• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.470-474
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• 2016

Madsen et al. (2002)이 제안한 일차원 고차 Boussinesq 방정식에 대하여 불연속갤러킨 유한요소법(Discontinuous Galerkin Finite Element Method)을 적용하였다. 연속적인 Boussinesq 방정식에서 각 요소경계에 불연속을 허용할 수 있도록 공간차분하고, 시간방향으로 4차 Runge-Kutta 시간적분법, 각 요소사이에는 Lax-Friedrichs 수치흐름률을 사용하였다. 계산영역의 양쪽에 불필요한 파랑의 반사를 억제하도록 흡수층을 설치하였으며, 영역 내부에서 조파할 수 있도록 하였다. Luth et al.(1994)의 수중잠제 실험에 적용하여 관측값과 잘 일치함을 확인하였다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.2
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• pp.136-145
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• 2007

When waves propagating over an underwater shoal break at the top of the shoal, wave heights are drastically decreased in the downstream breaking zone, but a secondary current shooting downstream with strong velocity can be induced by the breaking waves themselves. In the case that an offshore structure is placed in the breaking zone, the estimation of wave farce purely based on the visible wave height may cause an under-design of the structure. Thus, for the safe design of the structure, the breaking wave induced current should be necessarily considered in the comprehensive estimation of design load. In the present study, Boussinesq equation model to calculate the wave height distribution and breaking wave induced current was set up and applied to the scheme of a hydraulic model test previously undertaken. Based on the results of the Boussinesq model, fluid forces acting on the model structure were calculated and compared with the experimental results. The importance of the breaking wave induced current was quantitatively assessed by comparing fluid forces with or without current.

• Ecology and Resilient Infrastructure
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• v.1 no.1
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• pp.1-7
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• 2014

In this study, a numerical simulation technique for coastal area where wave and current interactions are observed is proposed. Considering the spatial scale of coastal area and the coastal processes such as wave, current, shoaling, wave breaking, and inundation processes, boussinesq equation model is used. A depth-integrated transport model based on the consistent assumption with the boussinesq equation model is used for the prediction of solute transport. To solve the equations, finite volume method with an approximate riemann solver is used. The proposed model is applied to a coastal area and reasonable computational results are obtained.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.5
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• pp.1061-1071
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• 2015

In the present study, the Navier-Stokes (N-S) equations delineating water flows inside porous media were derived applying Reynolds transport theorem in order to provide a basis for analyzing water wave problems inside the porous media. Then, the derived N-S equations were compared with the same species of equations in existing researches. Based on the N-S equations, a set of Boussinesq equations was then derived in such a form that the dispersiveness and nonlinearity of water waves inside the porous media can be properly reproduced. Finally, numerical analyses were carried out to demonstrate the validity of the equations. The reflection and transmission coefficients of porous breakwaters were calculated and compared with the results of existing hydraulic experiments. The numerical results showed a rather sensitive dependency on the virtual mass coefficient of grains constituting the porous media. The selection of the coefficient with zero turned out to give nice agreements with numerical and experimental results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.23 no.4
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• pp.276-284
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• 2011

The rip current occurred at Haeundae beach was numerically investigated under directional random wave environment. The numerical simulation was performed using a fully nonlinear Boussinesq equation model, FUNWAVE which is capable of simulating nearshore circulation since it includes the effect of wave-induced momentum flux and horizontal turbulent mixing. The results of numerical simulation show the time-dependent evolution of the wave-induced nearshore circulation system (including rip current) that are caused by nonlinear transformation of directional irregular waves due to unique topography of Haeundae. From the results, it was found that rip current is well generated and developed where relatively lower wave height and relatively deeper water depth along the longshore direction, and sudden and strong events of rip current were observed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.2
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• pp.96-106
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• 2000

Though the recent years, large scale structures have been built on offshore for utilization of coastal ocean space as offshore airport and marine terminals. Sometimes, those big scale structures, however, happened to act as significant barriers against waves and severe beach erosion would take place on the coast. The present study deals nearshore topography changes affected by construction of an offshore structure with different distance from the shore. The series of three dimensional movable bed experiments have been examined in detail. Moreover, in order to make clear the relation of nearshore currents and local erosions behind offshore structure, the nearshore currents are calculated by Boussinesq equation model and compared with the same scale condition of the physical model experiments.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.26 no.5
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• pp.314-326
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• 2014

On 31 March 2007, the abnormal wave occurred along the western coast of Korea. In order to investigate the generation mechanism of abnormal waves and to understand the amplification process of the abnormal waves, the observed data were analyzed and one-dimensional numerical model experiments were performed by using both the linear shallow water equation and the linear Boussinesq equation models. Various types of pressure jump for the abnormal waves previously proposed by other researchers were reviewed. As a result, it was not possible to reproduce the abnormal waves from the previously proposed pressure jumps. In this study, we proposed a new form of pressure jump, and numerical simulations were performed in order to check the validity of the proposed pressure jump. The numerical results showed that the calculated period of abnormal waves and the maximum water elevations agreed reasonably well with those of the observations.

• Journal of the Society of Naval Architects of Korea
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• v.59 no.2
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• pp.64-71
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• 2022

In this paper, we simulate the collision of a solitary wave on a vertical wall in a uniform water channel and investigate the effect of damping on the amplitude attenuation. In order to take into account the damping effect, we introduce the Stokes damping whose dissipation is dependent on the velocity of wave motion on the surface of a thin layer of oil. That is, we use the improved Boussinesq equation with Stokes damping to describe the damped wave motion. Our work mainly focuses on the amplitude attenuation of a propagating solitary wave, which may depend on the Stokes damping together with the initial position and initial amplitude of the wave. We utilize the method of images and a powerful numerical tool (functional iteration method) for solving the improved Boussinesq equation, yielding an effective numerical simulation. This enables us to find the amplitudes of the incident wave and reflected one, whose ratio is a measure of the (wave) amplitude attenuation. Accordingly, we have shown that the reflection of a solitary wave by a vertical wall is dependent on not only the initial amplitude and position of a solitary but the Stokes damping.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.274-281
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• 2002

Numerical analysis for the Bragg reflection due to a sinusoidally and a doubly-sinusoidally varying seabeds was performed by using a couple of ordinary differential equations derived from the Boussinesq equations. Incident waves are a train of cnoidal waves. The effects of the dispersion and shape of seabed were investigated. It is shown that the reflection of a sinusoidally varying seabed is enhanced by increasing the dispersion and the amplitude of a seabed. The reflection of waves over a doubly-sinusoidally varying seabed can also be enhanced by increasing the amplitude of seabed decreasing the difference of wave numbers of seabed components.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.253-264
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• 2012

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in the mathematical physics via the (1+1)-dimensional Boussinesq equation by using the following two methods: (i) A further improved ($\frac{G}{G}$) - expansion method, where $G=G({\xi})$ satisfies the auxiliary ordinary differential equation $[G^{\prime}({\xi})]^2=aG^2({\xi})+bG^4({\xi})+cG^6({\xi})$, where ${\xi}=x-Vt$ while $a$, $b$, $c$ and $V$ are constants. (ii) The well known extended tanh-function method. We show that some of the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before which gives more exact solutions than the second method (ii).