Coupled Boundary Element Method Research Articles

Propeller-Wing Interaction: A Simplified Method for Coupling BEM and CFD

This paper presents a numerical procedure for studying the interaction between the wake generated by a propeller and the wing, considering a tiltrotor model framed within the T-TECH Italian project, which has the scope to develop innovative technologies for a flight demonstrator. A tiltrotor is an aircraft that generates lift and propulsion by way of powered rotors mounted on rotating shafts or nacelles at the ends of a fixed wing; in which, in contrast with conventional aircraft, the dimension of the propeller is comparable with the vehicle one. The procedure proposes to couple a 3D low-order unsteady Boundary Element Method (BEM) approach, to evaluate the performance of the isolated propeller, and a Reynolds-Averaged Navier-Stokes (RANS) solution for the analysis of the flow field interaction between the propeller (simulated as actuator disk) and the wing.

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.

A spectral coupled boundary element method for the simulation of nonlinear surface gravity waves

The challenge of simulating the broad open sea with limited computational resources has long been of interest in ocean engineering research. In view of this issue, this paper proposes a fully nonlinear potential flow method named the spectral coupled boundary element method (SCBEM). By leveraging the approach of domain decomposition, SCBEM achieves significantly reduced computational cost and an order of magnitude increase in computational domain compared to the conventional boundary element method (BEM). The SCBEM encompasses the marine structure with only a tiny BEM domain and employs a high-order spectral layer to simulate the broad water outside the BEM domain. The performance of the SCBEM is evaluated through comparison with the wave damping approach and literature results for regular waves, modulated wave trains, focused waves, and diffraction of a vertical cylinder. The numerical results demonstrate the effectiveness and accuracy of the SCBEM in simulating a wide range of wavelengths and nonlinear wave interactions.

Modeling of Magnetoelectric Effects in Composite Structures by FEM–BEM Coupling

In this paper, a coupling of the Finite Element Method (FEM) and the Boundary Element Method (BEM) is used to model the behavior of magnetoelectric effects in composite structures. This coupling of numerical methods makes it possible not to have to consider a free space domain, and thus to use a single mesh for the magnetic, mechanical and electrical problems. This results in a consequent reduction of the number of unknowns which is accompanied by shorter computation times compared to a classical FEM approach. A mixed magnetic vector potential, reduced magnetic scalar potential formulation is used for the magnetic problem, and classical FEM formulations are used for electrical and mechanical problems. The resulting global algebraic system is solved by a block Gauss-Seidel solver.

Efficient spectral coupled boundary element method for fully nonlinear wave–structure interaction simulation

Accurately analyzing wave–structure interactions is crucial for the design and operational safety of ships and marine structures. This paper presents a fully nonlinear potential-flow approach for simulating wave–structure interactions using the newly proposed spectral coupled boundary element method (SCBEM). The SCBEM efficiently models an extensive water body that encompasses structures by establishing a boundary element method (BEM) computational domain solely around the object of interest while accurately simulating the far-field broad water by a spectral layer. To further improve efficiency, graphics processing unit acceleration is hired during iterative solving of the boundary value problem in the already small-sized interior BEM domain. Simulations are conducted to validate the accuracy of the method on cases with strong nonlinear phenomena, including wave run-up on a single cylinder, diffraction of a four-cylinder array, near-trapped modes for closely spaced columns, and gap resonance that occurred in side-by-side offloading. The wave run-up, diffraction wave pattern, near-trapped mode, and gap resonance frequency obtained by the proposed method are in good agreement with data from experiments and published literature. The quite good accuracy and the exceptional computational efficiency of the SCBEM demonstrate its promising potential for more application in practical marine problems.

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.

A multiscale method coupling peridynamic and boundary element models for dynamic problems

A novel multiscale method coupling peridynamics (PD) and boundary element method (BEM) is proposed for dynamic problems. In the coupling model, the discontinuous behaviors of materials such as crack development and branching processes are simulated by PD while the boundary and infinite domain are modeled by time-domain BEM, which can take full advantage of their salient features. A general stiffness matrix is introduced in the coupling model to combine the PD and BEM governing equations in such a way that the continuity of displacement and the equilibrium of tractions at the PD-BEM interface are satisfied. A variable horizon method is developed to further eliminate boundary effects and ghost forces at the coupling interface between PD and BEM. Then, a concurrent coupling procedure of PD and BEM is established and its implementation is also introduced based on the dynamic explicit algorithm, i.e. the central difference method. The proposed coupling method is verified by comparing its predictions with those from analytical and experimental results. Numerical examples demonstrate the applicability of the proposed model for wave propagation, infinite domain and fracture problems under dynamic loads.

