analyses with ANSYS, the percentages of difference were within 2%, while the CPU time spent by the BEM algorithm was about 1/8 of that of ANSYS, not to mention the meshing efforts saved by adopting by a treatment of equivalent convection.

Complex Crustal Deformation Controlled by the 3D Geometry of the Chile Subduction Zone

ABSTRACT The Chilean subduction zone hosts Mw>8 earthquakes, which could trigger earthquakes on crustal faults located along the plate margin. Using synthetic earthquakes from a quasi-dynamic boundary element method model, we obtain traction fields and perform a slip tendency analysis to obtain synthetic faults, which we compare with existing potentially seismogenic crustal faults. With our results, we find geometric patterns of the highest slip tendency planes with deformations induced by synthetic subduction events, such that north of the rupture area of each event, correlate with normal N20°W–50°W/N60°SW fault planes, and to the south, correlate with normal N30°E–80°E/N60°NW faults planes. These observations agree with observed fault traces in central and northern Chile, and past observations of crustal fault reactivation.

Numerical modelling of a box-type and bottom-detached oscillating water column wave energy conversion device: a comparison with experimental data and between BEM and CFD numerical modelling

Utilization of Boundary Element Method (BEM) based on linear potential flow for modelling Oscillating Water Column (OWC) devices has gained popularity in the last two decades. The commercial BEM solver WAMIT has been used widely for modelling OWCs and validated using experimental modelling (Delauré et. al. 2003, Bingham et. al. 2015, Faÿ 2020). The open-source BEM solver NEMOH has however been mostly ineffective in modelling OWCs since the main approach adopted previously modelled the imaginary piston as a thin disk. In this research, the multi-body interaction problem has been adopted in modelling a box-type and bottom-detached OWC device in NEMOH, where the imaginary piston has been modelled to the length of the internal water column (Penalba et.al. 2017) and compared with experimental data. A further comparison is drawn with the numerical method of Computational Fluid Dynamics (CFD) , which has shown to be accurate for modelling OWC devices (Simonetti et. al. 2015), yet requires significantly higher computational resources than BEM. A two-dimensional CFD numerical wave tank, developed generating and absorbing waves with the waves2Foam toolbox (Jacobsen et al., 2012) of the open-source package OpenFOAM, is used for comparative purposes.
 REFERENCES:
 Delauré, Y. & Lewis, A. (2003). “3D hydrodynamic modelling of fixed oscillating water column wave power plant by a boundary element methods.” Ocean Engineering. 30. 309-330. 10.1016/S0029-8018(02)00032-X.
 Bingham, H.B.; Ducasse, D.; Nielsen, K. et al (2015). “Hydrodynamic analysis of oscillating water column wave energy devices.” J. Ocean Eng. Mar. Energy 1, 405–419 (2015). https://doi.org/10.1007/s40722-015-0032-4
 Faÿ F.-X. (2020). “Modelling and Control for the Oscillating Water Column in Wave Energy Conversion.” PhD Thesis, Universidad del País Vasco.
 Jacobsen, N.G., Fuhrman, D.R. & Fredsøe, J., (2012). “A wave generation toolbox for the open-source CFD library : OpenFoam”. International Journal for numerical methods in fluids, 70, pp.1073–1088.
 Simonetti, Irene & Cappietti, Lorenzo & Elsafti, Hisham & Oumeraci, Hocine. (2015). “Numerical Modelling of Fixed Oscillating Water Column Wave Energy Conversion Devices: Toward Geometry Hydraulic Optimization.” 10.1115/OMAE2015-42056.
 Penalba, M., Kelly, T., Ringwood, J. 2017, NEMOH for Modelling Wave Energy Converters: A Comparative Study with WAMIT. 12th European Wave and Tidal Energy Conference , Cork, Ireland. https://www.researchgate.net/publication/319160625.

A 3D BEM Model for the Hydrodynamic Analysis and Design of Heaving WEC Arrays Attached to a Breakwater

Assessment of the performance of arrays of wave energy converters (WECs) of the type of simple heaving floaters, operating in nearshore and coastal areas, is essential to estimate their power production capacity. The effective design and layout of such WEC farms can be supported by studying the system’s operational characteristics based on the wave climatology of the deployment region. Installation along the exposed side of harbor breakwaters in sea areas with substantial incoming energy potential is a promising option. In this study, a 3D hydrodynamic model based on the boundary element method (BEM) is presented and discussed, aiming to evaluate the performance of WEC arrays consisting of multiple heaving bodies attached to the exposed side of a harbor breakwater, modelled as a vertical wall, considering its reflective effects, as well as hydrodynamic interactions between the multiple floating devices. Numerical results of the predicted power performance for various configurations, including interactions of multiple WECs with the nearshore topography and the breakwater wall, as well as the effects of power take off (PTO) parameters, are presented and discussed. Finally, a case study is presented for a selected coastal site at the port of Heraklion, located in the north-central part of Crete Island in the South Aegean Sea, characterized by relatively increased wave energy potential, using long-term climatological data, illustrating the method and its applicability as a supporting tool for optimal design of WEC arrangements.

