• 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.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.497-518
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• 2021

In this study, a new method for treating the wall boundary in smoothed particle hydrodynamics (SPH) is proposed to simulate free surface flows effectively. Unlike conventional methods of wall boundary treatment through boundary particles, in the proposed method, the wall boundary condition is directly imposed by adding boundary truncation terms to the mass and momentum conservation equations. Thus, boundary particles are not used in boundary modeling. Doing so, the wall boundary condition is accurately imposed, boundary modeling is simplified, and computation is made efficient without losing stability in SPH. Performance of the proposed method is demonstrated through several numerical examples: dam break, dam break with a wedge, sloshing, inclined bed, cross-lever rotation, pulsating tank and sloshing with a flexible baffle. These results are compared with available experimental results, analytical solutions, and results obtained using the boundary particle method.

• Journal of Korean Society of Water and Wastewater
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• v.25 no.5
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• pp.627-634
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• 2011

In the present study, the flow behaviors of square jets surface discharged and submerged discharged into shallow water were each simulated using computational fluid dynamics, and the results were compared. As for the verification of the models, the results of the hydraulic experiment conducted by Sankar, et al. (2009) were used. According to the results of the verification, the present application of computational fluid dynamics to the flow analysis of square jets discharged into shallow water was valid. As for the wall jet, which is one form of submerged discharges, at the bottom wall boundary, the peak velocity of the jet rapidly moved from the center of the jet to the bottom wall boundary due to the restriction of jet entrainment and the no-slip condition of the bottom wall boundary, and, as for the surface discharge, because jet entrainment is limited on the free water surface, the peak velocity of the jet moved from the center of the jet to the free water surface. This is because jet entrainment is restricted at the bottom wall boundary and the surface so that the momentum of the central core of the jet is preserved for considerable time at the bottom wall boundary and the surface. In addition, due to the effect of the bottom wall boundary and the free water surface, the jet discharged into shallow water had a smaller velocity diminution rate near the discharge outlet than did the free jet; at a location where it was so distant from the discharge outlet that the vertical profile of the velocity was nearly equal (b/x =20~30), moreover, it had a far smaller velocity diminution rate than did the free jet due to the effect of the finite depth.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.307-316
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• 2021

We provide a gap theorem of Simons' type for free boundary minimal and constant mean curvature surfaces in the unit ball in 3-dimensional Euclidean space.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.979-982
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• 2003

In this study, because of change in electromagnetic force, deformation of the free surface motion of a magnetic fluid is changed. Deformation of the free surface motion of a magnetic fluid for the change in electromagnetic force is discussed and carried out theoretically and experimentally on the basis of Rosensweig Ferrohydrodynamic Bernoulli Equation. Objective of this study explicates free surface motion by electromagnetic force and planes to designed controller. To control free surface of magnetic fluid, it embody designed two-dimensional free surface form of magnetic fluid. By using this characteristics, they applied to oscillator for surface control, flow control, boundary layer control. Strength of magnetic field and height of free surface of magnetic fluid measure as a hall-effect sensor. As performing height control of magnetic fluid, the result will be presented possibility of free surface deformation control.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.1
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• pp.41-49
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• 1997

Computational results from Navier-Stokes equations are presented for the Stokes-wave/flat-plate boundary-layer and wake for small wave steepness(Ak=0.01), including exact and approximate treatments of the viscous free-surface boundary conditions. The macro-scale flow indicate that the variations of the external-flow pressure gradients cause acceleration or deceleration of the streamwise velocity component and alternating direction of the cross flow. Remarkably, the wake displays a greater response, i.e., a bias with regard to favorable as compared to adverse pressure gradients. The micro-scale flow indicates that the free-surface boundary conditions have a profound influence over the boundary layer and near/intermediate wake. Order-of-magnitude estimates are conformed to the computational results. And appreciable errors are introduced through approximations to the free-surface boundary conditions.

• Journal of Mechanical Science and Technology
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• v.19 no.12
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• pp.2231-2244
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• 2005

An efficient boundary-based optimization technique is applied in the numerical computation of free surface flow problems, by reformulating them into the equivalent optimal shape design problems. While the sensitivity in the boundary method has mainly been calculated using the boundary element method (BEM) as an analysis means, the finite element method (FEM) is used in this study because of its popularity and easy-to-use features. The advantage of boundary method is that the design velocity vectors are needed only on the boundary, not over the whole domain. As such, a determination of the complicated domain design velocity field, which is necessary in the domain method, is eliminated, thereby making the process easy to implement and efficient. Seepage and supercavitating flow problem are chosen to illustrate the accuracy and effectiveness of the proposed method.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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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.

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.175-187
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• 2020

The theories having been developed thus far account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In this paper, the effect of surface on the axial buckling and free vibration of nanobeams is studied using various refined higher-order shear deformation beam theories. Furthermore, these theories have strong similarities with Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and expressions of the resultant stress. The equations of motion and boundary conditions were derived from Hamilton's principle. The resultant system of ordinary differential equations was solved analytically. The effects of the nanobeam length-to-thickness ratio, thickness, and modes on the buckling and free vibration of the nanobeams were also investigated. Finally, it was found that the buckling and free vibration behavior of a nanobeam is size-dependent and that surface effects and surface energy produce significant effects by increasing the ratio of surface area to bulk at nano-scale. The results indicated that surface effects influence the buckling and free vibration performance of nanobeams and that increasing the length-to-thickness increases the buckling and free vibration in various higher-order shear deformation beam theories. This study can assist in measuring the mechanical properties of nanobeams accurately and designing nanobeam-based devices and systems.