• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.12 no.3
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• pp.133-141
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• 2007

A finite element model is developed for the extended Boussinesq equations that is capable of simulating the dynamics of long and short waves. Galerkin weighted residual method and the introduction of auxiliary variables for 3rd spatial derivative terms in the governing equations are used for the model development. The Adams-Bashforth-Moulton Predictor Corrector scheme is used as a time integration scheme for the extended Boussinesq finite element model so that the truncation error would not produce any non-physical dispersion or dissipation. This developed model is applied to the problems of solitary wave propagation. Predicted results is compared to available analytical solutions and laboratory measurements. A good agreement is observed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.1
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• pp.21-31
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• 2005

In this study, derivation is made of a one-grid source function for the extended Boussinesq equations of Nwogu (1993) in order to generate nonlinear waves internally. The energy velocity approach used in the line source method is verified analytically by the fractional step splitting method. The source function method is verified by generating accurately nonlinear waves as well as linear waves for horizontally one-dimensional cases. It is found that numerical solutions by the source function method are the same as those by the line source method.

• Journal of Ocean Engineering and Technology
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• v.31 no.5
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• pp.346-351
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• 2017

The aim of this paper is to apply the Crowhurst-Zhenquan scheme to one-dimensional Madsen-Sørensen extended Boussinesq equations. In order to verify the application of the aforementioned scheme, the propagation of solitary waves was simulated for two different cases of submarine topography; e.g., a plane beach and submerged breakwater. The simulated results are compared to the results of recent studies and show favorable agreement. The behavior of progressive waves is also investigated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.4
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• pp.197-200
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• 1999

An extension of the modified leap-frog scheme is made to solve the nonlinear shallow-water equations. In the extended model. the physical dispersion of the Boussinesq equations is replaced by the numerical dispersion resulted from the leap-frog finite difference scheme. The model is used to simulate propagations of a solitary wave over a constant water depth and a linearly varying water depth. Obtained numerical results are compared with available analytical and other numerical solutions. A reasonable agreement is observed.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.1
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• pp.47-57
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• 2010

Subgrid scale stabilization method is applied to Woo and Liu(2004)'s extended Boussinesq FEM numerical model to eliminate the 2dx wiggles. In order to optimize the computational efficiency, Hessian operator is introduced and the matrix of velocity vector is combined to one matrix for solving matrix equations. The mass lumping technique is also applied to the matrix equations of auxiliary variables. The newly developed code is applied to simulate Vincent and Briggs(1989)' wave transformation experiments and the results show that the numerical solution is almost wiggle-free and it matches very well with experimental data. Due to improvement of computational efficiency and wiggle reduction, it is plausible to apply this model to a realistic problem such as harbor oscillation problems.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.53-57
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• 2003

불규칙파를 사용하여 설계 자료로 이용하기 위해서는 설계해역에서 불규칙파의 파랑변형을 예측할 수 있는 수치모형의 개발이 선행되어야 한다. 비선형 불규칙파의 거동을 해석할 수 있는 Boussinesq 방정식은 상대파고인 $\alpha$/h($\alpha$는 수면의 진폭, h는 수심임)를 비선형의 매개변수로 하고 상대수심인 kh(k는 파수임)를 분산성의 매개변수로 하여 섭동법을 사용하여 유도된다. Boussinesq 식은 수심이 일정한 경우에 Boussinesq(1872)가 비선형 항을 O($\alpha$/h,(kh)$^2$)까지 포함하여 처음으로 개발하였고 수심의 변화가 완만한 경우에 Peregrine(1967)이 개발하였다. (중략)

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.11 no.3
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• pp.149-155
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• 1999

A treatment of wave breaking is included in the extended Boussinesq equations of Nwogu. A spatially distributed source function and sponge layers are used to reduce the reflected waves in the computa¬tional domain. The model uses fourth-order Adams predictor-corrector method to advance in time, and discretizes first-order spatial derivatives to fourth-order accuracy, and thus reducing all truncation errors to a level smaller than the dispersive terms. The generated wave fields are found to be good and the corresponding wave heights are very close to their target values. For the tests of wave breaking, although agreement is considered to be reasonable, wave heights in the inner surf zone are over-predicted. This indicates the breaking parameters in the model should be adjusted.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2004.08a
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• pp.55-66
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• 2004

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2004.08a
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• pp.310-319
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• 2004

• Ocean Systems Engineering
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• v.5 no.4
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• pp.319-329
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• 2015

Submerged breakwaters are used to prevent shore line erosion and sediment transportation. One of their advantages is low visual impact. In this paper, the effects of discontinuous submerged breakwaters over water surface elevation was numerically studied considering the extended Boussinesq equations as governing equations using MIKE21 software. The result of discontinuous breakwater was compared with a beach without breakwater. The results showed that the gap dramatically effects on surface elevation from shore line to offshore. It is also evident from results that with approaching the center of the gap, fluctuation of surface elevation is generated. It is because of passing longshore currents towards offshore through the gap which leads to an increase in sediment transportation rate. Nevertheless, transferring water mass from breakwater gap results in powerful rip currents leading to high changes on longshore wave profile.