• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.3
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• pp.240-246
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• 2002

Hydraulic model experiments were conducted fur a series of regular and uni-directional irregular waves propagating over a submerged elliptic shoal. Two different sets of experiments have been studied； one considers regular wave transformation with no breaking, and the other considers uni-directional irregular wave with partial breaking on top of the shoal. The numerical experiments are also performed using a numerical model based on the parabolic approximation equation. The result of the numerical experiments are compared with that of hydraulic experiments.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.93-99
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• 1998

Parabolic approximation and sponge layer are applied as open boundary condition for elliptic finite difference wave model. Generalized conjugate gradient method is used as a solution procedure. Using parabolic approximation a large part of spurious reflection is removed at the spherical shoal experiment and sponge layer boundary condition needs more than 2 wave lengths of sponge layer to give similar results. Simulating the propagation of waves on a rectangular harbor, it is identified that iterative scheme can be applied easily for the non-rectangular computational region.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.6
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• pp.565-573
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• 2007

The effect of wave and current interactions on irregular wave transformation over a submerged elliptic shoal is investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction-diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269-284]. The numerical simulations are conducted by a combination of REF/DIF S(a wave model) and SHORECIRC(a current model) and a time dependent phase-resolving wavecurrent model, FUNWAVE. In the simulations, the breaking-induced currents defocus waves behind the shoal and bring on a wave shadow zone that shows relatively low wave height distributions. The computed results of the combined model system agree better with the measurements than the computed results obtained by neglecting wave-current interaction do. In addition, the results of FUNWAVE show a good agreement with the measurements. The agreement indicates that it is necessary to take into account the effect of breaking-induced current on wave refraction when wave-breaking occurs over a submerged shoal.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.1
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• pp.39-44
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• 2009

To improve the accuracy of numerical simulation of wave trans- formation across the surf zone, nonlinear shoaling effect based on Shuto's empirical formula and breaking mechanism are induced in the elliptic modified mild slope equation. The variations of shoaling coefficient with relative depth and deep water wave steepness are successfully reproduced and show good agreements with Shuto's formula. Breaking experiments show larger wave height distributions than linear model due to nonlinear shoaling but breaking mechanism shows a little bit larger damping in 1/20 beach slope experiment.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.120-127
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• 1998

An Elliptic model for calculating the combined refraction/diffraction of monochromatic linear waves is developed, including a term which allows for the dissipation of wave energy. Conjugate gradient method is employed as a solution technique. Wave height variations are calculated for localized circular and rectangular dissipation areas. It is shown that the numerical results agree very well with analytical solution in the case of circular damping region. The localized dissipation area creates a shadow region of low wave energy and the recovery of wave height by diffraction occurs very slowly with distance behind the damping region.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.6
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• pp.557-564
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• 2007

The effect of wave and current interactions on regular wave transformation over a submerged elliptic shoal is investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction-diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269-284]. The numerical simulations are conducted by constituting two numerical model systems: a combination of SWAN(a wave model) plus SHORECIRC(a current model) and a combination of REF/DIF 1(a wave model) plus SHORECIRC. A time dependent phase-resolving wave-current model, FUNWAVE, is also utilized to simulate the experiment. In the simulations, the breaking-induced currents defocus waves behind the shoal and bring on a wave shadow zone that shows relatively low wave height distributions. The computed results of the two model systems agree better with the measurements than the computed results obtained by neglecting wave-current interaction do. However, it is found that the radiation stresses for standing waves are misevaluated in the wave models. In addition, the results of FUNWAVE show very good agreement with the measurements. The agreement indicates that it is necessary to take into account the effect of breaking-induced current on wave refraction when wave-breaking occurs over a submerged shoal.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.619-633
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• 1994

A wave deformation model for general purpose combined refraction, diffraction, and breaking is developed in the shallow water. A parabolic approximation equation considered a higher order diffraction term is derived from the previous mild slope equation. A wave energy dissipation term due to bottom friction and breaking is introduced from the turbulence model. The Crank-Nicoloson implicit scheme is used in the numerical calculation, then the solutions are compared with the various hydraulic experiment data in the circular, the elliptic shoal, and the surf zone. The wave height decay in the surf zone is sensitively affected by the incident wave steepness, and the wave height variation around the elliptic shoal is well explained by the non-linear dispersion relation and the wave energy dissipation term. The model is also applied to a field coastal area and reasonable results are obtained.

• Journal of Ocean Engineering and Technology
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• v.18 no.4 s.59
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• pp.40-45
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• 2004

An efficient numerical model of the modified mild slope equation, based on the robust iterative method is presented. The model developed is verified against other numerical experimental results, related to wave reflection from an arc-shaped bar and wave transformation over a circular shoal. The results show that the modified mild slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild slope equation model yeilds large errors, as the mild slope assumption is violated.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.3
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• pp.231-238
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• 1992

Error vector propagation method is applied to the elliptic mild slope equation in order to reduce the computation time. Results from the elliptic, parabolic, and hyperbolic models are compared with experimental data for an elliptic shoal. Also, results of the elliptic and hyperbolic models are compared with experimental data for a detached breakwater. As a result of applying this model. it is concluded that the present model satisfactorily reduces the computation time compared with other numerical models. In the accuracy of solutions, there are some oscillations but the trend compares well with other models.