• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.260-265
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• 1994

A new set of elliptic wave equations describing the deformations of irregular waves on a large-scale current field in water of irregular depth is given, and using finite difference scheme an efficient numerical method is also presented. The elliptic equations are solved in a similar way to Initial value problem. This method is extensively used for the calculation of wave spectral transformation. and computation results agree very well with experimental data (Hiraishi, 1991). Finally numerical examples are presented concerning the interactions between waves and currents over a mildly sloping beach and also over a mound.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.156-161
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• 1993

Structures built in the coastal area often cause unexpectedly severe shoreline change on the adjacent beaches. Therefore, beach evolution is one of the most important problem in the coastal engineering. Beach evolution in the coastal area consisted of wave transform model and sediment transport model. Ebersoale's elliptic mild slope equation which considered the effect of combind wave refraction and perline and Dean's one line theory for the sediment transport model were used in this study. Kwangan beach was selected as study area and field observations were done. Numerical simulation for beach evolution in the Kwangan beach was performed and shoreline change predictions were suggested as results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.2
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• pp.164-173
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• 1994

A numerical model to solve mild slope equation is developed by use of a preconditioned conjugate gradient method (PCGM). In the present paper. accurate boundary conditions and a better preconditioner are employed which are improved from the existing method of Panchang et al. (1991). Computational procedures are focused on weakly nonlinear waves, and emerged problems to make a more accurate model are discussed. The results of model are tested against laboratory results of both circular and elliptic shoals. Model results of wave amplitude show excellent agreement with laboratory data and thes thus model can be used as a powerful tool to calculate wave transformation in shallow waters with complex bathymetry.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.22-30
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• 1989

Wave propagation is changed by the effect of shoaling, current-depth refraction and shelter-ing etc. To solve these problems. numerous models have been developed. In the present study, a coordinate system is proposed based on the wave ray equation with the wave number equation including diffraction effects . The governing equation for the study was derived from the mild slope wave equation in non-steady state, including current effects (Kirby, 1986a) and trans-formed into an orthogonal curvilinear coordinate system on the basis of the wave ray equation. To obtain a numerical solution, an explicit finite difference scheme was used, and solved by the relaxation method. This model was tested for various cases: Firstly a submersed circular shoal and a constant unit depth. Secondly a submerged elliptic shoal on a slope, and finally a breakwater harbour with obliquely incident waves on a slope. The model was found to simulate the experimental results and other theoretical results in wave height and wave angle fairy well, and the applicability of the model around an arbitrary shaped coastal structure was also verified. To demonstrate the general usefullness of the present approach , the model is to be applied to a field situation with a complex bed topography.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.1
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• pp.10-17
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• 1992

An elliptic finite difference numerical model is presented for the effective calculation of wave transformation on the water of slowly varying sea bed with currents. Elliptic governing equation has been used, which is derived by Joeng(1990) and Chae et al(1989). Numerical results are compared with analytic solution and laboratory data(Ito and Tanimoto, 1972), and show good agreement. This model is very efficient for modelling large area because of no numerical stable condition and high calculation speed. The capability and utility of the model are illustrated by application to current coexisting area.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.3
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• pp.216-225
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• 1994

By use of laboratory experiment data set for an elliptic shoal by Berkhoff et al. (1982), both accuracy and Performance tests of numerical results between PCGM (Preconditioned Conjugate Gradient Method) and PA(Parabolic Approximation) are compared. Although both results show good agreement with the experimental data the PA model gives better reproduction of the relatively high amplitudes in the section 4-5 downwave of the shoal, in comparison with the PCGM. The PA model has been proved to be a useful tool for predicting wave transformationsin large shallow water region, but it can be applied only to the case of negligible reflection. On the other hand, there is a need to improve the computational efficiency of the PCGM model which is a finite difference scheme directly derived from the mild slope equation and can handle reflection. By taking the results of th PA model as an input data of the PCGM, the CPU time can be reduced by about 40%.

• Journal of Ocean Engineering and Technology
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• v.24 no.6
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• pp.51-60
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• 2010

In this study, the performance evaluation of a conventional wave resonator at the entrance of a port or a pier against secondary undulation has been performed using 2D hydrodynamic modeling within port. A wave resonator has been designed for the attenuation of the secondary undulation induced by the long-periodic waves. The controlled performance of the wave resonator has been numerically investigated for CGWAVE MODULE of finite-element model of SMS (Surface water Modeling System) based on the elliptic mild-slope wave equation. SMS was verified though the comparisons with analytical solution performed by Ippen and Goda (1963). Also, It was confirmed that a wave resonator of a rectangular model harbor is effective enough to control the secondary undulation when it compares variation of water level with the case of no resonance system. From the above results, amplification phenomenon induced by long-period waves transferred from 1900 sec to 2100 sec when it applied a wave resonator in Busan Gamcheon Port which is a deep-sea. And it was confirmed that a wave resonator of Pohang New Port attenuates largely long-period waves which are within the range of 300 sec induced by long-period motion of the moored ship.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.2
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• pp.146-150
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• 1996

The waves are most important dynamical factors for the analyses of structural stability and topographical changes on coastal engineering field. However, wind-generated waves are very irregular in shape and transformed through refraction, diffraction and shoaling when they propagate into shallow water where bottom topography and water depth vary significantly. Recently, Vincent and Briggs (1989) reported hydraulic model experiments for the transformation of monochromatic and directionally-spread irregular waves passing over a submerged elliptical mound. They concluded that for the case of combined refraction-diffraction of waves by a shoal, the propagation characteristics of the irregular and equivalent regular wave conditions can be vastly different. On the irregular wave transformation have been made theoretical and numerical studies for several years. Although theoretical and laboratory studies on wave transformation have progressed considerably, field measurement and comparison of numerical results with related theories are still necessary for the prediction of the phenomena in reality. In this study, field measurement of both incident and transformed waves in Youngil Bay were made using various kinds of equipments, and numerical computations were made on the transformed frequency spectra of large waves propagating over the shoal using Chae and Jeong's (1992) elliptic model. It is shown that this model results agree very well with field data, and thus the applicability of the model is now validated.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.61-66
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• 2006

Two iterative solvers are applied to solve the modified mild slope equation. The elliptic formulation of the governing equation is selected for numerical treatment because it is partly suited for complex wave fields, like those encountered inside harbors. The requirement that the computational model should be capable of dealing with a large problem domain is addressed by implementing and testing two iterative solvers, which are based on the Stabilized Bi-Conjugate Gradient Method (BiCGSTAB) and Generalized Conjugate Gradient Method (GCGM). The characteristics of the solvers are compared, using the results for Berkhoff's shoal test, used widely as a benchmark in coastal modeling. It is shown that the GCGM algorithm has a better convergence rate than BiCGSTAB, and preconditioning of these algorithms gives more than half a reduction of computational cost.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.3
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• pp.135-140
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• 1999

To simulate the wave transformation by an energy dissipation region, a numerical model is suggested by discretizing the elliptic mild-slope equation. Generalized conjugate gradient method is used as solution algorithm to apply parabolic approximation to open boundary condition. To demonstrate the applicabil-ity of the numerical procedure suggested, the wave scattering by a circular damping region is examined. The feature of reflection in front of the damping region is captured clearly by the numerical solution. The effect of the size of dissipation coefficient is examined for a rectangular damping region. The recovery of wave height by diffraction occurs very slowly with distance behind the damping region.