• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.53-65
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• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• 한국연안방재학회지
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• 제1권1호
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• pp.1-9
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• 2014

In order to examine the characteristics of tsunami run-up heights on impermeable/permeable slope, a numerical wave tank by upgrading LES-WASS-3D was used in this study. Then, the model were compared with existing hydraulic model test for its verification. The numerical results well reproduced experimental results of solitary wave deformation, propagation and run-up height under various conditions. Also, the numerical simulation with a slope boundary condition has been carried out to understand solitary wave run-up on impermeable/permeable slope. It is shown that the run-up heights on permeable slope is 52.64-63.2% smaller than those on the impermeable slope because of wave energy dissipation inside the porous media. In addition, it is revealed that the numerical results with slope boundary condition agreed well with experimental results in comparison with the results by using stair type boundary condition.

• 한국해양공학회지
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• 제17권6호
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• pp.7-15
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• 2003

A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2003년도 춘계학술대회 논문집
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• pp.231-239
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• 2003

A Digital Wave Tank simulation technique based on a finite-difference method and a modified marker-and-cell (MAC) algorithm is applied to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach and Ohkushiri island, and to predict maximum wave run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain and the boundary values updated at each time step by a finite-difference time-marching scheme in the frame of rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the modified marker-density function technique. The Nearshore Tsunami is assumed to be a solitary wave and generated from the numerical wavemaker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods based on the shallow-water wave theory.

• 물과 미래
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• 제29권3호
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• pp.163-176
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• 1996

균일조도관이 경사지어 설치되어 있을 때, 적정량의 유체를 유송하기 위하여 요구되는 펌프의 동력은 양해법으로 바로 산정할 수 있다. 그러나 펌프의 동력이 기지값으로 주어져 있고 관내 유출률이나 관경을 구하고자 할 때 기존 방법은 상당한 반복과정을 거쳐야 된다. 이러한 경우 유동훈(1995b)은 펌프가 작동치 않는 자연경사관이나 수평관에 펌프만 작동할 때의 균일조도관에 대하여 양해법 산정식을 개발한 바 있다. 본 연구는 그의 연구결과에 기초하여 균일조도 경사관에 펌프가 동시에 작동할 때 반복 시산과정을 거치지 않고 관내 유출률이나 관경을 양해법으로 바로 산정하는 수식을 개발하여 제시하였다. 양해법 산정식의 선택에 있어 관로흐름의 수리특성을 다섯가지로 구분하여 각 수리 특성구간의 경계조건식도 양해법으로 도출하였다. 또한 개발된 양해법 근사식을 간단한 설계예에 적용하여 계산의 효율성과 정확성을 확인하였다.