• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1950-1960
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• 2006

Based on Banach fixed point theorem, a method to calculate nonlinear superposition for three interacting Stokes' waves is proposed in this paper. A mathematical formulation for the nonlinear superposition in deep water and some numerical solutions were investigated. The authors carried out the numerical study with three progressive linear potentials of different wave numbers and succeeded in solving the nonlinear wave profiles of their three wave-interaction, that is, using only linear wave potentials, it was possible to realize the corresponding nonlinear interacting wave profiles through iteration of the method. The stability of the method for the three interacting Stokes' waves was analyzed. The calculation results, together with Fourier transform, revealed that the iteration made it possible to predict higher-order nonlinear frequencies for three Stokes' waves' interaction. The proposed method has a very fast convergence rate.

• 한국해양공학회지
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• 제20권1호
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• pp.43-47
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• 2006

Superposition of three wave trains on finite depth is investigated. This paper is focused on how to improve the linear superposition of three waves. This was realized by introducing the scheme. The idea of the scheme is based on a fixed point approach. Application of the scheme to the superposition makes it possible to obtain a wave profile of wave-wave interaction. With the help of FFT, it was possible to analyze high-order nonlinear frequencies for three interacting Stokes' waves on finite depth.

• 한국해양공학회지
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• 제36권2호
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• 한국수자원학회논문집
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• 제45권6호
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• pp.545-555
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• 2012

컴퓨터 기술의 발달과 더불어 수치해석을 이용한 파랑변형에 대한 연구는 꾸준히 발전하고 있으며 점점 중요한 역할을 수행하고 있다. 하지만 수치모형을 이용한 연구에는 다양한 문제점이 발생할 우려가 있는데, 그 중 가장 빈번하게 발생하는 문제 중의 하나가 파랑의 조파지점에서 발생하는 수치수조내로의 재반사 문제이다. 재반사를 막기 위한 방법으로는 내부조파 기법을 이용하는 것이 일반적이다. Navier-Stokes 방정식 모형에서는 질량 원천항을 이용한 내부조파 기법을 주로 사용해 왔으나, 기존의 연구는 대부분 연직 2차원 수치모형을 이용한 연구에 국한되어 있었다. 그러나 3차원 수치모형을 이용한 연구가 점차 활발해지면서 3차원 Navier-Stokes 방정식 모형의 내부조파 기법에 대한 필요성이 증대되고 있다. 최근 RANS(Reynolds averaged Navier-Stokes) 방정식 모형에서 Boussinesq 방정식의 운동량 원천항을 활용하여 파랑을 내부조파하는 기법이 발표되어 3차원 공간에서 경사지게 입사하는 파랑을 성공적으로 재현하였다. 본 연구에서는 LES(large eddy simulation) 기반의 3차원 Navier-Stokes 방정식 수치모형에 운동량 원천항을 이용한 내부조파 기법을 적용하여 목표파랑을 조파하고 해석해와 비교하여 이를 검증하였다.

• 한국해양공학회지
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• 제10권3호
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• pp.62-73
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• 1996

Numerical simulation is made of the three-dimensional wave breaking motion about a part of a floating offshore structure containing a circular cylinder mounted vertically onto a lower hull in regular periodic gravity wave generated by a numerical wave maker. TUMMAC-VIII finite-difference method is newly developed for such a problem. By use of density-function technique the three-dimensional wave breaking motion is approximately implenented in the framework of rectangular grid system. A porosity technique is devised for the implementation of the no-slip bydy boundary conditions. The generation of breaking waves by the interaction of incident waves with the structure is well simulated and interesting features of breaking waves are revealed with containing degree of quantitative and qualitative accuracy.

• Journal of Advanced Research in Ocean Engineering
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• 제1권1호
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• pp.14-24
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• 2015

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

• International Journal of Ocean System Engineering
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• 제4권1호
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• pp.49-56
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• 2014

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

• 대한토목학회논문집
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• 제32권6B호
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• pp.379-385
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• 2012

최근의 컴퓨터 연산 성능의 향상과 전산유체역학 분야의 이론적 발전은 완전한 Navier-Stokes 방정식을 이용한 파랑의 수치모의를 가능하게 하였다. 본 연구에서는 질량원천함수를 이용한 내부조파 기법을 레블셋 유한요소법과 결합하였다. 수치모형은 먼저 2차원 파랑 조파와 전파에 적용되었다. 다음에 같은 문제의 3차원 파랑 모의에 적용되었다. 컴퓨터 자원의 효율적 활용과 연산속도 향상을 위하여 3차원 문제에는 병렬 계산 알고리즘이 고안되어 적용되었다. 수치모의에 의한 계산 결과를 이론적인 값과 비교하였으며, 잘 일치함을 확인할 수 있었다.

• 한국해안·해양공학회논문집
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• 제23권5호
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• pp.335-344
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• 2011

곡면의 경계를 가지는 수로에서 비선형 파랑의 상호작용을 모의하기 위한 비정수압 자유수면 모형이 개발되었다. 제안된 모형은 비선형의 3차원 Navier-Stokes 방정식을 곡선좌표 영역에서 계산단계 분리법의 일종인 압력수정법에 의하여 수치적으로 해석된다. 특히, 연직방향으로 변형된 형태의 엇갈린 격자를 이용하여 상대적으로 간단하게 압력방정식과 자유수면 경계조건을 구성하였다. 개발된 모형의 수치해석 정확도는 2차원의 수치 파수조에서 파랑의 비선형 정도에 대하여 5차의 스토스우크스 해석해와 비교하였다. 본 모형의 실제적 적용은 원형의 수로에서 회절과 반사에 의해 변형되는 비선형 파의 변형에 초점을 맞추어 수행하였다. 두개의 파를 중첩한 고비선형의 파에 대한 경우를 제외하고 수치해석 결과는 비선형적인 영향을 고려하지 않은 해석해의 선형적인 중첩과 일치하였다. 두개의 파를 중첩한 고비선형의 파에 대한 모의를 통하여 본 모형은 원형의 수로에서 비선형 군파의 변형에관한 수치적인 모의 가능성을 제시하였다.

• International Journal of Naval Architecture and Ocean Engineering
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• 제6권2호
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• pp.206-218
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• 2014

The wave attenuation by floating breakwaters in high amplitude waves, which can lead to wave overtopping and breaking, is examined by numerical simulations. The governing equations, the Navier-Stokes equations and the continuity equation, are calculated in a fixed Cartesian grid system. The body boundaries are defined by the line segment connecting the points where the grid line and body surface meet. No-slip and divergence free conditions are satisfied at the body boundary cell. The nonlinear waves near the moving body is defined using the modified marker-density method. To verify the present numerical method, vortex induced vibration on an elastically mounted cylinder and free roll decay are numerically simulated and the results are compared with those reported in the literature. Using the present numerical method, the wave attenuations by three kinds of floating breakwaters are simulated numerically in a regular wave to compare the performance.