• 한국해안해양공학회지
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• 제5권4호
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• pp.350-356
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• 1993

본 연구에서는 천수역 비선형 방정식인 Boussinesq 방정식을 방파제에 의한 산란문제에 적용하였다. 방파제에 의한 파랑변형을 수치계산하기 위하여 경계치문제는 유한요소법을 사용하였고 시간에 따른 진행은 Runge-Kutta 방법을 사용하였다. 수치모델로 2차원 수로에 입사파의 진행방향과 수직으로 방파제가 놓여있는 경우를 생각하였으며 방파제의 길이와 두께변화에 따른 파랑변형에 미치는 영향을 살펴보았다. 또한 후류 경계면이 막혀있는 경우와 열려있는 경우를 고려하였으며 선형결과와 비선형결과의 차이를 살펴보았다.

• 대한수학회보
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• 제60권6호
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• pp.1697-1704
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• 2023

We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

• 한국해양공학회지
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• 제20권6호
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• pp.35-40
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• 2006

In recent years, there's been strong demand for seawalls that havea gentle slope and permeability that serveswater affinity and disaster prevention from wave attack. The aim of this study is to examine wave transformation, including wave run-up that propagates on the coastal structures. A numerical model based on the weak nonlinear dispersive Boussinesq equation, together with the unsteady nonlinear Darcy law for fluid motion in permeable layer, is developed. The applicability of this numerical model is examined through Deguchi and Moriwaki's hydraulic model test on the permeable slopes. From this study, it is found that the proposed numerical model can predict wave transformation and run-up on the gentle slope with a permeable layer, but can't show accurate results for slopes steeper than about 1:10.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2001년도 추계학술대회 논문집
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• pp.138-143
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• 2001

Based on mild slope equation and parabolic approximation the forward diffraction of monochromatic waves by a straight breakwater are studied numerically. The characteristics and effects of stem wave along breakwater and the relations between the stem wave and incident wave angle are discussed.

• 한국항만학회지
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• 제12권1호
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• pp.75-86
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• 1998

To design a coastal structure in the nearshore region, engineers must have means to estimate wave climate. Waves, approaching the surf zone from offshore, experience changes caused by combined effects of bathymetric variations, interference of man-made structure, and nonlinear interactions among wave trains. This paper has attempted to find out the effects of two of the more subtle phenomena involving nonlinear shallow water waves, amplitude dispersion and secondary wave generation. Boussinesq-type equations can be used to model the nonlinear transformation of surface waves in shallow water due to effect of shoaling, refraction, diffraction, and reflection. In this paper, generalized Boussinesq equations under the complex bottom condition is derived using the depth averaged velocity with the series expansion of the velocity potential as a product of powers of the depth of flow. A time stepping finite difference method is used to solve the derived equation. Numerical results are compared to hydraulic model results. The result with the non-linear dispersive wave equation can describe an interesting transformation a sinusoidal wave to one with a cnoidal aspect of a rapid degradation into modulated high frequency waves and transient secondary waves in an intermediate region. The amplitude dispersion of the primary wave crest results in a convex wave front after passing through the shoal and the secondary waves generated by the shoal diffracted in a radial manner into surrounding waters.

• 한국해안해양공학회지
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• 제17권3호
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• pp.202-212
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• 2005

수중 천퇴 인근에 해양구조물을 설치하는 경우, 구조물에 작용하는 설계하중을 구하기 위하여 파고뿐만 아니라 천퇴 주변 파랑변형에 의하여 이차적으로 발생된 파랑류를 아울러 고려하여야 한다. 본 연구에서는 천퇴 주변의 파랑변형과 파랑류를 계산하기 위하여 비선형 Boussinesq방정식 모델과 선형 완경사방정식 모델을 각각 적용하였다. 대상 천퇴는 Vincent and Briggs(1989)의 수리실험에서와 동일하며 실험조건은 규칙파, 일방향 또는 다방향 불규칙파 입사를 포함하는 비쇄파조건으로 하였다. 두 수치모델은 공히 천퇴 중심선을 따라 파랑류가 대칭적으로 형성됨을 잘 보여주었다. 그리고 수리실험에서의 파고계측선을 따라 계산된 파고변화는 전체적으로 실험 결과와 잘 일치하였다.

• 호남수학학술지
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• 제37권4호
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• pp.411-421
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• 2015

This paper investigates the issue of analytic travelling wave solutions for some important coupled models of fractional order. Analytic travelling wave solutions of the considered model are found by means of the Q-function method. The results give us that the Q-function method is very simple, reliable and effective for searching analytic exact solutions of complex nonlinear partial differential equations.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2004년도 학술대회지
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• pp.90-95
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• 2004

During the past 50 years methods for predicting wave overtopping of coastal structures have coastal structures have continuously been developed Wave overtopping is one of the most important processes for the design of seawalls. The term 'wave overtopping' is used here to refer to the processes where waves hit a sloping structure run up the slope and, if the crest level of the slope is lower than the highest run up level, overtop the structure. Wave overtopping is dependent on the processes associated with breaking wave. The Numerical model is based on Navier-Stokes equation and Marker-Density Function of method for nonlinear free-surface flow by Miyata & Park(1995). The influence of how the slopes of seawalls, wave type and crest freeboard affect overtopping discharges has been investigated. The research of study using the new development nonlinear free-surface flow numerical model SOLA-VOF are presented.

• 대한수학회지
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• 제48권4호
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• pp.867-885
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• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Korean Journal of Mathematics
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• 제16권2호
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• pp.243-257
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• 2008

We seek the sign changing periodic solutions of the nonlinear wave equation $u_{tt}-u_{xx}=a(x,t)g(u)$ under Dirichlet boundary and periodic conditions. We show that the problem has at least one solution or two solutions whether $\frac{1}{2}g(u)u-G(u)$ is bounded or not.