• Journal of Advanced Research in Ocean Engineering
• /
• 제1권3호
• /
• pp.157-167
• /
• 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.

• 한국해양공학회지
• /
• 제11권2호
• /
• pp.77-90
• /
• 1997

Wave deformation due to Oscillating water column (OWC) plant was studied. To solve this problem, three dimensional numerical method based on Improved Green integral equation was applied. Method condition was considered as well as fixed condition and freely floating condition. From the calculation results, main characteriatic of wave deformation due to OWC plant were discussed. Also, some calculations for the floating barge were performed to confirm the validity of numerical solution of the method.

• 대한조선학회논문집
• /
• 제41권3호
• /
• pp.22-27
• /
• 2004

Waveheight attenuation efficiencies of floating breakwaters in water of finite depth for a VLFS are studied numerically in accordance with the two body radiation-diffraction problem. Four different forms of the breaker are tested with a solid VLFS. The radiation-diffraction wave elevations between the breakwater and the VLFS are predicted directly instead of the far-field transmission-reflection coefficients of the breakwater.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2010년 춘계학술대회논문집
• /
• pp.365-367
• /
• 2010

In this paper, we presented the exact Riemann solver for the air-water two-phase shock tube problems where the strength of the propagated sock wave is moderately weak. The shock tube has a diaphragm in the middle which separates water medium in the left and air medium in the right. By rupturing the diaphragm, various waves such as rarefaction wave, shock wave and contact discontinuity are propagated into water and air. Both fluids are treated as compressible, with the linearized equations of state. We used the isentropic relations for the air and water assuming a weak shock wave. We solved the shock tube problem considering a high pressure in the water and a low pressure in the air. The numerical results cleary showed a left-traveling rarefaction wave in the water, a right-traveling shock wave in the air, and the right-traveling material interface.

• 한국방재학회:학술대회논문집
• /
• 한국방재학회 2011년도 정기 학술발표대회
• /
• pp.198-198
• /
• 2011

The numerical simulation of dam break problem suffers from several challenges in terms of accuracy, stability, and versatility of the simulation algorithm since the water flow is generally discontinuous and presents abrupt variations. Thus, to obtain stable and accurate solutions, flow models for this purpose require numerical schemes provided with shock-capturing properties, and with the ability to work with flexible two-dimensional meshes. In this context, SU/PG method(Hughes and Brooks, 1979) is excellent candidate for the solution of the dam break problem. The weak formulation of the equations and the discontinuous polynomial basis lead to an accurate representation of bore waves(shocks). Furthermore, the discretization of the domain in finite elements is extremely effective in modeling complex geometries. In this study, a finite element model based on the SU/PG scheme is developed to solve shallow water equations and the model is applied to dam break problem. It is found that the present model accurately captures the bore wave that propagates downstream while spreading laterally and the depression wave that moves upstream. Furthermore, the propagation and formation of water surface profile compared favorably with those obtained by the previously published results.

• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.45-60
• /
• 2008

Here we consider the evaluation of the the dynamic component of the second order force due to wave diffraction by a circular cylinder analytically and numerically. The cylinder is fixed, vertical, surface piercing in water of finite uniform depth. The formulation of the wave-structure interaction is based on the assumption of a homogeneous, ideal, incompressible, and inviscid fluid. The nonlinearity in the wave-structure interaction problem arises from the free surface boundary conditions, namely, dynamic and kinematic free surface boundary conditions. We expand the velocity potential and free surface elevation functions in terms of a small parameter and then consider the second order diffraction problem. After deriving the pressure using Bernoulli's equation, we obtain the analytical expression for the dynamic component of the second order force on the cylinder by integrating the pressure over the wetted surface. The computation of the dynamic force component requires only the first order velocity potential. Numerical results for the dynamic force component are presented.

• 한국해양공학회:학술대회논문집
• /
• 한국해양공학회 2006년 창립20주년기념 정기학술대회 및 국제워크샵
• /
• pp.373-376
• /
• 2006

In general, a method for generating irregular wave by combination of component waves obtained from linear wave theory is widely used. In these method, however, mean water surface elevation is rising from time to time because of nonlinear effect of wave. In this study, for the rising problem of mean water surface elevation and stabilization of calculation from time to time, mass transport velocity for horizontal velocity at wave source position is considered. The rising problem of mean water surface elevation is checked by comparing calculated wave profile from numerical technique proposed in this study with target wave profile at wave source position in numerical wave tank by using CADMAS-SURF code. And, by generating irregular wave, the validity of wave overtopping rate estimated from this numerical analysis is discussed by comparing computed results with measured results in hydraulic model experiments for vertical seawall located on a sloping sea bottom. As a results, the computations are validated against the previously experimental results by hydraulic model test and numerical results of this study and a good agreement is observed. Therefore, numerical technique of this study is a powerful tool for estimating wave overtopping rate over the crest of coastal structure.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.53-65
• /
• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1017-1031
• /
• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.

• 한국신재생에너지학회:학술대회논문집
• /
• 한국신재생에너지학회 2007년도 춘계학술대회
• /
• pp.621-625
• /
• 2007

Oscillating wave amplitude in a bottom-mounted owe chamber designed for wave energy converter is investigated by applying characteristic wave conditions in Korean coastal water. The effects of shape parameters of OWC chamber in a view of wave energy absorbing capability are analyzed. Both experimental and numerical approaches are adopted and their results are compared to optimize the shape parameters which can result in a maximum power production under given wave distribution. The experiment was carried out in a wave flume under 2-D assumption of OWC chamber. In numerical scheme, the potential problem inside the chamber is solved by use of the Green integral equation associated with the Rankine Green function, while outer problem with the Kelvin Green function taking account of fluctuating air pressure in the chamber. Air duct diameter, chamber width, and submerged depths of front skirt and back wall of chamber changes the magnitude and peak frequency of wave absorption significantly.