• 제목/요약/키워드: System of nonlinear wave equations

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A Numerical Solution. Method for Two-dimensional Nonlinear Water Waves on a Plane Beach of Constant Slope

  • Lee, Young-Gill;Heo, Jae-Kyung;Jeong, Kwang-Leol;Kim, Kang-Sin
    • Journal of Ship and Ocean Technology
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    • 제8권2호
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    • pp.61-69
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    • 2004
  • Unsteady nonlinear wave motions on the free surface over a plane beach of constant slope are numerically simulated using a finite difference method in rectangular grid system. Two-dimensional Navier-Stokes equations and the continuity equation are used for the computations. Irregular leg lengths and stars are employed near the boundaries of body and free surface to satisfy the boundary conditions. Also, the free surface which consists of markers or segments is determined every time step with the satisfaction of kinematic and dynamic free surface conditions. Moreover, marker-density method is also adopted to allow plunging jets impinging on the free surface. The second-order Stokes wave theory is employed for the generation of waves on the inflow boundary. For the simulation of wave breaking phenomena, the computations are carried out with the plane beach of constant slope in surf zone. The results are compared with other existing experimental results. Agreement between the experimental data and the computation results is good.

Coupled Motion Simulation of the Mobile Harbor and Anti-Rolling Devices in Waves

  • Yoon, Hyeon-Kyu;Kang, Joo-Nyun;Lew, Jae-Moon;Moon, Seok-Joon;Chung, Tae-Young
    • 한국항해항만학회지
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    • 제34권4호
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    • pp.271-279
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    • 2010
  • The Mobile Harbor(MH) is a new transportation platform that can load and unload containers to and from very large container ships in the sea. This loading and unloading by crane can be performed with only very small movements of the MH in waves because MH is operated outside of the harbor. For this reason, an anti-rolling tank(ART) and an active mass driving system(AMD) were designed to reduce MH's roll motion, especially at the natural frequency of MH. In the conceptual design stage, it is difficult to confirm the design result of theses anti-rolling devices without modeling and simulation tools. Therefore, the coupled MH and anti-rolling devices' dynamic equations in waves were derived and a simulation program that can analyze the roll reduction performance in various conditions, such as sea state, wave direction, and so on, was developed. The coupled equations are constructed as an eight degrees of freedom (DOF) motion that consists of MH's six DOF dynamics and the ART's and AMD's control variables. In order to conveniently include the ART's and AMD's control dynamics in the time domain, MH's radiated wave force was described by an impulse response function derived by the damping coefficient obtained in the frequency domain, and wave exciting forces such as Froude-Krylov force and diffraction force and nonlinear buoyancy were calculated at every simulation time interval. Finally, the roll reduction performances of the designed anti-rolling devices were successfully assessed in the various loading and wave conditions by using a developed simulation program.

규칙파와 수평판의 비선형 상호작용에 의한 고차 조화항 발생 (Higher Harmonic Generation by Nonlinear Interaction between Monochromatic Waves and a Horizontal Plate)

  • 고혁준;조일형
    • 한국해안해양공학회지
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    • 제19권5호
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    • pp.484-491
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    • 2007
  • 규칙파와 수면아래 잠긴 수평판 사이의 비선형 상호작용을 규명하기 위하여 수치파동수조를 이용하여 수치 실험을 수행하였다. 수치모델로 비선형 포텐셜 이론을 근거로 한 고차 경계요소법과 Navier Stokes 방정식과 엄밀한 자유표면 경계조건식을 푸는 CADMAS-SURF을 사용하였다. 두 모델 모두 수평판 위의 천수역에서 발생하는 고차 조화항들을 예측할 수 있으며 점성효과를 포함하는 CADMAS-SURF는 수평판 양단에서 발생하는 와류와 박리에 의한 고차 조화항의 발생을 재현할 수 있다. 수평판의 잠긴 깊이와 길이 변화에 따른 반사율과 투과율을 Patarapanich and Cheong(1989)의 모형실험결과와 비교하였고 서로 잘 일치함을 확인하였다. 수평판의 길이가 길어지고 잠긴 깊이가 얕아질수록 입사파의 에너지가 고차 조화항으로 더 많이 전이됨을 확인하였다.

원유 생산.저장.하역선의 갑판침수에 관한 연구 (A Study on the Deck Wetness of the FPSO)

  • 임춘규;이호영
    • 대한조선학회논문집
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    • 제41권1호
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    • pp.8-14
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    • 2004
  • As the number of offshore structure is glowing in deep waters, there have been increased damages of it. These floating structures in offshore locations exposed to harsh environmental conditions. In recent years, there has been a slowing attention around damages on bow and deck on FPSO caused by waves in steep storm condition. This paper describes a study of the water on deck due to the dynamic behavior of a FPSO with turret mooring system. The nonlinear motions of the FPSO are simulated under external forces due to wave, current, wind, and mooring forces in the time domain. The direct integration method is employed to estimate low frequency drift wave forces. The current forces are calculated by using slow motion maneuvering equations in the horizontal plane. The coefficients of a model for wind forces are calculated from Isherwood's experimental data and the variation of wind speed is estimated by wind spectrum according to the guidelines of API-RP2A.