Numerical study on dynamic analysis of a nine-module floating aquaculture platform under irregular waves

A numerical study of the dynamics of a nine-module floating aquaculture platform in irregular waves is proposed, to examine the effect of the connector type between net cages and incident wave direction on the hydrodynamic response. A numerical model based on the coupled boundary element method and lumped-mass model was used to simulate the dynamic behavior of the aquaculture platform. Time-domain statistical analysis, and time-frequency analysis based on Hilbert-Huang transform on the motion responses of net cages and the mooring force responses of the platform were then carried out. The results indicate that the mooring system has a decisive influence on the frequency-domain characteristics of surge motion, while the influence of connector can be ignored. The surge motion under flexible hawser connector is less sensitive to wave incident direction, while the wave direction has a greater impact on surge motion under spherical joint connector. The amplitudes of pitch motion under two different connectors decrease significantly under oblique incident waves, compared with perpendicular incident wave condition. The wave incident direction has little effect on the overall mooring force response of the platform. The mooring force responses at different positions show completely different frequency characteristics when the cages are connected by spherical joints. The larger the pitch response of the cage, the smaller the mooring force response of the mooring chain connected to the net cage. There is a positive correlation between the gravity frequency of the mooring force response and the gravity frequency of the pitch response of the net cage.

BEM modeling for the hydrodynamic analysis of the perforated fish farming vessel

As the aquaculture industry progresses from coast to deep sea, the higher strength requirement for aquaculture infrastructure has promoted the rapid development of fish farming vessels. To consider the interaction between waves and floating aquaculture systems, the hydrodynamic and seakeeping performances of the perforated fish farming vessel are studied by using an efficient numerical method, which combines porous theory and potential flow theory. The linear pressure drop porous condition is incorporated into the potential flow boundary conditions. The submerged porous shell of negligible thickness is represented by a dipole distribution to construct a boundary element method (BEM) modeling the wave interactions with a fish farming vessel. A perforated fish farming vessel with openings on the sidewalls is taken for an example, and the effects of the openings and other important factors such as the opening ratio of the metal net and the number of openings on the motion response, wave load, and hydrodynamic coefficients are analyzed by numerical stimulation. The variation of the opening ratio is represented by the discharge coefficient. The natural frequencies of the modified fish farming vessel are significantly altered, and an improved seakeeping performance is exhibited, especially in terms of the roll, because of wave energy dissipation by the porous shell. The added mass and damping in the low frequency range significantly change due to the effect of tank fluid, which decreases as the discharge coefficient and the number of openings increase. With the increases in the discharge coefficient and the number of openings, the hydrodynamic coefficients of heave increase, with a lower natural frequency. The wave loads of surge, heave, and pitch exhibit a fluctuating behavior within a certain frequency range and become pronounced with the effect of tank fluid increases. The spectral analysis results indicate a better performance of the perforated vessel in the extreme sea state, making it feasible for offshore operations.

Evaluating the influence of anatomical accuracy and electrode positions on EEG forward solutions

Generating realistic volume conductor models for forward calculations in electroencephalography (EEG) is not trivial and several factors contribute to the accuracy of such models, two of which are its anatomical accuracy and the accuracy with which electrode positions are known. Here, we investigate effects of anatomical accuracy by comparing forward solutions from SimNIBS, a tool which allows state-of-the-art anatomical modeling, with well-established pipelines in MNE-Python and FieldTrip. We also compare different ways of specifying electrode locations when digitized positions are not available such as transformation of measured positions from standard space and transformation of a manufacturer layout.Substantial effects of anatomical accuracy were seen throughout the entire brain both in terms of field topography and magnitude with SimNIBS generally being more accurate than the pipelines in MNE-Python and FieldTrip. Topographic and magnitude effects were particularly pronounced for MNE-Python which uses a three-layer boundary element method (BEM) model. We attribute these mainly to the coarse representation of the anatomy used in this model, in particular differences in skull and cerebrospinal fluid (CSF). Effects of electrode specification method were evident in occipital and posterior areas when using a transformed manufacturer layout whereas transforming measured positions from standard space generally resulted in smaller errors.We suggest modeling the anatomy of the volume conductor as accurately possible and we hope to facilitate this by making it easy to export simulations from SimNIBS to MNE-Python and FieldTrip for further analysis. Likewise, if digitized electrode positions are not available, a set of measured positions on a standard head template may be preferable to those specified by the manufacturer.

