Order Boundary Element Method Research Articles

The dynamics and stability of circular cylindrical shells containing and submerged in flowing fluid using a higher order boundary element method

This paper presents a higher order, three-dimensional boundary element method for investigating the dynamics and stability of elastic structures containing and/or submerged in flowing fluid. The method developed can be applied to any shape of elastic structures partially or completely in contact with fluid. In the mathematical model, it is assumed that the fluid is ideal (i.e. inviscid, incompressible and its motion is irrotational). The fluid—structure interaction forces are calculated using the higher order boundary element method, and the finite element method is employed for the structural analysis. In this study, it is assumed that the elastic structure vibrates in its in vacuo modes when it is in contact with flowing fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. The in vacuo dynamic properties of the dry elastic structure are obtained by using standard finite element software. In the wet part of the analysis, the wetted surface of the elastic structure is idealized by using appropriate boundary elements, referred to as hydrodynamic panels. Over each hydrodynamic panel, higher order distributions (linear and quadratic) are adopted in the present study in order to obtain a better convergence, in contrast to Ugurlu and Ergin (2006) assuming constant distribution over each hydrodynamic panel. The fluid—structure interaction forces are calculated in terms of the generalized added mass coefficients, generalized Coriolis fluid force coefficients, and generalized centrifugal fluid force coefficients. To assess the influence of flowing fluid and end support conditions (e.g. simply supported ends, clamped ends, and cantilever cylindrical shell) on the dynamic response behaviour and stability of the cylindrical shells, the non-dimensional wet frequencies and associated vibration modes are presented as a function of the non-dimensional axial flow velocity, and the calculations compare well with the analytical solutions found in the open literature.

3 차원 시간영역 전진속도 자유표면 Green 함수와 2 차 경계요소법을 사용한 선체의 방사포텐셜 수치계산

The radiation potential of a ship advancing in waves is studied using the 3D time-domain forward-speed free-surface Green function and the Green integral equation. Numerical solutions are obtained by making use of the 2nd order BEM(Boundary Element Method) which make it possible to take account of the line integral along the waterline in a rigorous manner. The 6 degree of freedom motion memory functions of a hemisphere and the Wigley seakeeping model obtained by direct integration of the time-domain 3D potentials over the wetted surface are presented for various Froude numbers.

Removing irregular frequencies by a partial discontinuous higher order boundary element method

The phenomenon of irregular frequencies is a puzzle in the course of calculating the interaction of waves and structures by the boundary element method. To remove the irregular frequencies, the modified integral domain method is adopted, and continuous higher order elements and partial discontinuous higher order elements are used for discretization. By these means, the effects of the irregular frequencies are effectively removed. Effective strategies have been adopted to deal with singular integrals and nearly singular integrals at different situations. The numerical results of the horizontal wave force on a uniform cylinder in the first order and second order diffraction problems show that the present method has a good validity. At the same time, the influence of collocation parameter on accuracy of numerical results is examined in detail.

An Electrode-Matrix Cell for Electrolytic Conductivity Measurements

Preliminary results on the design and investigation of an electrode-matrix cell for electrolytic conductivity measurements are presented. A cell prototype has been conceived with the end of studying the electrical and current field behavior in aqueous solutions with different electrode configurations. The cell has been modeled using the boundary element method in order to obtain suitable cells for electrochemical measurements with computable constant. The calculated cell constants, corresponding to different configurations of the electrodes, were compared with the measured values. Measurements were performed on aqueous solutions with different ion concentrations while varying the supplied electrode configuration.

Progress on Nonlinear-Wave-Forced Sediment Transport Simulation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we report on the use of a numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) equations, in driving simulations of flow and sediment transport around partially buried obstacles. The suspended sediment transport is modeled in the near-field in a Navier–Stokes (NS) model using an immersed-boundary method and an attached sediment transport simulation module. Turbulence is represented by large eddy simulation (LES). The NWT is based on a higher order boundary element method (BEM), with an explicit second-order time stepping. Hence, only the NWT boundary is discretized. The solution for the velocity potential and its derivatives along the boundary is obtained in the BEM, which subsequently provides a solution at any required internal point within the domain. At initial time, the NS–LES model domain is initialized with the 3-D velocity field provided by the NWT and driven for later time by the pressure gradient field obtained in the NWT. Incident wave fields, as specified in the NWT to drive sediment transport, can be arbitrary. Applications are presented here for single frequency waves, such as produced by a harmonic piston wavemaker in the laboratory, and modulated frequency wave groups. The feasibility of coupling the irrotational flow and NS solutions is demonstrated. </para>

