• 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 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.

• 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 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.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.45-56
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• 1994

A computationally efficient numerical method based on potential flow is developed for time-domain simulation of the nonlinear free-surface flows around a 2-dimensional hydrofoil. This numerical method, namely, spectral/boundary-element method, is a mixed one of the high-order spectral method and the boundary-element method in time-domain. The high-order spectral method is used to calculate the nonlinear evolution of free-surface, and the boundary-element method is used to calculate the effects of the hydrofoil and the shed vortex. As application examples, nonlinear free-surface flows around a 2-dimensional hydrofoil which starts from the rest and translates near the free-surface with or without harmonic oscillations are calculated. Nonlinear/unsteady results of free-surface waves and hydrodynamic farces are shown and discussed. Particularly, the results of steady-state which are obtained as a special case of the present unsteady solution are compared with others' calculated and experimental results, and good agreements are observed.

• Journal of the Society of Naval Architects of Korea
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• v.40 no.2
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• pp.11-20
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• 2003

In this paper, the high-order spectral/boundary-element method is developed to calculate the 3-dimensional water waves generated by a submerged body. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated Tn time-domain. Three-dimensional free-surface flows generated by a submerged sphere which is moving under the free-surface are calculated. Through example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown. Comparisons with others' results show good agreements.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.595-612
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• 2014

The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

• Journal of Ocean Engineering and Technology
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• v.7 no.2
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• pp.9-18
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• 1993

Numerical wave tank is a robust tool by which the nonlinear interactions between the body and the free-surface can be treated in time-domain. In this paper, a two-dimensional numerical wave tank based on the Spectral/Boundary-Element Method is developed, and applied successfully to the study of nonlinear wave diffraction around a submerged circular cylinder. Particularly, it is shown that the high-order wave components of significant wave height are developed in the lee-side of the cylinder and that these waves result in a negative drift force on the circular cylider.