Hybrid Boundary Element Method Research Articles

A hybrid boundary element method based model for wave interaction with submerged viscoelastic plates with an arbitrary bottom profile in frequency and time domain

This study investigates the scattering of surface ocean waves by a submerged viscoelastic plate placed over the variable bottom topography under the assumptions of linear theory. The solution is derived using the hybrid boundary element method. The boundary element method is faster and easier to use when compared to the most widely used analytical method, such as the eigenfunction expansion method. Moreover, the application of analytical methods is restricted to structures with regular geometries and flat sea bottom. However, the present solution technique works for the plate at any angle placed over the variable bottom topography. Furthermore, as a particular case, the scattering problem is analyzed when a rigid wall is placed downstream. Energy balance relations are derived to check the accuracy of the computed numerical results. The effect of sinusoidally varying bottom topography, damping parameter, and plate edge conditions on the Bragg resonance phenomenon is analyzed. Initially, the solutions are presented in the frequency domain using the hybrid boundary element method and then extended to the time domain using the Fourier transform. It is observed that when the edges of the submerged plate are fixed, the Bragg resonance occurs at lower values of the frequency parameter. However, the Bragg resonance occurs around the primary Bragg value when the plate has free edges. For certain incident wave frequencies, the viscoelastic plate that completely covers the undulating bed dissipates a greater amount of wave energy than when the plate only partially covers the seabed.

Efficient simulation of stochastic seismic response of long-span bridges in river valleys using hybrid BEM-FEM

Determining ground motions is essential for seismic analysis of long-span bridges located at complex sites. However, there is a lack of earthquake records for local site conditions. Thus, this study focused on the effect of local site conditions on the stochastic response of long-span high-pier rigid frame bridges crossing a valley with an overlying water layer. For this purpose, a hybrid boundary element and finite element method (BEM-FEM) is proposed to investigate the stochastic seismic response of long-span bridges at such a complex site. First, a simulation method for 3-D spatially varying ground motions ascribed to wave scattering from irregular surface topography, sedimentary soil, and water layers was established based on the BEM combined with the spectral representation method. Furthermore, the statistical properties of the bridge response were explored based on the FEM and Monte Carlo simulations. The advantage of this work is that it reveals how the seismic wave propagation in this particular valley topography and water layer affects the stochastic response of the bridge considered. Moreover, the results indicate that seismic wave scattering leads to a significant energy redistribution of the input waves in the tri-directions related to the surface location, and a decrease in the coherency loss functions at all frequencies. Owing to this change, the peak ground accelerations (PGAs), bridge response means, and response variability are doubled. The beneficial effect of the water layer on the PGAs is weakened, while the adverse effect of hydrodynamic pressure dominates. The parameter analysis results demonstrate that a 10-m-deep sedimentary soil layer produces a 47% increase in the internal force of the pier bottom. The solid-liquid dynamic coupling effect should be accurately quantified for bridges located at saturated sites. Considering the local site conditions, the coefficient of variation (COV) of the response of the pier top exceeded 0.3, indicating strong randomness.

Study on pile cap effects of pile group foundations under linear wave action by a hybrid BEM and EEM method

For pile group foundations (PGFs) subjected to ocean wave action, diffraction waves from the large-scale pile cap can remarkably change wave loads on slender piles below the pile cap (i.e., pile cap effects). However, relevant influencing factors and the variation pattern of wave loads on piles are still unclear. To this end, this study develops a three-dimensional hybrid method for calculating wave loads on slender piles in PGFs under linear wave action. The presented method is implemented by combining the boundary element method (BEM) and the eigenfunction expansion method (EEM) and can consider the effect of diffracted waves from the pile cap. The proposed method is then applied to a truncated cylinder and a PGF with a square pile cap, and the calculated results are respectively compared with the analytical and numerical results. Excellent agreements verify the validity of the presented method. The effects of various factors, including cap shapes, cap dimensions, cap drafts, wave propagation directions, wave numbers, pile slopes, and pile tilt directions, on wave loads of piles are investigated using the presented method. The results show that wave numbers and cap horizontal dimensions have a very strong effect on wave forces on slender piles in PGFs, and wave forces on piles decrease substantially as they increase. However, the influence of cap drafts is weaker. The wave propagation direction determines the distribution pattern of wave load magnitudes at different pile locations, and this distribution pattern varies with different cap shapes. For tilted piles, the wave propagation direction and the pile tilt direction jointly affect (enhance or weaken) wave loads on piles, and the pile slope can amplify this effect. Wave loads on the external piles of the pile group are generally stronger and these external piles need to be reasonably strengthened. This research can assist with the design and optimization of PGFs for offshore bridges.

