• Journal of Ocean Engineering and Technology
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• v.4 no.1
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• pp.62-70
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• 1990

Cauchy의 적분공식을 복소속도(complex velocity)에 적용하여 포텐시얼 유동을 해석하는 복소경계요소법이 개발되었다. 이 결과로 얻어지는 적분방정식은 경계면에서의 접선속도(tangential velocity)와 법선속도(normal velocity)의 함수로 주어진다. 자유수면에서의 접선속도의 시간변화(evolution of tangential velocity)를 수식화하기 위하여 새로운 비선형 동역학적 자유수면경계조건(nonlinear dynamic free surface boundary condition)을 유도하였다. 복소포텐시얼 대신 복소속도를 이용하는 이 방법은 유장내의 특이점(field singularity)을 용이하게 고려할 수 있으며, 수치미분없이 직접 경계면에서의 유속을 해로서 구하게 된다. 그러나 자유수면이 존재하는 문제의 경우에는, 자유수면에서의 동역학적 경계조건을 만족 시키기 위한 계산과정에 접선 벡타의 변화량을 추정하는 것이 포함되게 되어, 계산과정이 다소 복잡하게 된다.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.2 s.42
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• pp.71-80
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• 2005

The solution to a liquid sloshing problem is challenge to the field of engineering. This is not only because the dynamic boundary condition at the free surface is nonlinear, but also because the position of the free surface varies with time in a manner not known a priori. Therefore, this nonlinear phenomenon, which is characterized by the oscillation of the unrestrained free surface of the fluid, is a difficult mathematical problem to solve numerically and analytically. In this study, three-dimensional boundary element method(BEM), which is based on the so-called an arbitrary Lagrangian-Eulerian(ALE) approach for the fluid flow problems with a free surface, was formulated to solve the behavior of the nonlinear free surface motion. An ALE-BEM has the advantage to track the free surface along any prescribed paths by using only one displacement variable, even for a three-dimensional problem. Also, some numerical examples were presented to demonstrate the validity and the applicability of the developed procedure.

• Journal of Navigation and Port Research
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• v.30 no.8 s.114
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• pp.631-636
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• 2006

In this paper, the wave pattern around the hull with the transom stern advancing on the free surface with a constant speed was taken into consideration. To solve the problem the numerical analysis program was developed using Rankine source panel method based on potential flow analysis technique. The non-linearity of the free surface boundary conditions was fully satisfied. To verify the validity of the developed program the numerical calculations for Athena hull and KCS(KRISO container ship) hull was performed. The results of the numerical computation was compared with the ones of the model test experiment.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.3
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• pp.204-211
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• 1993

Boundary element method is applied to simulate nonlinear water waves using Green's identity formula in a numerical wave flume. A system of linear equations is formulated from the governing equation and free surface boundary conditions in order to calculate velocity potential and water surface elevation at each nodal point. The velocity square terms are included in the dynamic free surface boundary condition. The free surface is treated as a moving boundary. the vertical variation of velocity potential being considered in calculating the time derivative of the velocity potential at the free surface. The present method is applied to simulate solitary wave and Stokes 2nd order wave, and shows excellent agreements with their theoretical values.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.29 no.1
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• pp.41-46
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• 2005

In this paper, the flow phenomena and free surface wave pattern around the hull with a transom stern advancing on the free surface in steady state had been studied and the numerical analysis program had been developed using Rankine source panel method based on potential flow analysis in which the non-linearities of the free surface boundary conditions had been fully satisfied. To verify the validity of the developed program the numerical calculations for Athena hull and KCS(KRISO container ship) hull had been performed and the results of the numerical computation had been compared with the ones of the model test experiment.

