• Korean Journal of Mathematics
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• 제23권1호
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.395-398
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• 2007

In this study, new dispersion-correction terms are added to leap-frog finite difference scheme for the linear shallow-water equations with the purpose of considering the dispersion effects of the linear Boussinesq equations for the propagation of tsunamis. The new model is applied to near Gadeok island in Pusan about The Central East Sea Tsunami in 1983 and The Hokkaldo Nansei Oki Earthquake Tsunami in 1993 one simulated in the study.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.181-185
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• 2007

A free-surface correction(FSC) method is presented to solve the 3-D shallow water equations. Using the mode splitting process, FSC method can simulate shallow water flows under the hydrostatic assumption. For the hydrostatic pressure calculation, the momentum equations are firstly discretized using a semi-implicit scheme over the vertical direction leading to the tri-diagonal matrix systems. A semi-implicit scheme has been adopted to reduce the numerical instability caused by relatively small vertical length scale compare to horizontal one. and, as the free surface correction step the final horizontal velocity fields are corrected after the final surface elevations are obtained. Finally, the vertical final velocity fields can be calculated from the continuity equation. The numerical model is applied to the calculation of the simulation of flow fields in a rectangular open channel with the tidal influence. The comparisons with the analytical solutions show overall good agreements between the numerical results and analytical solutions.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2004년도 학술대회지
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• pp.229-234
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• 2004

A Typhoon wave is generated by wind fields during the Passage of Typhoon. Transporting wind field makes wind wave and swell in the open sea, and then, those wave components are transported in the shallow water. Typhoon waves in the shallow water is generated by Typhoon wind field and incident wave. Bisides, Incident waves to the shallow water are deformated by topographic conditions. This paper estimated the analysis of the Typhoon waves by wind fields and incident waves according to wave action balance equation model. As the result of wave numerical experiment, wave field during the passage of Typhoon 'Memi' in the shallow water is strongly effect by wind fields. Wave action balance equaion can be partially used for Typhoon wave simulations.

• 한국전산유체공학회지
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• 제10권2호
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• pp.7-14
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• 2005

In this study, the shallow water equations on the sphere is simulated by the proposed method which has high spatial resolution and is based on the CIP(Cubic Interpolated Pseudoparticle) method. The governing equations are approximated on the longitude-latitudinal coordinate system. To avoid the problems resulting from the convergence of the meridians toward high-latitude and singularities on the poles, the semi-Lagrangian and finite volume method are employed. in addition, the CIP method is employed to solve the advection equations and is extended to apply on the equations in the polar coordinate system. The mathematical formulation and numerical results are also described. To verify of the efficiency, accuracy and capability of proposed algorithm, the standard test cases proposed bv Williamson et. al are simulated and the results are compared with other results. As a result, it is found that the present scheme gives a good properties in preserving shapes of solution and settles the pole problems in solving the shallow water equations on the sphere.

• 한국해안해양공학회지
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• 제4권2호
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• pp.108-120
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• 1992

천수방정식의 유한 차분에 많이 이용되는 ADI 방법에 다른 Factorization 방법을 적용하여 각 방법에 의한 모형을 비교 검토하였다. 낙 모형을 해석해가 존재하는 선형 일차원 간제에 적용하여 수표, 저면마찰 및 시간간격에 따른 모형의 정확성을 분석하였다. 2차원 간제의 경우 선형 천수 방정식의 해석해를 구하여, 이 해석해와 각 모형의 수치 결과를 비교 검토하였다. 선형 천수 방정식의 경우 본 연구에서 제시한 ADI 방법이 기존 ADI 방법보다 정확하고 안정된 결과를 얻었다.

• 한국해양공학회지
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• 제22권5호
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• pp.69-74
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• 2008

This study performed a numerical simulation to predict the development of ship waves and their propagation in the shallow water region of Gunzang New Port and to examine the stability of taut line mooring at the sea wall using the design criteria. In order to predict the propagation of ship waves based on the speeds of various ships under complicated and shallow water depths, a computer model was constructed based on the Boussinesque equation with a fixed coordinate system. Additionally, an investigation if the stability was made by applying MOSES under the environmental loadings estimated by OCIMF.

• 대한토목학회논문집
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• 제13권3호
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• pp.119-127
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• 1993

근래 천수방정식과 같은 2차원 수치해석에서 가장 널리 쓰이는 방법 중의 하나로 ADI 방법을 들 수 있다. 그러나 서해안과 같이 수심의 변화가 심하며 특히 해저협곡이 곳곳에 발달된 해역에서 조석에 관한 문제해결시 ADI 방법을 사용하면 소위 ADI 효과가 크게 우려된다. 이를 극복하기 위하여 완전 음해법으로 차분되고 CGS(conjugate gradient squared) 방법으로 해를 구하는 알고리즘을 개발하였다. 조간대 모의가 포함된 본 모형용 새만금 수역에 적용한 결과 지형의 복잡성에도 불구하고 유속장과 조간대 형성에 관한 수치적 모의가 만족스러운 결과를 보였다.

• 대한조선학회논문집
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• 제60권5호
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• pp.341-350
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• 2023

In this paper, numerical experiments are performed to examine the collision between a solitary wave and a wave-packet (dispersive wave) in shallow water. We attempt to introduce the improved Boussinesq equation governing the experiments, which is solved by using a semi-analytical approach, called Pseudo-parameter Iteration method(PIM). Using various numerical experiments, we have observed that the wave-packet (propagating dispersive wave) experiences a phase shift after collision with a solitary wave. This phenomenon may be considered as a nonlinear wave-wave interaction in shallow water.

• 한국해안해양공학회지
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• 제18권4호
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• pp.360-371
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• 2006

천해역의 파랑을 추산하기 위한 포물형 근사식에 대해 기존 모형을 도출할 수 있는 일반화된 모형을 제시하고 이를 수정 완경사 파랑식에 대한 포물형 근사식으로 확장하였다. 제시한 수치모형을 Berkhoff et al.(1982)의 수리모형 실험과 비교하였으며 이 경우에는 기존 포물형 근사모형과 수정 포물형 근사모형의 결과가 거의 같으며 수리실험 결과와 아주 잘 일치하는 것으로 나타났다. 따라서 계산이 빠르고 안정성이 높은 기존 포물형 근사식은 천해역의 파랑 추산에 유용한 도구라 판단된다.