부유식 구조물의 접합부 형태에 따른 동적응답 특성 연구

This paper investigates the characteristics of dynamic responses of floating structures with connections under sea wave loads. Direct method using higher order boundary element method (HOBEM) and finite element method (FEM) is adopted for numerical analysis. A 500 m-long and 250-m width very large floating structure (VLFS) with four units are considered in numerical analysis. Hinge connection and spring connection with various strength are considered as connection types. Displacements and stresses of VLFS according to the connection types are compared considering wave period and heading angle reduction.

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble–wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.

A comparison of different regularization methods for a Cauchy problem in anisotropic heat conduction

In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady‐state heat conduction problem in an anisotropic medium. The convergence and the stability of the numerical methods are investigated and compared. The numerical results obtained confirm that stable numerical results can be obtained by various regularization methods, but if high accuracy is required for the temperature, or if the heat flux is also required, then care must be taken when choosing the regularization method since the numerical results are substantially improved by choosing the appropriate method.

An iterative boundary element method for solving the one-dimensional backward heat conduction problem

In this paper, the iterative algorithm proposed by V.A. Kozlov and V.G. Maz'ya [Leningrad Math. J. 5 (1990) 1207–1228] is numerically implemented using the boundary element method (BEM) in order to solve the backward heat conduction problem (BHCP). The convergence and the stability of the numerical method are investigated and a stopping criterion is proposed. The numerical results obtained confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.

Effect of free surface and strut on fins attached to a strut

An extensive experimental and computational investigation of the combined and separate effects of free surface and body on the lift characteristics of a pair of fins attached to a strut and fin alone is conducted. The results reveal that the free-surface effect becomes significant when the depth of submergence to chord ratio ( H/ c) is less than three. The effect of the strut is also realized for shallower depth of submergence of the fins through free-surface deformation leading to a significant change in the incidence angle of the flow to the fins. The numerical results based on the Higher Order Boundary Element Method with the linearized free-surface condition show good agreement with the experimental results for fin (foil) alone even at shallow submergence, but some discrepancies appear for the fin attached to the strut at higher speeds mostly due to the neglect of the nonlinear free-surface effect.

A parallel multipolar indirect boundary element method for the Neumann interior Stokes flow problem

A multipolar expansion technique is applied to the indirect formulation of the boundary element method in order to solve the two-dimensional internal Stokes flow second kind boundary value problems. The algorithm is based on a multipolar expansion for the far field and numerical evaluation for the near field. Due to the nature of the algorithm, it is necessary to resort to the use of an iterative solver for the resulting algebraic linear system of equations. A parallel implementation is designed to take advantage of the natural domain decomposition of fast multipolar techniques and bring further improvements. Copyright © 2000 John Wiley & Sons, Ltd.

A parallel multipolar indirect boundary element method for the Neumann interior Stokes flow problem

A multipolar expansion technique is applied to the indirect formulation of the boundary element method in order to solve the two-dimensional internal Stokes flow second kind boundary value problems. The algorithm is based on a multipolar expansion for the far field and numerical evaluation for the near field. Due to the nature of the algorithm, it is necessary to resort to the use of an iterative solver for the resulting algebraic linear system of equations. A parallel implementation is designed to take advantage of the natural domain decomposition of fast multipolar techniques and bring further improvements. Copyright © 2000 John Wiley & Sons, Ltd.

Extension de la DRBEM à la propagation guidée en écoulement cisaillé

The present study aims to extend the Dual Reciprocity Boundary Element Method in order to solve acoustic wave propagation equations in the frequency domain for a parallel shear flow. The Linearized Euler Equations are written as a coupled pair of equations, which are second-order in terms of acoustic pressure and first-order in terms of normal acoustic velocity. Good agreement between numerical results and analytical solutions for a low Mach number shear flow ( M<0.1) shows the interest of the method.