Dynamic response of pile embedded in unsaturated soil under SH waves considering effect of superstructure

Soil is usually treated as one-phase or two-phase media in previous soil-pile dynamic studies. However, the air inside the soil pores can induce strong matrix suction to the skeletons, which would significantly affect the propagation of the shear horizontal waves within the soil. In addition, the superstructure's effect on the soil-pile system's dynamic response is often neglected. This can result in the underestimation of the dynamic impedance of a pile, which would further lead to the overdesign of the pile dimensions. In this study, a novel unsaturated soil–pile–superstructure model induced by vertically propagating shear horizontal waves is established to investigate the seismic performance of a pile under the influence of superstructures. The analytical solutions of the kinematic amplification and interaction factors (IU and AU, respectively) are derived using the Laplace transform and variable separation method. The developed solution is verified by comparing results from the hybrid boundary element method and the dynamic Winkler model in previous studies. Based on the obtained solutions, a parametric study is conducted to investigate the effects of pile and soil properties on the system's seismic response. The main conclusions can be drawn as follows: (1) When 0.2 < a0 (normalized frequency) < 0.7, IU and AU decrease with the increase of soil water saturation. This trend becomes extremely evident when the saturation is above 0.95. (2) Resonance appears at 0 < a0 < 0.7, and the resonance frequency decreases with the increase of the superstructure mass. (3) The vibration of the free-field soil has a non-negligible effect on reducing the system's seismic response.

Hybrid boundary element and eigenfunction expansion method for wave trapping by a floating porous box near a rigid wall

ABSTRACT The interaction between oblique waves and a surface-piercing floating porous box located near to an impermeable sea wall is studied under the hypothesis of linearised water wave theory. The solution for the associated boundary value problem is developed using combined eigenfunction expansion and multi-domain boundary element methods. The reflection coefficients, surface elevation and hydrodynamic loads on the system are computed to examine the effect of different waves and structural parameters. The study reveals that waves reflected by the structure and wall decrease for increasing the porosity of the structure. The normalised spacing from permeable box to the sea wall plays a major role in the attenuation of wave load on the impermeable sea wall. Furthermore, the wave reflection follows a periodically oscillatory trend as the spacing from the box to the wall increases. The study concluded that on the inshore side, a serene environment can be formed in the presence of the floating permeable box.

A Computational Model for Nonlinear Biomechanics Problems of FGA Biological Soft Tissues

The principal objective of this work was to develop a semi-implicit hybrid boundary element method (HBEM) to describe the nonlinear fractional biomechanical interactions in functionally graded anisotropic (FGA) soft tissues. The local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) were used to solve the nonlinear fractional dual-phase-lag bioheat governing equation. The boundary element method (BEM) was then used to solve the poroelastic governing equation. To solve equations arising from boundary element discretization, an efficient partitioned semi-implicit coupling algorithm was implemented with the generalized modified shift-splitting (GMSS) preconditioners. The computational findings are presented graphically to display the influences of the graded parameter, fractional parameter, and anisotropic property on the bio-thermal stress. Different bioheat transfer models are presented to show the significant differences between the nonlinear bio-thermal stress distributions in functionally graded anisotropic biological tissues. Numerical findings verified the validity, accuracy, and efficiency of the proposed method.

