• 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 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.

• 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 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.

• 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 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.

• Journal of Ship and Ocean Technology
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• v.8 no.2
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• pp.61-69
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• 2004

Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with other existing experimental results. Agreement between the experimental data and the computation results is good.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1517-1525
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• 2005

Liquid sloshing displays the highly nonlinear free surface fluctuation when either the external excitation is of large amplitude or its frequency approaches natural sloshing frequencies. Naturally, the accurate tracking of time-varying free surface configuration becomes a key task for the reliable prediction of the sloshing time-history response. However, the numerical instability and dissipation may occur in the nonlinear sloshing analysis, particularly in the long-time beating simulation, when two simulation parameters, the relative time-increment parameter a and the fluid mesh pattern, are not elaborately chosen. This paper intends to examine the effects of these two parameters on the potential-based nonlinear finite element method introduced for the large amplitude sloshing flow.

• 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 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.