A parallel multipolar boundary element method for internal stokes flows

A multipolar expansion technique is applied to the Boundary Element Method (direct and indirect formulation) in order to solve the two-dimensional internal Stokes Flow with first kind boundary conditions. The algorithm is based on a multipolar expansion for the far field and numerical evaluation for the inner field. Due to the nature of the algorithm, it is necessary to resort to the use of an iterative solver for the resulting algebraic linear system of equations. In comparison with the direct BEM formulation, the indirect formulation is more stable with iterative solvers, and does not need to be preconditioned to obtain a fast rate of convergence. A parallel implementation is designed to take advantage of the natural domain decomposition of fast multipolar techniques and bring further improvement. A good result in memory saving and computing time is obtained that enable us to run huge examples which are prohibitive for traditional BEM implementations.

A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number

A multipolar methodology is applied to the boundary element method (direct and indirect formulation) in order to solve bidimentional Stokes cavity flow. The algorithm based on mixed multipolar expansion and numerical integration is applied not only for very large problems but also for intermediate and small problems. In comparison with the direct formulation, the indirect formulation is more stable with the iterative solvers, and does not need to be preconditioned to obtain a fast convergence. A good result in memory saving and computing time is obtained that enables us to run huge examples which are prohibitive for traditional BEM implementations.

Development of Higher Order BEM Program for Wave Response Analysis of Very Large Floaring Structures

This paper presents development of a Higher Order Boundary Element Method (HOBEM) program for analyzing wave response of box-like Very Large Floating Structures (VLFS). In order to analyze such structures, the problems that 1) elastic deformation of the structure should be considered in the hydroelastic analysis, and 2) large size of its computation in CPU time and required storage size, should be overcome. The program, developed utilizes modal superposition method for both rigid body motions and bending modes of the floating plate in order to account for dynamic coupling between fluid and structure responses. The computation size has been reduced by employing higher order BEM which utilizes 2nd order 8-noded panels and utilizing double-symmetry with respect to χ- and y-axis. A box-like VLFS having the length of 2000m, the width of 400m, and the draft of 4m has been successfully analyzed up to L/λ= 50 (L: length of structure, λ: incident wave length).

Development of an analysis method for acoustic–structural coupling systems using the BEM for the acoustic field: The validity of the method developed and comparison with the FEM acoustic field

A formulation is developed for the analysis of coupled acoustic–structural systems using the boundary element method (BEM) in order to apply the coupled method to the open field in addition to the closed field. In this formulation the most general mode superposition method by Ma-Hagiwara, namely, the high- and low-order truncatable mode superposition method, is used where the higher and the lower modes are truncated. The propriety of this formulation is verified by comparing it with a theoretical solution in a one-dimensional problem and with the solution by a method in an interior noise problem, which was developed using the finite-element method (FEM).

Simulated annealing coupled with the tabu search method for continuum optimization in electromagnetics

The simulated annealing algorithm coupled with the tabu search method for continuum optimization problems is presented. Basically, the new algorithm is obtained by assembling certain characteristics of the tabu search method into the standard simulated annealing. The numerical performance of the new algorithm is discussed based on the optimization of some classical test functions. Finally, an electrostatic insulator geometry is optimized using this algorithm coupled with the boundary element method in order to test it in electromagnetics.

Boundary element analysis of free boundary field-reversed configurations

Field-reversed configuration (FRC) plasmas are governed by the nonlinear Grad-Shafranov equation and it is difficult to analyze this equation for FRC devices by using domain-type methods because the plasma boundary is a free boundary. In the present work, the authors solve the Grad-Shafranov equation using the boundary element method (BEM) in order to study equilibrium configurations for the FRC with a free boundary. In the numerical analysis, the simple iterative method is used to obtain nonlinear solutions of the equation. As a result it is found that a stable solution can only exist for parameter K, which denotes the ratio of the electromagnetic force to the plasma pressure. In addition, the equilibrium configuration is calculated by using BEM for the rigid drift model and the slitted model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of stress intensity factors for three dimensional mixed mode cracks by an influence function method.

The authors have developed an influence function method (IFM) to analyze effectively the stress intensity factor, K, for surface cracks subjected to arbitrarily distributed surface stresses. In the developed IFM the influence coefficients are calculated by boundary element method in order to save the computing time and the labor of generating the input data. Some examples show that the developed method gives accurate values of K and that it is effective especially for the analysis of the mixed mode cracks.