Meshfree reduced order model for turbomachinery blade flutter analysis

The paper introduces a development and application of boundary element based meshfree reduced order model for subsonic flutter analysis of turbomachinery blade cascade. The prime objective of the present work is to demonstrate the efficient use of meshfree hybrid boundary element method for subsonic flutter analysis of low pressure stage steam turbine blades . The meshfree incompressible fluid solver is developed employing 3D inviscid panel method . To model the flow separation inviscid-PM is hybridized with integral boundary layer approach using inviscid-viscous coupling mechanism along with discrete vortex particle method. A 3D annular test cascade is modeled using proposed meshfree solver for the flutter analysis. The comparison of estimated pressure coefficient and aerodynamic damping highlights a good agreement with experimental data and mesh based CFD-model’s results. Moreover, it have observed that the computational time for flutter analysis using proposed method is significantly lower compared to traditionally used CFD based numerical models for subsonic flutter in 3D blade cascade.

Interaction Magnetic Force of Cuboidal Permanent Magnet and Soft Magnetic Bar Using Hybrid Boundary Element Method

The hybrid boundary element method for solving a three-dimensional magnetostatic problem is presented in this paper for the first time. The interaction force between the cuboidal permanent magnet and the bar, made of soft magnetic material, is calculated. Results of the presented approach are confirmed using COMSOL Multiphysics as well as with the results of the image theorem that is applicable when the dimensions of the bar are large enough; so it could be considered an infinite soft magnetic plane.

A Flexible FEM-BEM-DDM for EM Scattering by Multiscale Anisotropic Objects

In this article, a nonconformal domain decomposition method (DDM) based on the hybrid finite element method (FEM) and boundary element method (BEM) is proposed to solve arbitrary 3-D anisotropic (including bianisotropic and single anisotropic) multiscale composite objects. The object is divided into interior and exterior regions. The interior region is solved by the bianisotropic finite element domain decomposition method (FEM-DDM), and the exterior region is solved by the discontinuous Galerkin (DG) method based on the combined field integral equation (CFIE). In order to decouple the electric and magnetic fields of the bianisotropic object, a new finite element–boundary element–domain decomposition method (FEM-BEM-DDM) formulation is derived. To ensure the continuity of electric current and electric field between anisotropic FEM subdomains, a new auxiliary current is introduced into the interface of different subdomains of FEM and the interface of FEM subdomains with BEM subdomains. The former uses second-order transmission conditions (SOTCs) to ensure continuity, whereas the latter uses Robin transmission conditions (RTCs) to ensure continuity. The BEM dense matrix–vector multiplication is accelerated by a multilevel fast multipole algorithm (MLFMA). The proposed FEM-BEM-DDM allows for nonconformal discretization between any touching subdomains and provides an effective preconditioner. In numerical examples, the accuracy and effectiveness of the method are verified.

Analysis of Bi-Isotropic Media using Hybrid Boundary Element Method

This paper proposes the application of the hybrid boundary element method (HBEM) for analysis of bi-isotropic media of Tellegen type. In previous applications of this method it was possible to analyze only the electromagnetic problems in isotropic media. The main contribution of this paper is the modification of the method itself, in order to solve a large scale of quasi-static TEM problems in bi-isotropic media. Detailed theoretical analysis and HBEM procedure are described and applied. Characteristic parameters of a microstrip line with bi-isotropic substrate are analyzed. Obtained results have been compared with available numerical and software simulation results. A close results match can be noticed.

Modelling wide perforated breakwater with horizontal slits using Hybrid-BEM method

A hybrid boundary element method has been developed to efficiently solve the hydrodynamic response of a wide perforated breakwater with arbitrary hull geometry and multiple horizontal slits. The fluid subdomains inside the slits were considered as rectangular and analytical eigenfunctions of the slit area were applied to derive the boundary condition at the interface. The involvement of analytical solutions in the numerical boundary element method (BEM) is the novelty of the present approach. The 2D numerical solution was verified with analytical solution of perforated rectangular breakwater to show the validity of the proposed hybrid BEM. Parametric studies have been performed to study the effect of porosity, position and layout of the slits. It has been found that the slits generally reduce the diffracted and radiation potentials, and would be most effective when placed near the free surface. The approach was also extended to 3D channel flow and the results were calibrated against an experimental study performed in the wave flume.

