• Title/Summary/Keyword: boussinesq equation

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A Study on Wave Transformation Analysis using Higher-Order Finite Element (고차유한요소의 파랑변형해석에의 적용에 관한 소고)

  • Jung, Tae-Hwa;Lee, Jong-In;Kim, Young-Taek;Ryu, Yong-Uk
    • 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.

Practical Dispersion-Correction Scheme for Linear Shallow-Water Equations to Simulate the Propagation of Tsunamis (지진해일 전파모의를 위한 선형 천수방정식을 이용한 실용적인 분산보정기법)

  • Cho, Yong-Sik;Sohn, Dae-Hee;Ha, Tae-Min
    • Proceedings of the Korea Water Resources Association Conference
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    • 2006.05a
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    • pp.1935-1939
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    • 2006
  • In this study, the 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 such as linear Boussinesq equations for the propagation of tsunamis. And, dispersion-correction factor is determined to mimic the frequency dispersion of the linear Boussinesq equations. The numerical model developed in this study is tested to the problem that initial free surface displacement is a Gaussian hump over a constant water depth, and the results from the numerical model are compared with analytical solutions. The results by present numerical model are accurate in comparison with the past models.

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Numerical Analysis of the Depression Effect of Hybrid Breaker on the Run Up Height due to Tsunami based on the Modified Leading Depression N (LDN) Wave Generation Technique (Leading Depression N (LDN) Wave 조파기법에 기초한 Hybrid Breaker의 지진해일 처오름 저감효과 수치해석)

  • Cho, Yong Jun;Na, Dong Gyu
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.27 no.1
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    • pp.38-49
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    • 2015
  • Past study of tsunami heavily relied on the numerical modelling using 2D Boussinesq Eq. and Solitary wave. Lately, based on the fact that numerically simulated run up heights based on solitary wave are somewhat smaller than the measured one, Leading Depression N (LDN) Wave has been elaborated, which can account the advancement of a shore line before tsunami strikes a shore. Thereafter it is reported that more accurate simulation can be possible once LDN is deployed. On the other hand, there were numerous reports indicating that stable LDN wave can't be sustained in the hydraulic model test. These conflicts between the hydraulic model tests and numerical results have their roots on the assumption made in the derivation of Boussinesq type wave model such as that wave nonlinearity is equally balanced with wave dispersiveness. Hence, in the numerical simulation based on the Boussinesq type wave model, wave dispersiveness is inevitably underestimated, especially in deep water. Based on this rationale, we developed the modified methodology for the generation of stable LDN wave in the 3D numerical wave flume, and proceeded to numerically analyze the depression effect of Hybrid Breaker on the run up height due to tsunami using the Navier Stoke Equation. The verification of newly proposed wave model in this study was carried out using the run up height from the hydraulic model test. It was shown that Hybrid Breaker consisting of three water chamber and slope at its front can reduce 13% of run up height for H = 5m, and 10% of run up height for H = 6m.

Numerical Prediction of Ship Induced Wave and its Propagation Using Nonlinear Dispersive Wave Model (비선형분산파랑모형을 이용한 항주파의 발생과 전파에 관한 수치예측모형 개발)

  • Shin, Seung-Ho;Jeong, Dae-Deug
    • 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.

Numerical Study on a Dominant Mechanism of Rip Current at Haeundae Beach: Honeycomb Pattern of Waves (수치모의를 통한 해운대 이안류의 주요 메커니즘 연구: 파랑의 벌집구조)

  • Choi, Junwoo;Park, Won Kyung;Bae, Jae Seok;Yoon, Sung Bum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.5B
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    • pp.321-329
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    • 2012
  • Two regular progressive wave trains, the directions of which are slightly different from each other, develop a honeycomb pattern of wave crests due to their nonlinear interaction. In the honeycomb pattern of wave crest, the nodal line area, which has very low wave energy, is formed. When the honeycomb pattern is developed near the beach area, rip current evolves through the nodal line area formed in the cross shore direction. In this study, to confirm that the formation of honeycomb pattern of waves near the beach area is a dominant mechanism of rip current occurred at Haeundae beach, we performed a numerical simulation of nearshore circulation at Haeundae beach under an unidirectional and monochromatic wave condition by using a nonlinear Boussinesq equation model. As a result, wave refraction due to topographical characteristics (i.e., submerged shoal) of Haeundae gave rise to several wave trains propagating with slightly different directions toward the beach, and consequently rip currents well developed through the nodal line area of honeycomb patterns of wave crest. In addition, we found that a narrow-banded spectral wave condition (i.e., a swell spectrum) increases more likelihood of rip current than a broad-banded spectral wave condtion based on the simulations employing various wave spectra with an equivalent wave height and period.

