• 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.

• 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.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.369-372
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• 2002

Under the assumption of potential flow, free-surface flows around a 2-dimensional hydrofoil are calculated by high-order spoctral/boundary-integral method. This method is one of the most efficient numerical methods by which the nonlinear interactions between hydrofoil and free-surface can be simulated in time-domain. Comparisons of the calculated free-surface profiles with other experimental results show relatively good agreements. As another example, free-surface flow generated by the heaving and translating hydrofoil is calculated and discussed.

• 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 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 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09b
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• pp.842-845
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• 2005

A method for the numerical simulation of two-dimensional free-surface flow resulting from the propagation of regular gravity waves over topography with arbitrary bottom shape is presented. The method is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. The formulation includes a boundary-fitted transformation, and is suitable for extension to incorporate large-eddy simulation (LES) and large-wave simulation (LWS) terms for turbulence and breaking wave modeling, respectively. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:20, two different inflow wave lengths and two different inflow wave heights. An absorption outflow zone is utilized and the results indicate minimum wave reflection from the outflow boundary. Over the bottom slope, lengths of waves in the linear regime are modified according to linear theory dispersion, while wave heights remain more or less unchanged. For waves in the nonlinear regime, wave lengths are becoming shorter, while the free surface elevation deviates from its initial sinusoidal shape.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.39 no.1
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• pp.27-32
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• 2003

Under the assumption of potential flow, free-surface flow around a hydrofoil is calculated by the high-order spectra1!boundary-integral method, This method is one of the most efficient numerical methods by which the nonlinear interactions between hydrofoil and free-surface can be simulated in time-domain. In this method. the wave potential which represents the nonlinear evolution of free-surface is solved by the high-order spectral method and the body potential which provides the effects of hydrofoil and shed vortex is solved by the boundary-integral method. The calculated free-surface profiles which are generated by a uniformly translating hydrofoil are compared with other experimental results. And they show relatively good agreements each other. As another example, free-surface flow generated by a heaving and translating hydrofoil is calculated and discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1455-1462
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• 2005

In this paper, we intend to introduce a nonlinear finite element method based on the fully nonlinear potential flow theory in order to simulate the large amplitude sloshing flow in two-dimensional baffled tank subject to horizontally forced excitation. The free surface is tracked by a direct time differentiation scheme with the four-step predictor-corrector time integration method. The flow velocity is accurately recovered from the velocity potential by second-order least square method. In order to maintain the finite element mesh regularity and total mass, the semi-Lagrangian surface tracking method with area conservation is applied. According to the numerical formulae, we perform the parametric experiments by varying the installation height and the opening width of baffles, in order to examine the effects of baffle on the nonlinear liquid sloshing. From the numerical results, the hydrodynamic characteristics of the large amplitude sloshing are investigated.

• Journal of Advanced Research in Ocean Engineering
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• v.4 no.4
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• pp.163-173
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• 2018

There are many issues in fluid structure interactions when dealing with the free surface flows in a sloshing tank. For example the problem of how yielding a highly nonlinear wave with a simple forced motion over a short duration is of concern here. Nonlinear waves are generated in a rectangular tank which is forced horizontally; its motion consists of a single cycle of oscillation. One of the objectives is to end up with a shape of the free surface yielding a wide range of critical flows by tuning few parameters. The configuration that is studied here concerns a plunging breaker accompanied with a critical jet where great kinematics are simulated. The numerical simulations are performed with a twodimensional code which solves the fully nonlinear free surface boundary conditions in Potential Theory.