선수부 갑판침입수의 수치시뮬레이션에 대한 기초연구 (A Fundamental Study for the Numerical Simulation Method of Green Water Occurrence on Bow Deck)

  • 정광열;이영길;김남철
    • 대한조선학회논문집
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    • 제47권2호
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    • pp.188-195
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    • 2010
  • Green water load is an important parameter to be considered in designing a modern ship or offshore structures like FPSO and FSRU. In this research, a numerical simulation method for green water phenomenon is introduced. The Navier-Stokes equations and the continuity equation are used as governing equations. The equations are calculated using Finite Difference Method(FDM) in rectangular staggered grid system. To increase the numerical accuracy near the body, the Cartesian cut cell method is employed. The nonlinear free-surface during green water incident is defined by Marker-density method. The green waters on a box in regular waves are simulated. The simulation results are compared with other experimental and computational results for verification. To check the applicability to moving ship, the green water of the ship which is towed by uniform force in regular wave, is simulated. The ship is set free to heave and to surge.

불규칙파 중에서 돌핀 계류된 해상공항에 대한 운동 해석 (Motion Analyses for a Very Large Floating Structure with Dolphin Mooring Systems in Irregular Waves)

  • 이호영;신현경;임춘규;강점문;윤명철
    • 한국해양공학회:학술대회논문집
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    • 한국해양공학회 2000년도 추계학술대회 논문집
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    • pp.57-62
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    • 2000
  • The very large flcating structure which am be used for as airport may be as large as several kilomet wide. The first order wave forces as well as wave drift forces are very important forces on such a very large floating In the present studv, the time simulation of motion responses with dolphin-moored VLFS in waves is presented The coeffcients and wave forces involved in the equations are obtained from a three-dimensionul panel method in the frequc The horizontal drift forces and mooring forces for dolphin systems are taken into account. As for numerical example, analyses are carried out for a VLFS in irregular wave condition

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해양환경공학의 다목적 수치시뮬레이션을 위한 Virtual Reality 기술 (Virtual Reality Technology for Multipurpose Numerical Simulation in Marine Environmental Engineering)

  • 박종천
    • 한국해양공학회:학술대회논문집
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    • 한국해양공학회 2002년도 추계학술대회 논문집
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    • pp.174-180
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    • 2002
  • A virtual reality technology for multipurpose numerical simulation is developed to reproduce and investigate a variety of ocean environmental problems in a 3D-Numerical Wave Tank. The governing equations for solving incompressible fluid motion are Navier-Stokes equation and continuity equation, and the Marker-Density function technique is adopted to implement the fully-nonlinear free-surface kinematic condition. The marine environmental situations, i.e. waves, currents, wind, etc., are reproduced by use of multi-segmented wavemaker on the basis of the so-called "snake-principle". In this paper, some numerical reproduction techniques for regular and irregular waves, multi-directional waves, Bull's-eye wave, wave-current, and solitary wave are presented, and a model test in motion with large amplitude of roll angle is conducted in the developed 3D-NWT, using a overlaid grid system.

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경계요소법을 이용한 비선형파의 재현 (Simulation of Nonlinear Water Waves using Boundary Element Method)

  • 오영민;이길성;전인식
    • 한국해안해양공학회지
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    • 제5권3호
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    • pp.204-211
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    • 1993
  • Laplace 방정식을 Green 공식으로 해석한 경계요소법을 이용하여 수치수조에서 비선형파를 재현하였다. 미지수는 유체영역의 경계에 설정한 각 절점에서의 속도포텐셜과 수면변위이며 이를 구하기 위하여 지배방정식과 자유수면 경계조건을 기본식으로 하는 연립 1차방정식을 구성하였다. 동력학적 자유수면 경계조건에서 속도의 제곱항을 고려하였으며 자유수면 경계에서 속도포텐셜의 연직변화를 고려하여 이의 시간미분을 계산하였다. 본 수치모델을 이용하여 고립파와 Stokes의 2차 파낭을 재현한 결과, 이론치와 매우 잘 일치함을 확인하였다.

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Influence of Tether Length in the Response Behavior of Square Tension Leg Platform in Regular Waves

  • El-gamal, Amr R.;Essa, Ashraf
    • International Journal of Ocean System Engineering
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    • 제4권1호
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    • pp.19-28
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    • 2014
  • The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark's beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated. Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.

다공벽을 전파하는 압축파에 관한 수치해석적 연구 (Numerical Study of Compression Waves Propagating Through Porous Walls)

  • 김희동
    • 대한기계학회논문집B
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    • 제21권11호
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    • pp.1403-1412
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    • 1997
  • When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates through the tunnel, compressing and accelerating the rest air in front of the wave. At the exit of the tunnel, an impulsive wave is emitted outward toward the surrounding, which causes a positive impulsive noise like a kind of sonic boom produced by a supersonic aircraft. With the advent of high-speed train, such an impulsive noise can be large enough to cause the noise problem, unless some attempts are made to alleviate its pressure levels. In the purpose of the impulsive noise reduction, the present study calculated the effect of porous walls on the compression wave propagating into a model tunnel. Two-dimensional unsteady compressible equations were differenced by using a Piecewise Linear Method. Calculation results show that the cavity/porous wall system is very effective for a compression wave with a large nonlinear effect. The porosity of 30% is most effective for the reduction of the maximum pressure gradient of the compression wave front. The present calculation results are in a good agreement with experimental ones obtained previously.