Improving the Efficiency of Hybrid Boundary Element Method for Electrostatic Problems Solving

This paper describes a modification of the Hybrid Boundary Element Method (HBEM) for electrostatic problems solving. Such improved method is applied for transmission lines analyses. By taking a quasi-static TEM approach, the Hybrid Boundary Element Method is applied to determine the effective relative permittivity and the characteristic impedance of different stripline structures. Comparisons with already published numerical results and software simulation have been also performed with an aim to test the validity of the proposed approach. A close results match can be noticed. The main novelties of the proposed HBEM modification are better accuracy and ability to determine the polarization charges distribution on the separating surface between a strip and a dielectric layer. This was not possible before, using the previous version of the method.

Influence of the magnetization vector misalignment on the magnetic force of permanent ring magnet and soft magnetic cylinder

The aim of this paper is to emphasize the influence of the magnetization vector misalignment to the magnetic force. In this concrete example the force between permanent ring magnet and soft magnetic cylinder was analyzed. Configuration that can be seen in different devices that incorporate permanent magnets. Magnetic force between permanent ring magnet and soft magnetic cylinder is calculated using hybrid boundary element method and semi-analytical approach based on fictitious magnetization charges. By selecting the angle of the magnetization vector inclination, obtained expression can be used for the force calculation of axially or radially magnetized permanent magnet and magnetic body of finite dimension.

An efficient computation of cascade-gust interaction noise based on a hybrid analytical and boundary element method

This paper presents a hybrid analytical and boundary element method to compute the airfoil cascade-gust interaction noise. We assume that the acoustic response of an airfoil to the oncoming gust depends on the locally non-uniform mean flow such that the analytical solution based on a generalised Prandtl-Glauert transformation is utilised to compute the sound generation. The radiation of sound from an airfoil is scattered by other airfoils, which is resolved by a high-efficiency boundary element method. An averaging approach is proposed to efficiently compute the periodic Green's function due to the cascade. The predicted results are validated against numerical simulations for flat plate cascades, and the results match reasonably well. The cut-off properties due to the geometry restriction are discussed, and the critical gust wavelengths for the different orders of acoustic mode are derived. The low-frequency components are trapped in the space between the blades if the stagger angle is zero, while the plane waves are likely to propagating otherwise. For cascades with real airfoil geometry, the background mean flows are computed based on the potential theory. The omission of the refraction effect and approximation errors in the analytical solution of the acoustic response can cause errors for real airfoils, but the hybrid method can capture the sound reduction due to the finite thickness, and yield closer agreement with the numerical solution than the flat plate.

Multi-DOF WEC Performance in Variable Bathymetry Regions Using a Hybrid 3D BEM and Optimization

In the present work a hybrid boundary element method is used, in conjunction with a coupled mode model and perfectly matched layer model, for obtaining the solution of the propagation/diffraction/radiation problems of floating bodies in variable bathymetry regions. The implemented methodology is free of mild-slope assumptions and restrictions. The present work extends previous results concerning heaving floaters over a region of general bottom topography in the case of generally shaped wave energy converters (WECs) operating in multiple degrees of freedom. Numerical results concerning the details of the wave field and the power output are presented, and the effects of WEC shape on the optimization of power extraction are discussed. It is demonstrated that consideration of heave in combination with pitch oscillation modes leads to a possible increase of the WEC performance.

Efficient Simulation of Substrate-Integrated Waveguide Antennas Using a Hybrid Boundary Element Method

This paper presents a hybrid boundary element method for the efficient simulation of substrate-integrated waveguide (SIW) horn antennas. It is applicable with good accuracy to relatively thin structures with conventional circular ground vias. In the multiscale simulations, a 2-D contour integral method is used for the modeling of the fields inside the structure with numerous vias and a method of moments is used for the radiated fields outside. The contour integral method is extended in this paper by a new waveguide port of finite size based on the unit cell analysis of an SIW segment. Several SIW horn antennas are studied to validate the proposed method in terms of the input impedance, the field distribution on the aperture, and the radiation diagram. The proposed method shows good to reasonable accuracy and has a numerical efficiency which is about 2–3 orders higher than FEM-based full-wave simulations. It is therefore well suited for fast optimizations.

