• Journal of the Society of Naval Architects of Korea
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• v.39 no.4
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• pp.1-10
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• 2002

For the time-domain simulation of incipient breaking waves, usually the boundary integral method has been used so far, and it seems to be successful except a problem of too much computation time. The present paper shows a new computation technique for the simulation of breaking wave experiment. This technique uses the high-order spectral/boundary element method and the boundary integral method in sequence, and reduces the computation time remarkably. The wave generation and energy focusing process is efficiently simulated by the high-order spectral/boundary element method. Only the wave over-turning process is simulated by the boundary integral method. In the example calculation result, salient features of breaking waves such as high particle velocities and accelerations are shown.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.382-385
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved fly using the high-order spectral method and body potential is solved fly using the high-order boundary element method. Through the combination of these two methods, the wave-making problems fly a submerged sphere moving with the large amplitude oscillation are solved in time-domain. With the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.113-120
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• 1999

In this paper, mathematical formulation of the high-order spectral/boundary-element method is shown. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated in time-domain. Three-dimensional waves generated by a uniformly translating suriace pressure are calculated and discussed. The obtained results are compared with others results, The comparisons show good agreements.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.4
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• pp.1000-1013
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• 2014

This paper presents some of the efforts by the authors towards numerical prediction of springing of ships. A time-domain Higher Order Boundary Element Method (HOBEM) based on cubic shape function is first presented to solve a complete second-order problem in terms of wave steepness and ship motions in a consistent manner. In order to avoid high order derivatives on the body surfaces, e.g. mj-terms, a new formulation of the Boundary Value Problem in a body-fixed coordinate system has been proposed instead of traditional formulation in inertial coordinate system. The local steady flow effects on the unsteady waves are taken into account. Double-body flow is used as the basis flow which is an appropriate approximation for ships with moderate forward speed. This numerical model was used to estimate the complete second order wave excitation of springing of a displacement ship at constant forward speeds.

• Journal of Power System Engineering
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• v.16 no.5
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• pp.40-46
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• 2012

For free surface flow problem, a high-order spectral/boundary element method is adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. Using the combination of these two methods, the free surface flow problems of a submerged moving body are solved in time domain. In the present study, lifting surface theory is added to the former work to include effects of lift force. Therefore, a new formulation for the basic mathematical theory is introduced to contain the lift body in calculation.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.67-74
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time-domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. By the combination of these two methods, the wave-making problems by a submerged sphere oscillating with large amplitude under the free~surface are solved in time-domain. Through the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Journal of Power System Engineering
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• v.14 no.6
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• pp.75-82
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• 2010

In this study, the topics for free-surface wave simulation, nonlinear hydrodynamic force, and the critical resonance frequency of so-called ${\tau}=U{\omega}/g$=1/4 are discussed. A high-order spectral/boundary element method is newly adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. By the combination of these two methods, the wave-making problems by a submerged sphere oscillating with forward speed under the free-surface are solved in time domain.

• Coupled systems mechanics
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• v.12 no.4
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• pp.365-389
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• 2023

Dynamic analysis of a typical concrete gravity dam-reservoir system is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the H-W (i.e., Hagstrom-Warburton) high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially reviewed which was originally proposed in a previous study. Thereafter, the response of Pine Flat dam-reservoir system is studied due to horizontal and vertical ground motions for two types of reservoir bottom conditions of full reflective and absorptive. It should be emphasized that study is carried out under high order of H-W condition applied on the truncation boundary. The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by FE-(FE-HE) approach (referred to as exact method). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.