Study on Influential Mechanism of Trailing Edge Sweep Angle on Aerodynamic Noise of a Centrifugal Air Compressor

As the main noise source in the hydrogen fuel cell system, the noise level of the centrifugal air compressor greatly affects the comfort of the hydrogen fuel cell vehicle, and can be effectively reduced by optimizing the trailing edge sweep angle of the blade. In this paper, the computational fluid dynamics model was used to study the influence of the trailing edge sweep angle on the aerodynamic performance and flow characteristics of a centrifugal air compressor for vehicle fuel cells. The Ffowcs Williams–Hawkings equation and the computational fluid dynamics–boundary element coupling method were adopted to calculate the dipole source strength on the surface of the blade and the radiated aerodynamic noise, respectively, under the different trailing edge sweep angles. The results showed that the trailing edge sweep could lead to an increase in pressure ratio as well as isentropic efficiency, and a decrease in the intensity of flow separation. Meanwhile, the sound pressure level of the compressor under each working condition could be effectively reduced by the trailing edge sweep. When the rotation speed was 80,000 r·min−1 and the blade trailing edge sweep angle was 15°, the sound pressure level of the radiated aerodynamic noise was 5.8 dBA lower than that without sweep.

Influence of scour on the vertical response of rock‐socketed piles in layered saturated rock–soil mass

AbstractThe influence of scour on the vertical response of rock‐socketed piles in a layered saturated rock–soil mass is studied through the finite element‐boundary element coupling method. By utilizing the theoretical solution of layered saturated media as the kernel function, the boundary element method (BEM) is used to deduce the boundary integral equations of rock–soil mass. Meanwhile, the pile is modelled with the three‐node bar element and the global stiffness matrix of the pile is assembled by the finite element method (FEM). Then according to the scour type, the flexibility matrix of the foundation is recombined and extended, which is consistent with the stiffness matrix dimension of the pile. In consideration of the force balance and continuity conditions at the pile‐soil‐rock interface, the FEM–BEM coupling equation is established to solve the interaction between layered rock–soil mass and rock‐socketed pile that considers different scour types. A corresponding MATLAB program is compiled to verify the correctness of the present theory by comparisons with the existing literature solutions, field tests and the finite element solutions. The influences of the scour type, scour depth, socketed length as well as pile‐rock mass modulus ratio and rock mass stratification on the vertical response of a rock‐socketed single pile are further discussed through several numerical examples.

MicroROM: An efficient and accurate reduced order method to solve many-query problems in micro-motility

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable amount of time. Various approximations of the Stokes equation have been considered in the past to ease such computational efforts but they introduce non-negligible errors that can easily make the solution of the problem inaccurate and unreliable. Reduced order modeling solves this issue by taking advantage of a proper subdivision between a computationally expensive offline phase and a fast and efficient online stage. This work presents the coupling of Boundary Element Method (BEM) and Reduced Basis (RB) Reduced Order Modeling (ROM) in two models of practical interest, obtaining accurate and reliable solutions to different many-query problems. Comparisons of standard reduced order modeling approaches in different simulation settings and a comparison to typical approximations to Stokes equations are also shown. Different couplings between a solver based on a HPC boundary element method for micro-motility problems and reduced order models are presented in detail. The methodology is tested on two different models: a robotic-bacterium-like and an Eukaryotic-like swimmer, and in each case two resolution strategies for the swimming problem, the split and monolithic one, are used as starting points for the ROM. An efficient and accurate reconstruction of the performance of interest is achieved in both cases proving the effectiveness of our strategy.

