• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.45-60
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• 2008

Here we consider the evaluation of the the dynamic component of the second order force due to wave diffraction by a circular cylinder analytically and numerically. The cylinder is fixed, vertical, surface piercing in water of finite uniform depth. The formulation of the wave-structure interaction is based on the assumption of a homogeneous, ideal, incompressible, and inviscid fluid. The nonlinearity in the wave-structure interaction problem arises from the free surface boundary conditions, namely, dynamic and kinematic free surface boundary conditions. We expand the velocity potential and free surface elevation functions in terms of a small parameter and then consider the second order diffraction problem. After deriving the pressure using Bernoulli's equation, we obtain the analytical expression for the dynamic component of the second order force on the cylinder by integrating the pressure over the wetted surface. The computation of the dynamic force component requires only the first order velocity potential. Numerical results for the dynamic force component are presented.

• 대한토목학회논문집
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• 제28권6B호
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• pp.691-696
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• 2008

본 연구에서는 자유수면 흐름에 적용할 수 있는 연직방향에 대해 좌표변환된 3차원 동수압 모형을 제시하였다. 제시한 모형은 자유수면과 동수압의 해석을 위하여, 2중 예측-수정(double predictor-corrector)방법을 적용하였다. 본 연구에서는 정확한 동역학적 경계조건(자유수면에서의 압력은 0인 조건)을 적용하는 방법을 검토하였고, 이 경계조건은 기존에 개발된 모형에 미소한 수정을 통하여 적용 가능함을 보여주었다. 본 연구에서 제시한 모형과 기존 모형의 계산결과를 비교하였을 때 동역학적 경계조건의 정확한 적용이 매우 중요함을 알 수 있다.

• 한국방재학회 논문집
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• 제10권1호
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• pp.103-109
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• 2010

본 연구에서는 자유수면 흐름에 적용할 수 있는 연직방향에 대해 좌표변환된 3차원 동수압 모형을 제시하였다. 제시한 모형은 자유수면과 동수압의 해석을 위하여, 2중 예측-수정(double predictor-corrector)방법을 적용하였다. 본 연구에서는 정확한 동역학적 경계조건(자유수면에서의 압력은 0인 조건)을 적용하는 방법을 검토하였고, 제시한 모형을 이용한 수치모의 결과를 해석해와 비교하여 본 연구에서 제시한 모형의 우수성을 검증하였다.

• Selected Papers of The Society of Naval Architects of Korea
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• 제2권1호
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• pp.63-78
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• 1994

This paper deals with the treatment of the open boundary in two-dimensional free-surface wave problems. Two numerical schemes are investigated for the implementation of the open boundary condition. One is to add the artificial damping term to the dynamic free-surface boundary condition, in which the determination of suitable damping coefficient and the damping zone is the most important. The other is a modified Orlanski's method, which is known to be very useful for the uni-directional waves. Using these two schemes, numerical tests have been conducted for a few typical free-surface wave problems. To obtain the numerical solution of the free-surface boundary value problem, the fundamental source-distribution method is used and the fully nonlinear free-surface boundary conditions are applied. The computed results are presented in comparison with those of others for the proof of practicality of these two schemes.

• Ocean Systems Engineering
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• 제14권3호
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• pp.301-314
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• 2024

In this study, the lift coefficient and wave deformations for a two-dimensional flat-plate in non-cavitating condition were computed using a closed-form (analytic) solution. This plate moves at a constant speed beneath a free surface in water of finite depth. The model represents the flat-plate using a lumped vortex element within the constraints of potential flow theory. The kinematic and dynamic free surface conditions were combined and linearized. This linearized free surface condition was then applied to get the total velocity potential. The method of images was utilized to account for the effects of finite depth in the calculations. The lift coefficient of the flat-plate and wave elevations on the free surface were calculated using the closed-form solution. The lift coefficients derived from the present analytic solution were validated by comparing them with Plotkin's method in the case of deep water. Wave elevations were also compared with those obtained from a numerical method. A comprehensive discussion on the impact of Froude number, submergence depth of flat-plate from the calm free surface, the angle of attack and the depths of finite bottom on the results - namely, lift coefficients and free surface deformations - is provided.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 춘계 학술대회논문집
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• pp.145-155
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• 1998

A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

• International Journal of Ocean System Engineering
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• 제1권1호
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.

• International Journal of Ocean System Engineering
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• 제2권1호
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• pp.32-36
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• 2012

This paper presents a comparison of potential and viscous computational codes for the water entry problem. A po-tential code was developed which adopted the boundary element method to solve the problem. A nonlinear free surface boundary condition was integrated to find new locations of free surface. The dynamic boundary condition was simplified by taking constant potential values for every time steps. The simplified dynamic boundary condition was applied in the new position of the free surface not at the mean level, which is the usual practice for linearized theory. The commercial code FLUENT was used to solve the water entry problem from the viscosity point of view. The movement of the air-liquid interface is traced by distribution of the volume fraction of water in a computational cell. The pressure coefficients were compared with each other, while experimental results published by other researchers were also examined. The characteristics of each method were discussed to clarify merits and limitations when they were applied to the water entry problems.

• Journal of Advanced Research in Ocean Engineering
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• 제2권1호
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• pp.1-11
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• 2016

The objective of this paper is to present an analytical solution in deep water waves and verify the validity of the theory (Shin, 2015). Hence this is a follow-up to Shin (2015). Instead of a variational approach, another approach was considered for a more accurate assessment in this study. The products of two coefficients were not neglected in this study. The two wave profiles from the KFSBC and DFSBC were evaluated at N discrete points on the free-surface, and the combination coefficients were determined for when the two curves pass the discrete points. Thus, the solution satisfies the differential equation (DE), bottom boundary condition (BBC), and the kinematic free surface boundary condition (KFSBC) exactly. The error in the dynamic free surface boundary condition (DFSBC) is less than 0.003%. The wave theory was simplified based on the assumption tanh $D{\approx}1$ in this paper. Unlike the perturbation method, the results are possible for steep waves and can be calculated without iteration. The result is very simple compared to the 5th Stokes' theory. Stokes' breaking-wave criterion has been checked in this study.

• Journal of Ship and Ocean Technology
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• 제6권2호
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• pp.37-50
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• 2002

In the present numerical simulation of viscous free surface flow around a ship, two-fluids in-compressible Reynolds-averaged Navier-Stokes equations with the standard $\textsc{k}-\varepsilon$turbulence model are discretized on a regular grid by using a finite volume method. A local level-set method is introduced for capturing the free surface movement and the influence of the viscous layer and dynamic boundary condition of the free surface are implicitly considered. Partial differential equations in the level-set method are discretized with second order ENO scheme and explicit Euler scheme in the space and time integration, respectively. The computational results for the Series-60 model with $C_B=0.6$ show a good agreement with the experimental data, but more validation studies for commercial complicated hull forms are necessary.