A Study on the Flow and Dispersion in the Coastal Unconfined Aquifer (Development and Application of a Numerical Model) (해안지역 비피압 충적 대수층에서의 흐름 및 분산(수치모형의 개발 및 적용))

  • Kim, Sang Jun
    • Journal of Korea Water Resources Association
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    • v.49 no.1
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    • pp.61-72
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    • 2016
  • In Korea, the aquifers at the coastal areas are mostly shallow alluvial unconfined aquifers. To simulate the flow and dispersion in unconfined aquifer, a FDM model has been developed to solve the nonlinear Boussinesq equation. Related analysis and verification have been executed. The iteration method is used to solve the nonlinearity, and the model shows 3-D shape because it is a 2-D y model that consider the undulation of water table and bottom. For the verification of the model, the output of flow module is compared to the 1-D analytic solution of Lee (1989) which have the drawdown or uplift boundary condition, and the two results show almost the same value. and the mass balance of dispersion module shows about 10% error. The developed model can be used for the analysis and design of the flow and dispersion in the unconfined aquifers. The model has been applied to the estuary area of Ssangcheon watershed, and the parameters have been deduced as a result : hydraulic conductivity is 90 m/day, and longitudinal dispersivity is 15 m. And the analysis with these parameters shows that the wells are situated in the influence circle of each others except for No. 7 well. Groundwater discharge to sea is $3700m^3/day$. And the chlorine ion ($cl^-$) concentration at the pumping wells increase at least 1000 mg/L if groundwater dam is not exist, so the groundwater dam plays an important role for the prevention of sea water intrusion.

Analytic solution for the interaction between a viscoelastic Bernoulli-Navier beam and a winkler medium

  • Floris, Claudio;Lamacchia, Francesco Paolo
    • Structural Engineering and Mechanics
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    • v.38 no.5
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    • pp.593-618
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    • 2011
  • This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

Three-dimensional crack analysis by fractional linear mapping (선형분수사상을 이용한 3차원 균열해석)

  • 안득만
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.1
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    • pp.61-78
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    • 1995
  • In this study the method of analysis for three-dimensional plane crack problem by fractional linear mapping is given. Using this method we can obtain the exact solutions of significantly different configurations of the crack. In the example image crack configurations by mapping of elliptic crack are illustrated. And the stress intensity factors along the image crack tips are calculated.

Theoretical Study on the Generation of Directional Extreme Waves (다방향 극한파 생성의 이론적 연구)

  • Key-Yong Hong;Shuxue Liu;Seok-Won Hong
    • Journal of the Society of Naval Architects of Korea
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    • v.39 no.1
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    • pp.38-48
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    • 2002
  • Theoretical development to generate the directional extreme waves in model basin is established based on wave focusing method. The effects of associated parameters, such as the directional range, frequency width, and center frequency, are investigated in terms of wave focusing efficiency. The two different spectral models of constant wave amplitude and constant wave slope are applied to control the wave characteristics. The wave packets simulated by theory are compared with numerical results based on Boussinesq equation and FEM. Both controls of direction and frequency spectrum are essential to focus directional waves effectively. It is noticed that wave focusing ability depends on the frequency bandwidth of spectrum rather than center frequency, and both spectral models with same parameters result in the equivalent efficiency of wave focusing.

The Prediction of Wave Groups within a Harbor to Assist Ship Operation at the Entrance

  • Cho Ik-Soon
    • Journal of Navigation and Port Research
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    • v.30 no.2
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    • pp.125-130
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    • 2006
  • Waves, which are the main source of ship motions in a seaway, considerably affect the performance of a ship. The study of waves and their impact on ship motions within harbors is an important aspect of the design and operation of harbors. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor. Such a prediction makes it possible to evaluate ship safety more accurately. The wave transformation model reported here is applied to actual ports based on Boussinesq wave equations both non-linear and dispersive wave processes be considered in order to capture physical effects such as wave shoaling, refractions, reflection and diffraction in variable depth environments. The prediction of incoming groups of waves is particularly important for evaluating ship motion within a harbor, Such a prediction makes it possible to evaluate ship safety more accurately and provide safe wave informations for navigation. Furthermore, a wave information support system is proposed for entering ships as one technique for improving the safety of ship operations. This system predicts the run of waves and reduces the danger by identifying the most dangerous point near the harbor entrance at the small wave groups.