• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.3
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• pp.610-625
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• 2015

In this paper the wave run-up around a circular column in regular waves is numerically calculated to investigate the applicability of the Modified Marker-Density (MMD) method to prediction of wave run-up around an offshore platform. The MMD method is one of the methods to define the highly nonlinear free surface. The governing equations are the Navier-Stokes equations and the continuity equation which are computed in Cartesian grid system. To validate incident waves generated by numerical simulation, those are compared with the solutions of the Stokes $5^{th}$ order wave theory. The wave run-up simulations are performed varying the steepness and period of incident waves as referred experimental data. The numerical results are compared to the experimental data and the results show good agreements.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.179-182
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• 2004

This paper deals with a new mathematical formulation of nonlinear wave profile based on Banach fixed point theorem. As application of the formulation and its solution procedure, some numerical solutions was presented in this paper and nonlinear equation was derived. Also we introduce a new operator for iteration and getting solution. A numerical study was accomplished with Stokes' first-order solution and iteration scheme, and then we can know the nonlinear characteristic of Stokes' high-order solution. That is, using only Stokes' first-oder(linear) velocity potential and an initial guess of wave profile, it is possible to realize the corresponding high-oder Stokian wave profile with tile new numerical scheme which is the method of iteration. We proved the mathematical convergence of tile proposed scheme. The nonlinear strategy of iterations has very fast convergence rate, that is, only about 6-10 iterations arc required to obtain a numerically converged solution.

• Selected Papers of The Society of Naval Architects of Korea
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• v.1 no.1
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• pp.45-51
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• 1993

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5B
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• pp.559-573
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• 2008

In this study, we newly proposed 3-D nonlinear wave driver utilizing the Navier-Stokes Eq. the numerical integration of which is carried out using SPH (Smoothed Particle Hydrodynamics), an internal wave generation with the source function of Gaussian distribution and an energy absorbing layer. For the verification of new 3-D nonlinear wave driver, we numerically simulate the sloshing problem within a parabolic water basin triggered by a Gaussian hump and uniformly inclined water surface by Thacker (1981). It turns out that the qualitative behavior of sloshing caused by relaxing the external force which makes a free surface convex or uniformly inclined is successfully simulated even though phase error is visible and an inundation height shrinks as numerical simulation more proceeds. For the more severe test, we also simulate the nonlinear shoaling and refraction over uniform beach of wedge shape. It is shown that numerically simulated waves are less refracted than the linear counterpart by Hamiltonian ray theory due to nonlinearity, energy dissipation at the bottom and side walls, energy loss induced by breaking, and the hydraulic jump occurring when breaking waves encounter a down-rush by the preceding wave.

• Coupled systems mechanics
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• v.2 no.1
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• pp.111-126
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• 2013

The structural design requirements of an offshore platform subjected to wave induced forces and moments in the jacket can play a major role in the design of the offshore structures. For an economic and reliable design; good estimation of wave loadings are essential. A nonlinear response analysis of a fixed offshore platform under structural and wave loading is presented, the structure is discretized using the finite element method, wave plus current kinematics (velocity and acceleration fields) are generated using 5th order Stokes wave theory, the wave force acting on the member is calculated using Morison's equation. Hydrodynamic loading on horizontal and vertical tubular members and the dynamic response of fixed offshore structure together with the distribution of displacement, axial force and bending moment along the leg are investigated for regular and extreme conditions, where the structure should keep production capability in conditions of the 1-yr return period wave and must be able to survive the 100-yr return period storm conditions. The result of the study shows that the nonlinear response investigation is quite crucial for safe design and operation of offshore platform.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.5
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• pp.1-11
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• 2001

The purpose of this study is to develop the main program and pre/post processor for the geometric and plastic non-linear analysis of steel jacket structures subjected to wave and earthquake loadings. In this paper, steel jackets are modelled using geometric non-linear space frames and wave loadings re evaluated based on Morrison equation using the linear Airy theory and the fifth Stokes theory. Random wave is generated using JONSWAP spectrum. For earthquake analysis, dynamic analysis is performed using artificial earthquake time history. Also the plastic hinge method is presented for limit analysis of steel jacket. In the companion paper, the pre/post processor is developed and the numerical examples are presented for linear and non-linear dynamic analysis of steel jackets.

• Journal of Advanced Marine Engineering and Technology
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• v.37 no.6
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• pp.617-622
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• 2013

The sloshing of liquid inside an ocean floater is caused by disturbances due to waves. For the analysis of sloshing impact within the floater and that of waves on the floater, the coupled analysis method is used. The Stokes $5^{th}$ order non-linear wave theory equations were adapted for wave making. Furthermore, Navier-Stokes equation and Shear-Stress Transport (SST) turbulent model were used to Computational Fluid dynamics, where the ocean floater motions are considered the heave and the pitch motion. The results obtained confirms the mutual relationship between the rigid body motions and that of sloshing, where the sloshing behaviour within the floater is characterized by the wave effects on the floater.

• New Physics: Sae Mulli
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• v.68 no.11
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• pp.1225-1230
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• 2018

Schwinger pair production of electrons and positrons in a strong electric field is a prediction of nonperturbative quantum field theory, in which the out-vacuum is superposed of multi-particle states of the in-vacuum. Solving the Dirac or Klein-Gordon equation in the background field, though a linear wave equation, and finding the pair-production rate is a difficult or nontrivial job. The phase-integral method has recently been introduced to compute the pair production in space-dependent electric fields, and a complex analysis method has been employed to calculate the pair production in time-dependent electric fields. In this paper, we apply the complex analysis method to a Sauter-type electric field and other hyperbolic-type electric fields that vanish in the past and future and show that the Stokes phenomena in pair production occur when the time-dependent frequency for a given momentum has finite simple poles (polons) with pure imaginary residues.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.395-406
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• 2011

In this research a numerical simulation method is developed for moving body in free surface flows using fixed staggered rectangular grid system. The non-linear free surface near the body is defined by marker-density method. The body boundary is defined by line segment connecting the points where the body surface and grid line meet. Continuity equation and Navier-Stokes equations are used as governing equations and the equations are coupled with two-step projection method. The velocities and pressures of body boundary and free surface cells are calculated with simultaneous iterative method. To treat a body movement in a fixed grid system, the volume displaced by moving body is added to the divergence of the body boundary cell. For the verification of the present numerical method. vortex shedding period of advancing cylinder is calculated and the period is compared with existing experiment results. Moreover, added mass and damping coefficients of a vertically excited box are calculated and the computed results are compared with published experiment results. Impulsive pressure and water level variation due to sloshing phenomenon are simulated and the results are compared with published experiment results. Varying the plunger shape, the waves generated by plunging type wave maker are compared with the 2nd order Stokes wave theory The plunger shape generating the wave that shows the best agreement with the theory is represented.