Dynamics of a capsule flowing in a tube under pulsatile flow

We analyze numerically the behavior of a deformable micro-capsule confined in a pipe under a pulsatile flow. The capsule moves and is deformed by the action of a pulsatile flow inside the tube with a non-null mean velocity. This configuration can be found in the nature and in many bioengineering systems where artificial capsules are driven by micro-pumps through micro-channels. The capsule is considered as a thin hyperelastic membrane, which encloses an internal fluid. As it has been demonstrated in the literature, this model represents a wide range of artificial capsules, for example, the alginate-based capsules, typically used in bioengineering applications. A hybrid isogeometric finite element method and boundary element method based on a T-spline discretization and formulated in the time domain is used to solve the mechanical and hydrodynamical equations. The influence of the relative rigidity of the membrane, frequency and amplitude of the pulsatile flow is studied. Results show that the behavior of the capsule differs from steady flows and it depends strongly on the frequency of the flow and mechanical characteristic of the capsule.

ANALYSIS OF BOWMAN SQUARES USING HYBRID BOUNDARY ELEMENT METHOD

The characteristic parameters of the Bowman squares are determined using the hybrid boundary element method. Influences of different parameters on characteristic impedance values are analysed. Also, the case of multilayered dielectric is considered. The results for the characteristic impedance have been compared with the results obtained by other methods. Key words: Bowman squares, characteristic impedance, diamondwise structure, finite element method, hybrid boundary element method.

RADIALLY MAGNETIZED RING PERMANENT MAGNET MODELLING IN THE VICINITY OF SOFT MAGNETIC CYLINDER

Radially magnetized ring permanent magnet placed above the soft magnetic cylinder is modelled in this paper using Hybrid Boundary Element Method (HBEM) and a discretization approach based on fictitious magnetic charges. The obtained results are compared to those obtained with Finite Element Method results (FEM). Key words: Hybrid boundary element method (HBEM), magnetization charges, magnetic force, permanent magnet (PM).

Investigation of pumping mechanism for non-Newtonian blood flow with AC electrothermal forces in a microchannel by hybrid boundary element method and immersed boundary-lattice Boltzmann method.

Efficient pumping of blood flow in a microfluidic device is essential for rapid detection of bacterial bloodstream infections (BSI) using alternating current (AC) electrokinetics. Compared with AC electro-osmosis (ACEO) phenomenon, the advantage of AC electrothermal (ACET) mechanism is its capability of pumping biofluids with high electrical conductivities at a relatively high AC voltage frequency. In the current work, the microfluidic pumping of non-Newtonian blood flow using ACET forces is investigated in detail by modeling its multi-physics process with hybrid boundary element method (BEM) and immersed boundary-lattice Boltzmann method (IB-LBM). The Carreau-Yasuda model is used to simulate the realistic rheological behavior of blood flow. The ACET pumping efficiency of blood flow is studied in terms of different AC voltage magnitudes and frequencies, thermal boundary conditions of electrodes, electrode configurations, channel height, and the channel length per electrode pair. Besides, the effect of rheological behavior on the blood flow velocity is theoretically analyzed by comparing with the Newtonian fluid flow using scaling law analysis under the same physical conditions. The results indicate that the rheological behavior of blood flow and its frequency-dependent dielectric property make the pumping phenomenon of blood flow different from that of the common Newtonian aqueous solutions. It is also demonstrated that using a thermally insulated electrode could enhance the pumping efficiency dramatically. Besides, the results conclude that increasing the AC voltage magnitude is a more economical pumping approach than adding the number of electrodes with the same energy consumption when the Joule heating effect is acceptable.