A Hybridizable Discontinuous Galerkin and Boundary Element coupling method for electromagnetic simulations

In this paper, the hybridizable discontinuous Galerkin (HDG) method is combined with the electric field integral equation (EFIE) for the numerical simulation of time-harmonic Maxwell’s equation. The key feature of HDG-EFIE is that the HDG method and the boundary element method (BEM) can be coupled naturally through the extra hybrid variable on the faces of elements, the combined method produces a linear system in term of the degrees of freedom of the extra hybrid variable only. A numerical solution was compared to the analytical solution and found to be in excellent agreement.

Stabilized solution of the 3-D MHD flow problem with FEM–BEM coupling approach

In this study, we obtain the numerical solution of the different problem configurations of the 3-D Magnetohydrodynamic (MHD) flow. We solve the MHD flow inside an unbounded conducting domain or around a conducting solid problems which require to consider both MHD equations and the Laplace equation on the connected domains with the coupled boundary conditions. As a numerical procedure we will propose the BEM (Boundary Element Method) and FEM (Finite Element Method) coupling approach with stabilization in order to eliminate the instabilities due to the numeric formulation. We consider the formulations of the MHD equations on the spherical or cubic domains inside an unbounded domain as a first problem and also on the annular spherical or annular cubic region around a conducting solid for the second problem with stabilized FEM. Then obtained discretized equations are combined with BEM formulation of the Laplace equations just only on the boundary. Finally, the BEM is used in order to obtain the rest of the unknown values on the Laplace domain using the boundary values obtained from the coupled formulation. Different values of the problem parameters and configurations are tested, and obtained solutions are displayed in terms of the figures as the 2-D slices of the 3-D solutions.

Numerical Modeling of Injection-Induced Earthquakes Based on Fully Coupled Thermo-Poroelastic Boundary Element Method

Numerical Modeling of Injection-Induced Earthquakes Based on Fully Coupled Thermo-Poroelastic Boundary Element Method

Coupling BEM and VEM for the Analysis of Composite Materials with Damage

Numerical tools which are able to predict and explain the initiation and propagation of damage at the microscopic level in heterogeneous materials are of high interest for the analysis and design of modern materials. In this contribution, we report the application of a recently developed numerical scheme based on the coupling between the Virtual Element Method (VEM) and the Boundary Element Method (BEM) within the framework of continuum damage mechanics (CDM) to analyze the progressive loss of material integrity in heterogeneous materials with complex microstructures. VEM is a novel numerical technique that, allowing the use of general polygonal mesh elements, assures conspicuous simplification in the data preparation stage of the analysis, notably for computational micro-mechanics problems, whose analysis domain often features elaborate geometries. BEM is a widely adopted and efficient numerical technique that, due to its underlying formulation, allows reducing the problem dimensionality, resulting in substantial simplification of the pre-processing stage and in the decrease of the computational effort without affecting the solution accuracy. The implemented technique has been applied to an artificial microstructure, consisting of the transverse section of a circular shaped stiff inclusion embedded in a softer matrix. BEM is used to model the inclusion that is supposed to behave within the linear elastic range, while VEM is used to model the surrounding matrix material, developing more complex nonlinear behaviors. Numerical results are reported and discussed to validate the proposed method.

On the treatment of hydroelastic slamming by coupling boundary element method and modal superposition method

An efficient fluid and structure interaction (FSI) coupling strategy between boundary element method, i.e. BEM (fluid part), and modal superposition method (structure part) is proposed to study hydroelastic slamming of wedge sections. The coupling strategy possesses simplicity in coding construction by transmission of coordinates, velocity and pressure on the fluid-solid interface. Convergence property of grid size, time step and modal number are first investigated. After that, the accuracy of the model is verified by comparing the numerical results with published ones. Hydroelastic effect associated with plate thickness, deadrise angle, impact velocity and boundary condition is discussed by the comparison between quasi-static, decoupling and coupling solutions, where quasi-static and decoupling solutions are established by neglecting the influence of elastic response of structure on the water flow field. The results show that quasi-static solution underestimates structural maximum response under specified hydroelastic parameters, and a time-lag effect is found between results of decoupling and coupling solutions.