H-Matrix BEM application and validation for space habitat

Acoustic requirements for space habitats are stringent and involve a combination of noise sources minimization and public address and general alarm (PAGA) system validation. Simulation solutions are essential for demonstrating compliance requirement as early as possible and continuously throughout the development cycle of the spacecraft. Space habitats' sound field can be computationally challenging to predict in a deterministic manner for most of the audible spectrum as the volume can be important. For this application, an initial PAGA system design assessment was performed using Ray-Tracing, a geometric statistical method, which must be validated using a deterministic method. For validation purpose, the Boundary Element Method (BEM) was chosen for this application. Given the size of the structure and the desired frequency range, the BEM model was very large, containing over 250,000 wetted nodes, and a standard BEM solver required approximately 200GB of RAM. To limit computing hardware constraints, a newly implemented commercially available H-Matrix BEM solver was used. Pressure maps of a PAGA system simulation on a generic space habitat resulting from the Ray-Tracing and H-Matrix BEM solvers are compared to a standard BEM simulation. Results are compared both in terms of accuracy and computational performance, showing the advantages of using multiple simulation methods at various stages of the design.

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).

Modified BEM for scattering analysis by a flaw at interface in an anisotropic multi-layered plate

In this paper, a modified boundary element method (BEM) for time-harmonic scattering computation analysis in two-dimensional (2-D), homogeneous, anisotropic and linear elastic plates is proposed. The aim of modification is to correct the spurious scattering introduced by inevitable model truncation at far-field in the traditional BEM model. The far-field wave displacement fields beyond the truncation points of BEM model are assumed to be the superposition of orthogonal propagating guided wave patterns, and are finally incorporated into BEM equation systems as the modified items to account for the contribution of infinite boundaries traditionally omitted. This method is simple and elegant, which has advantages on dimension reduction and needs no absorption medium or perfectly matched layer to suppress the reflected waves compared to FEM. Also, we can obtain the reflection and transmission coefficients of each mode directly without post-processing. This modified BEM is implemented to solve wave scattering problems due to a cavity-type defect at the interface in an infinite anisotropic multi-layered plate. The formulation is finally validated for several benchmark problems.

Effects of gravity on natural oscillations of sessile drops

Natural oscillations of sessile drops with a free or pinned contact line in different gravity environments are studied based on a linear inviscid irrotational theory. The inviscid Navier–Stokes equations and boundary conditions are reduced to a functional eigenvalue problem by the normal-mode decomposition. We develop a boundary element method model to numerically solve the eigenvalue problem for predicting the natural frequencies. Emphasis is placed on the frequency shifts of modes due to gravity for a wide range of contact angles $\alpha$ and Bond numbers $Bo$ . Three types of $\alpha$ – $Bo$ diagrams reflecting how gravity shifts the frequency are identified. Specifically, the frequency of zonal modes shifts downwards (upwards) when $\alpha$ is smaller (larger) than a critical value, while the frequencies of most sectoral modes are shifted downwards regardless of $\alpha$ . As a result, gravity can transform the lowest mode from a zonal mode to a sectoral mode. The spectral degeneracy of hemispherical drops inherited from the Rayleigh–Lamb spectrum is also broken by gravity. However, we discover that gravity has no effect on the mode associated with the horizontal motion of the centre of mass, whose frequency is always zero regardless of $\alpha$ and $Bo$ . This implies that the ‘walking’ drop instability reported in previous literature does not exist.

Experimental characterization of a shape optimized acoustic lens: Application to compact speakerphone design

This work presents the shape optimization and subsequent experimental validation of an acoustic lens with application to a compact loudspeaker, such as found in commercial speakerphones. The shape optimization framework is based on a combined lumped parameter and boundary element method model using free form deformation geometry parameterization. To test the optimized design, the loudspeaker lens is three-dimensionally printed and experimentally characterized under anechoic conditions on a finite baffle with respect to its off-axis frequency response. The overall tendencies of the frequency responses agree well between measurement and simulations within the optimization frequency range and at low frequencies. The optimization process is applied to a model including acoustic lumped parameter approximations. The shortcomings of the assumptions made in the model are revealed by laser Doppler vibrometer measurements of the loudspeaker driver and modelling of the mechanical vibrations of the lens.