• Honam Mathematical Journal
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• v.30 no.2
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• pp.391-397
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• 2008

The existence of solutions and the occurrence of a Hopf bifurcation for the free boundary problems with Pushchino dynamics was shown in [1]. In this paper, we shall show a Hopf bifurcation occurs for the free boundary for Pushchino dynamics with a spatial dependency.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.7-14
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• 2004

The existence of solutions and the occurence of a Hopf bifurcation for the free boundary problem with Pushchino dynamics was shown in [3]. In this paper we shall show a Hopf bifurcation occurs for the free boundary which is given by (1).

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.25-40
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• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.159-166
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• 2000

Non-destructive out-hole tests, impact-echo and impact-response are widely applied to evaluate integrity of drilled shafts. In these tests, vibratory motions of drilled shafts are interpreted, which induced by impacts on the shaft head. In applying the tests to evaluating integrity of shaft, it has been attended whether the tests have resolutions enough to distinguish existence of slime at between the shaft end and a bearing soil deposit. To distinguish existence of slime by tests, modes of shaft vibrations need to be reasonably interpreted, which generally vary according to a shaft boundary condition such as, a free-free or a free-fixed condition. The boundary condition of a shaft is, however, found to be significantly affected by stiffness of soil deposits around shaft as well as penetration depths of shaft into a bearing soil deposit. Thus, these effects on the boundary condition of a shaft should be considered reasonably in interpreting test results to decide the existence of slime. To investigate the effects, in this study, vibratory motions of shafts constructed in various soil conditions and end penetration depths are examined analytically. Based on the studies, variations of boundary condition are characterized in terms of soil stiffness contrast between a shaft perimeter and a shaft end, and also the ratio of a penetration depth to a shaft length. The results can be applied to verify the applicability of tests to identify the slime.

• Journal of Advanced Research in Ocean Engineering
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• v.2 no.1
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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.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.61-69
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• 2000

The free-surface boundary conditions are persistent problem in elastic wave equation modeling by finite-difference method, which can be summarized with the degradation of the accuracy of the solution and limited stability range in Poisson's ratio. In this paper, we propose the mid-point averaging scheme as an alternative way of implementing the free-surface boundary conditions, and present the solution to Lamb's problem to verify our approach.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.233-243
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• 2019

In this paper, numerical and experimental studies are performed to investigate the liquid impact on a free falling wedge. In the numerical simulation, the structure is assumed to be rigid and the elastic response is ignored. The fully nonlinear coupling between wedge and water is considered by an auxiliary function method based on the Boundary Element Method (BEM). At the intersection of the wedge surface and liquid surface, two coincident nodes are used to decouple the boundary conditions. The Eulerian free surface conditions in the local coordinate system are adopted to update the deformed free surface. In the experiments, five pressure sensors are fixed on each side of the wedge which is released from an experimental installation. Steel and aluminum wedges that have different structural elasticity are used in the experiments to investigate the influence of structural elasticity on the impact force. Numerical results are compared with experimental data and they agree very well. The influence of fluid gravity, body mass, initial entry speed and deadrise angle on the impact pressure are further investigated.

• Bulletin of the Society of Naval Architects of Korea
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• v.19 no.2
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• pp.13-18
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• 1982

The method of Rankine source distribution is emerging as a powerful yet simple alternative for the solution of complicated free surface problems. But it has been uncertain whether the radiation condition could be satisfied exactly by distributing the simple sources on the free surface only. In this paper, it is proved rigorously that the Rankine sources, whose intensities are varying sinusoidally along the axis satisfying the free surface boundary condition, generate the radiation waves both in the infinite and finite-depth flows. A formula is derived to give the upper and lower bounds of the errors in the induced velocity computation that will be introduced by truncating the extent of source distribution on the free surface. Since the truncation is inevitable in the numerical analysis, this formula may be used as a criterion to limit the position of the field points, where velocity computation is made, away from the truncation boundary. A typical analysis shows that the maximum error will be 3.4 percent of the exact induced velocity when the field point is on the free surface two wave lengths away from the truncation boundary.

• 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.