• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.171-182
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• 2005

An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures, the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the non-homogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.381-384
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• 2002

The free surface flow problem has been one of the most interesting and challenging topic in the area of the naval ship hydrodynamics and ocean engineering field. The problem has been treated mainly in the scope of the potential theory and its governing equation is well known Laplace equation. But in general, the exact solution to the problem is very difficult to obtain because of the nonlinearlity of the free surface boundary condition. Thus the linearized free surface problem has been treated often in the past. But as the computational power increases, there is a growing trend to solve the fully nonlinear free surface problem numerically. In the present study, a time-dependent finite element method is developed to solve the problem. The initial-boundary problem is formulated and replaced by an equivalent variational formulation. Specifically, the computations are made for a highly nonlinear flow phenomena behind a transom stern ship and a vertical strut piercing the free surface.

• Ocean Systems Engineering
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• v.7 no.4
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• pp.371-398
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• 2017

Calm water wave resistance plays a very important role in ship hull design. Numerical methods are meaningful for this reason. In this study, two prevailing methods, the Neumann-Kelvin and the Rankine source method, were implemented and compared. The Neumann-Kelvin method assumes linearized free surface boundary condition and only needs to mesh the hull surface. The Rankine source method considers nonlinear free surface boundary condition and meshes both the ship hull surface and free surface. Both methods were implemented and the wave resistance of a Wigley III and three Series 60(Cb=0.6, 0.7, 0.8) hulls were analyzed. The results were compared with experimental results and the merits of both numerical techniques were quantified. Based on the results, it is concluded that the Rankine source method is more accurate in the calculation of the wave-making resistance. Using the Neumann-Kelvin method, it is found to be easier to model the hull and can be used for slender ships to solve problems like wave current coupling calculation.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.90-100
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• 2006

A digital wave tank (DWT) simulation technique has been developed by authors to investigate the interactions of fully nonlinear waves with 3D marine structures. A finite-difference/volume method and a modified marker-and-cell (MAC) algorithm have been used, which are based on the Navier-Stokes (NS) and continuity equations. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique or the Level-Set (LS) technique developed for one or two fluid layers. In this paper, some applications for various engineering problems with free-surface are introduced and discussed. It includes numerical simulation of marine environments by simulation equipments, fully nonlinear wave motions around offshore structures, nonlinear ship waves, ship motions in waves and marine flow simulation with free-surface. From the presented simulations, it seems that the developed DWT simulation technique can handle various engineering problems with free-surface and reliably predict hydrodynamic features due to the fully-nonlinear wave motions interacting with such marine structures.

• Journal of Ship and Ocean Technology
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• v.8 no.3
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• pp.8-17
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• 2004

A numerical method is developed for computing the free surface flows around a transom stern of a ship at a high Froude number. At high speed, the flow may be detached from the flat transom stern. In the limit of the high Froude number, the problem becomes a planning problem. In the present study, we make the finite-element computations for a transom stern flows around a wedge-shaped floating ship. The numerical method is based on the Hamilton's principle. The problem is formulated as an initial value problem with nonlinear free surface conditions. In the numerical procedures, the domain was discretized into a set of finite elements and the numerical quadrature was used for the functional equation. The time integrations of the nonlinear free surface condition are made iteratively at each time step. A set of large algebraic equations is solved by GMRES(Generalized Minimal RESidual, Saad and Schultz 1986) method which is proven very efficient. The computed results are compared with previous numerical results obtained by others.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.4
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• pp.38-44
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• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• 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.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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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.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.2
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• pp.8-19
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• 1998

Nonlinear flow characteristics of a hydrofoil running under the free surface are investigated based on potential flow theory using singularity distribution techniques. Following Hess & Smith's method[12], sources and vortices are distributed on the surface of the foil and Rankine sources are distributed at a distance above the undisturbed free surface to solve the nonlinear free surface waves(so called Raised Panel Method). Using the linearized Neumann-Kelvin solution, the conversed solutions which rigidly satisfy the nonlinear free surface condition is obtained through an iterative technique. It is validated that the nonlinear solutions are compared with Duncan's experimental results(NACA 0012, $\alpha=5^{\circ}$), showing good correlations with each other. At a very shallow submergence and a very high speed the converged solutions are obtained. As the speed increases higher, it is shown that the difference between the nonlinear and linear solutions are trivial. Finally, the effects of the camber and thickness on the nonlinear flow characteristics of the foil are investigated.