Investigation of hydroelasticity in water entry of flexible wedges with flow detachment

Prediction of structural response during water entry is of great significance for the design of naval architecture and aircraft. In order to study fluid-structural interaction (FSI) of flexible wedge during water entry, coupling algorithms based on boundary element method (BEM)/Wagner theory and modal superposition method (MSM) are utilized. The first solution is a numerical method by coupling BEM and MSM based on domain decomposition technique. The second solution is a semi-analytical method by coupling Wagner theory and MSM. Non-linear pressure composition in the Bernoulli equation is used to improve the accuracy for wedge with moderate deadrise angles. The implicitly Newmark-β scheme is employed for time marching of structural dynamic equation. Effects of hydroelasticity on fluid pressure and structural response are studied by the comparison between coupling and decoupling solutions. The results show that the structural response is significantly affected by the presence of fluid added mass and damping. Structural response is lagged due to the fluid added mass and damping. Besides, the latter one causes the decrease of amplitudes of slamming load and structural response. This paper highlights the effect of hydroelasticity on slamming load and structural response during water entry of flexible structure.

Calculation of 3D transient Eddy current by the face‐smoothed finite element–boundary element coupling method

To calculate the distribution of the magnetic field and eddy current density on the surface of an aluminium plate, a method that couples the face-smoothed finite element method (FS-FEM) to the boundary element method (BEM) is proposed in this study. This method combines the advantages of the FS-FEM and BEM, which can rapidly and accurately calculate the distributions of vertical magnetic field and eddy current field on the surface of an aluminium plate. The structural parameters and material properties of the coil and aluminium plate are considered. An accurate three-dimensional calculation model is established. Then, the vertical magnetic field and eddy current field distributions are calculated in this study. In the case of the same grid density, compared with the finite element–boundary element coupling algorithm, the simulation results show that the FS-FEM and the boundary element coupling method have obvious advantage in improving the calculation accuracy. The maximum relative error between the calculated results and measured results is only 4%. The proposed method in this study is available for reference to the transient open-domain eddy current field analysis.

Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme

The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the problem, resulting in substantial simplification of the pre-processing stage and in the reduction of the computational effort, without jeopardizing the solution accuracy. In this contribution, we explore the possibility of a coupling VEM and BEM for computational homogenization of heterogeneous materials with complex microstructures. The test morphologies consist of unit cells with irregularly shaped inclusions, representative e.g., of a fiber-reinforced polymer composite. The BEM is used to model the inclusions, while the VEM is used to model the surrounding matrix material. Benchmark finite element solutions are used to validate the analysis results.

Sound Field Properties of Non-Cavitating Marine Propellers

The sound field properties of non-cavitating marine propellers are investigated using a hybrid method, in which the FWH (Ffowcs William-Hawkings) analogy is coupled with the BEM (Boundary Element Method) approach. The investigations include both the uniform and non-uniform inflow conditions. For both conditions, the dominant sound source terms and the decay rate of the noise with regard to the distance to propeller centre are investigated. The influence of the permeable surface dimensions in the permeable FWH approach on the hydroacoustic result is also investigated. To carry out the investigations, the formulation to calculate acoustic pressure generated by the propeller wake sheet is proposed for the first time. The issues associated to coupling permeable FWH approach and BEM are also discussed, including the fictitious volume flux problem and the consideration of the ship wake field. It was found that the influence of the permeable surface dimension is little for the 1st BPF (Blade Passage Frequency), but cannot be ignored for the 3rd BPF. In the uniform inflow situation the thickness terms are found to be dominant, while in the non-uniform inflow situation the loading terms are dominant.

Application of Biot’s Poroelasticity to Seismic Analysis of Subway Stations in a Saturated Poroelastic Half-space: Effects of Viscous Coupling

ABSTRACT This paper presents a parametric investigation on the effects of viscous coupling on the seismic responses of subway stations in a saturated poroelastic half-space which is modeled as a two-phase medium by the Biot’s theory. Moreover, an equivalent single-phase model for the saturated poroelastic half-space is introduced, and comparisons between the single-phase solutions and the two-phase solutions are made. The results are obtained by a finite element-indirect boundary element coupling method. The study shows that the viscous coupling has significant influences on the seismic internal forces and deformation of the subway stations, and the single-phase approximation can cause large errors.