• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.40-41
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• 2011

동해를 전파하는 지진해일은 세계적으로 다른 지역에서 발생하는 지진해일과 비교하였을 때 상대적으로 파장이 짧고, 이에 비해 먼 거리를 전파한다. 그러므로 동해에서 발생한 지진해일의 전파에 대한 해석을 수행할 때 물리적인 분산효과가 매우 중요하다. 따라서 지배방정식으로 분산 효과가 충분히 고려된 선형 Boussinesq 방정식을 사용한다. 기존의 연구에서는 leap-frog 기법을 사용하여 선형 천수방정식을 차분할 때 발생하는 수치분산항에 분산 보정계수를 이용하여 선형 Boussinesq 방정식의 물리적 분산항과 같은 형태로 나타나도록 유도하여 수치모의를 수행하였다. 그러나 기존에 사용한 지배방정식은 수심이 일정하다는 가정을 통하여 유도된 것으로, 수심에 변화가 있는 실제 지형을 통과하는 지진해일에 대한 수치모의를 수행한 결과의 정확도에 문제가 생길 수 있다. 본 연구에서는 기존의 연구에서 발생할 수 있는 수심 변화에 따른 오류를 개선하기 위하여 바닥 지형이 1차원으로 변한다는 가정을 이용하여 지배방정식을 유도하였으며, 이로 인해 발생하는 수심 변화가 고려된 항을 기존의 분산보정기법에 추가하였다. 그리고 적용성을 높이기 위하여 수치모의 기법의 제한을 최소화하는 연구를 진행하였다. 본 연구에서 제안한 수정 기법이 수심이 변화하는 지형을 전파하는 지진해일 수치모의 과정에서 경사에 대한 분산효과가 충분히 고려되는지 확인하기 위하여 Gaussian hump를 이용한 가상 지진해일을 원형 천퇴 지형에 통과시켰다. 본 연구에서 사용한 지형을 통과하는 Gaussian hump에 대한 해석해를 구하는 방법이 존재하지 않으므로, Boussinesq 방정식을 직접 차분하여 푸는 FUNWAVE를 사용하여 동일한 조건 하에서 수치모의를 수행하였다. 비교 결과를 통하여 본 연구에서 제안한 기법의 정확도 향상을 확인하게 되면, 실제 지형을 통과하는 지진해일의 수치모의에 대한 활용성을 높일 수 있을 것이다.

• Journal of Navigation and Port Research
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• v.27 no.5
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• pp.527-537
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• 2003

The characteristics of ship induced waves caused by navigation become widely different from both ship's speed and water depth condition. The ship induced waves specially generated in coastwise routes frequently give rise to call unforeseen danger for swimmers and small boats as well as shoreline erosion or sea wall destruction in coastal zones. The main concern of ship induced wave study until now is either how to reduce ship resistance or how to manoeuvre the ship safely under a constant water depth in the view point of shipbuilding engineers. Moreover, due to the trends for appearance of the high speed ships at the shallow coastal water, we are confronted with the danger of damages from those ship induced waves. Therefore, it is necessary to examine the development of ship induced waves and the influence of their deformation effects according to its propagation ray. In present study, in order to predict the development of the ship induced waves and their propagation under the conditions of complicate and variable shallow water depth with varying ship's speed, we constructed a computer model using Boussinesq equation with a fixed coordinate system and verified the model results by comparison with experimental results. Additionally, the model was applied under the variable water depth based on actual passage and we then confirmed the importance of the variable water depth consideration.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.4
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• pp.181-189
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• 2000

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks(1975). For the verification purposes of the present nonlinear model, the degenerate forms were compared with Airy(1845)'s non-dispersive nonlinear wave equation, classical Boussinesq equation, andsecond¬order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

• 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 Korean Society of Coastal and Ocean Engineers
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• v.21 no.2
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• pp.108-116
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• 2009

The present study introduces a Legendre interpolation function which is capable of analyzing wave transformation effectively in a finite element method. A Lagrangian interpolation function has been mostly used for a finite element method with a higher-order interpolation function. Although this function has an advantage of giving an accurate result with less number of elements, simulation time increases. Calculation time can be reduced by mass lumping, whereas the accuracy of solution is lowered. In this study, we introduce a modified Lagrangian interpolation function, Legendre cardinal interpolation, which can reduce simulation time with keeping up favorable accuracy. Through various numerical simulations using a Boussinesq equations model, the superiority of the Legendre cardinal interpolation function to a Lagrangian interpolation function was shown.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.51-57
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• 1990

Based on second-order Stokes wave and parabolic approximation, a refraction-diffraction model for linear and nonlinear waves is developed. With the assumption that the water depth is slowly varying, the model equation describes the forward scattered wavefield. The parabolic approximation equations account for the combined effects of refraction and diffraction, while the influences of bottom friction, current and wind have been neglected. The model is tested against laboratory experiments for the case of submerged circular shoal, when both refraction and diffraction are equally significant. Based on Boussinesq equations, the parabolic approximation eq. is applied to the propagation of shallow water waves. In the case without currents, the forward diffraction of Cnoidal waves by a straight breakwater is studied numerically. The formation of stem waves along the breakwater and the relation between the stem waves and the incident wave characteristics are discussed. Numerical experiments are carried out using different bottom slopes and different angles of incidence.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.358-361
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• 2008

A study is made of thermal plume flow model for the development of helicopter simulator over the forest fire. For numerical analysis, the Boussinesq fluid approximation and line fire model, which is assumed by the shape of forest fire spreading, are adopted. Comparing 3-D full numerical solutions with 2-D similarity solution, it has been built a new model that is capable of temperature prediction along the symmetric vertical axis in both cases of laminar and turbulent flows.

• Proceedings of the Korean Geotechical Society Conference
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• 2003.03a
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• pp.422-426
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• 2003

Model soil tank tests were conducted in sandy soil to investigate the effect of surcharge strip loads on vertical stress distribution in soil. A total number of 6 tests were performed using one loading plate and two relative density(55%, 65%). The soil was considered as an elastic material, while no friction was allowed between the wall and the soil. Measured stress values were compared to predictions defined by Frohlich, Boussinesq and Westergaard. The comparison of measured values and predictions used the ratio between the soil pressure and load value. Results of this study demonstrated that experimental values were generally larger than predictions. The Frohlich analysis provided the best prediction, while the Boussinesq analysis and Westergaard theory not presented a satisfactional result.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.350-356
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• 1993

We carry out a numerical calculation to understand the nonlinear wave deformation around breakwaters using the Boussinesq equation, which is weakly nonlinear and weakly dispersive shallow water equation. A numerical method based on a finite element scheme and fourth order Runge-Kutta algorithm is employed to investigate the diffraction of incident waves by the breakwater. As a computational model, two-dimensional wave flume is treated. The breakwaters is perpendicular to the side wall of a channel. From the numerical results, the wave deformations according to the change of the length and the thickness of breakwaters are investigated. We also investigate the effect of the nonlinearity by comparing the results with the linear solutions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.3 s.258
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• pp.273-282
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• 2007

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on finite volume method, for different Rayleigh numbers varying over the range of $10^4\;to\;10^6$. The study goes further to investigate the effect of an inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of cell strongly depend on Rayleigh number and the position of inner circular cylinder. The changes in heat transfer quantities have been presented.