• Journal of Korean Port Research
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• v.12 no.1
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• pp.87-93
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• 1998

For the calculation of the free-surface elevation, a new finite difference scheme is studied where the third derivative term for the wave elevation is artificially added in the Eulerian expression of the free-surface boundary condition. The paper presents a comparative analysis with simulations performed by the classical MAC method. More schematic computations are carried out by changing the submergence-depth and angle-of-attack. The present study shows that this new method is very efficient for the simulation of free-surface elevation around the trailing edge.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.23 no.5
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• pp.335-344
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• 2011

A curvilinear non-hydrostatic free surface model is developed to investigate nonlinear wave interactions in a circular channel. The proposed model solves the unsteady Navier-Stokes equations in a three-dimensional domain with a pressure correction method, which is one of fractional step methods. A hybrid staggered-grid layout in the vertical direction is implemented, which renders relatively simple resulting pressure equation as well as free surface closure. Numerical accuracy with respect to wave nonlinearity is tested against the fifth-order Stokes solution in a two-dimensional numerical wave tank. Numerical applications center on the evolution of nonlinear waves including diffraction and reflection affected by the curvature of side wall in a circular channel comparing with linear waves. Except for a highly nonlinear bichrmatic wave, the model's results are in good agreement with superimposed analytical solution that neglects nonlinear effects. Through the numerical simulation of the highly nonlinear bichramatic wave, the model shows its capability to investigate the evolution of nonlinear wave groups in a circular channel.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.80-86
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• 1994

A numerical method for simulations of inviscid incompressible flow fields around a ship advancing on the free surface is developed. A body fitted coordinate system, generated by numerically solving elliptic type partial differential equations is used to conform the ship and free surface configurations. Three dimensional Euler equations transformed to the non-staggered body fitted coordinate system are discretised by finite difference method. Time and spatial derivatives are discretised by forward and centered differencings, respectively, and artificial dissipations are added to discretised convection terms for improvements of numerical stability. At each time steps, free surface elevations are recomputed to satisfy nonlinear free surface conditions. Poisson equations for pressure field are solved iteratively and the velocity field for next time step is extrapolated. To verify the developed numerical method, flow fields around a Wigley model are simulated(Fn=0.250-0.408) and compared with experimental data to show good agreements.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.1
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• pp.54-62
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• 2008

A new solution method was developed to solve the free surface flow around a hull and named as 'Variable Free Surface Panel Method'. In the method the non-linearity of the free surface boundary conditions was fully taken into account and the raised panel method was employed to effectively solve the problem. The transom stern flow was also considered and the panel on the hull was generated using the panel cutting method. Numerical calculations were performed for KCS(KRISO Container Ship) hull form and compared with the experimental data to confirm the validity of the method. The comparison with the conventional free surface panel method was also accomplished. It is confirmed that new method gives more reliable results than the conventional method.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.114-131
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• 1992

In the present work, a two-dimensional boundary-value problem for a large amplitude motion is treated as an initial-value problem by satisfying the exact body-boundary and nonlinear free-surface boundary conditions. The present nonlinear numerical scheme is similar to that described by Vinje and Brevig(1981) who utilized the Cauchy's theorem and assumed the periodicity in the horizontal coordinate. In the present thesis, however, the periodicity in the horizontal coordinate is not assumed. Thus the present method can treat more realistic problems, which allow radiating waves to infinities. In the present method of solution, the original infinite fluid domain, is divided into two subdomains ; ie the inner and outer subdomains which are a local nonlinear subdomain and the truncated infinite linear subdomain, respectively. By imposing an appropriate matching condition, the computation is carried out only in the inner domain which includes the body. Here we adopt the nonlinear scheme of Vinje & Brevig only in the inner domain and respresent the solution in the truncated infinite subdomains by distributing the time-dependent Green function on the matching boundaries. The matching condition is that the velocity potential and stream function are required to be continuous across the matching boundary. In the computations we used, if necessary, a regriding algorithm on the free surface which could give converged stable solutions successfully even for the breaking waves. In harmonic oscillation problem, each harmonic component and time-mean force are obtained by the Fourier transform of the computed forces in the time domain. The numerical calculations are made for the following problems. $\cdot$ Forced harmonic large-amplitude oscillation(${\omega}{\neq}0,\;U=0$) $\cdot$ Translation with a uniform speed(${\omega}=0,\;U{\neq}0$) The computed results are compared with available experimental data and other analytical results.