Finite element method for strong reflection of water waves

In this study, the propagation of monochromatic water waves over an arbitrarily varying topography is numerically investigated. A finite element model is developed by formulating the diffraction of waves caused by depth changes. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of strong reflection of monochromatic waves over a sinusoidally varying topography. Predicted reflection coefficients are compared with those of available laboratory experiments and the eigenfunction expansion method. A very good agreement is observed.     

Finite element analysis of two-dimensional nonlinear sloshing problems in random excitations

A two-dimensional nonlinear random sloshing problem is analyzed by the fully nonlinear wave velocity potential theory based on the finite element method. A rectangular container filled with liquid subjected to specified horizontal random oscillations is studied. Both wave elevation and hydrodynamic force are obtained. The spectra of random waves and forces have also been investigated, and the effects of the peak frequencies and spectral width of the specified spectrum used for the generation of the random oscillations are discussed. It is found that the energy mainly concentrates at the natural frequencies of the container and is dominant at the ith order natural frequency when the peak frequency is close to the ith order natural frequency. Some results are compared between the fully nonlinear solutions, the linear solutions and the linear plus second-order solutions.     

A statistical analysis of non-linear random waves

A statistical analysis of unidirectional non-linear random waves is presented which is based on second-order random wave theory. The analysis technique is similar to a method which is available for the statistical analysis of a two-term Volterra series. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and eigenvectors of two real symmetric matrices, from which the cumulants, the characteristic function, and the probability density function of the surface elevation can be found. Various numerical examples are considered, and the possibility of extending the technique to deal with spreading seas is discussed.     

Extended KdV equation for transient axisymmetric water waves

The equation for non-linear water waves in shallow water with cylindrical symmetry is established in the form of the Extended KdV (EKdV) equation. The method of solution is based on the Split Step Fourier Algorithm. It is applicable in both directions; that is, given a wave record near the origin, the theory predicts the wave evolution. Similarly, given a wave record at a distance from the origin, the method is able to predict the original wave near the origin. Theory is applied to and verified by transient wave records obtained from underwater explosions and by dropping a large cylindrical plate in very shallow water. The difference between the KdV and the Extended KdV equation is emphasized for small valuev of Ursell parameter.     

Long non-linear waves in a confined basin, induced by transient atmospheric disturbances

In the non-linear statement, the paper studies long waves induced in a confined basin of variable depth by a low atmospheric pressure area, translating at constant speed over the basin. The study is conducted in terms of a non-stationary finite-difference model. Emphasis is made on the behaviour of the wave process after the departure of the disturbance. The dependence of the modal composition of fluid oscillations on the basin parameters and baric disturbances is determined. Translated by Vladimir A. Puchkin.     

Numerical simulation for the two-dimensional nonlinear shallow water waves

This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.     

Finite element analysis of ship structures using a new stiffened plate element

A new stiffened plate element is developed for the three-dimensional finite element analysis of ship structures. The plate element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. The new element provides a very economic global analysis of the complete ship structure with fewer elements and without any loss of accuracy. The global analysis of a rectangular box shaped vessel is carried out with the present element and compared with the general-purpose finite element software NISA. An Offshore Tug/Supply Vessel is analysed for crest at perpendiculars.     

A note on the derivation of potential energy for two-dimensional water waves

The potential energy available in a two-dimensional progressive water wave can be calculated in numerous ways. One derivation of this energy based on the first law of thermodynamics and on the linearized velocity potential for waves, is presented in this paper. The energy densities and total energy expressions are given for deep and finite depth water waves. It is also shown that the travelling component of the energy for deep water waves is the potential energy component.     

Finite element analysis of flow control using porous media

A finite element model is established for simulating flow in and out a porous media. The extended Darcy equation inside the porous media and the Navier–Stokes equations in the fluid are coupled via the continuity condition at the interface between the two media. The model is firstly validated against the analytical and the numerical results available in literature. Then it is applied to simulate flow past a circular cylinder covered by a porous layer. The effect of the porous layer on the reduction of lift coefficient is investigated numerically. It is found that the lift reduction can be achieved by properly choosing the porous material. However, the amount of reduction greatly depends on the Reynolds number, the permeability and the Forchheimer coefficient.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

具有裂纹损伤桩腿的海洋石油平台有限元分析

采用有限元分析方法和断裂力学方法,将含裂纹构件的裂纹以线弹簧处理,建立了带有裂纹损伤桩腿的等效梁和管单元的单元刚度矩阵的计算方法。对检验方法的正确性,使用该方法对几种损伤构件进行了强度计算,并与有限元细化网格计算结果和实验结果进行比较,最后将等效单元计算程序接入大型有限元程序ＳｕｐｅｒＳＡＰ,对受损后的平台整体结构进行了应力计算和强度分析。     

The coupled finite element and boundary element analysis of nonlinear interactions between waves and bodies

A coupled finite element (FEM) and boundary element (BEM) method is developed to analyse the nonlinear interaction between bodies and water waves. The former is used away from the body while the latter is used in a region near body. The combination is based on consideration of the efficiency of FEM and BEM in computation and mesh generation, respectively. Results for wave/body interactions are obtained by using auxiliary functions to decouple the mutual dependence of the body acceleration and the wave force.     

Generalized boussinesq model for periodic non-linear shallow-water waves

This paper presents the development of a generalized Boussinesq (gB) model for the periodic non-linear shallow-water waves. An incident cnoidal wave solution for the gB model is derived and applied to the wave simulation. A set of radiation boundary conditions is also established to transmit effectively the cnoidal waves out of the computational domain. The classical solutions of the second-order cnoidal waves are discussed within the content of the KdV equation and the generalized Boussinesq equations. An Euler's predictor-corrector finite-difference algorithm is used for numerical computation. The propagation of normally incident cnoidal waves in a channel is studied. The simulated wave profiles agree well with the analytical results. The temporal and spatial evolution of an obliquely incident cnoidal wave is also modelled. The phenomenon of Mach reflection is discussed.     

离岸深水全直桩码头承载性能有限元分析

全直桩码头是适于软土地基上离岸深水海域的新型高桩码头结构型式,其承载机理与传统高桩码头存在较大差异,且软土地基循环软化效应显著。建立全直桩码头结构与地基相互作用三维弹塑性有限元模型,基于二次开发采用拟静力法对土体循环软化效应进行模拟。通过有限元模型研究全直桩码头的承载特性与破坏模式,并探讨水平极限承载力的影响因素。研究表明水平荷载作用下,基桩的塑性破坏是结构失稳的控制因素,地基土体的承载力对结构水平极限承载力不起决定性作用;竖向荷载作用下,结构竖向极限承载力由地基土体强度决定。研究范围内入土深度对结构水平极限承载力影响不大,但桩壁厚度减小或考虑土体软化后,结构水平极限承载力明显降低。设计中,增加入土深度可有效减小土体软化引起的水平极限承载力降低程度,且应考虑结构腐蚀和土体软化对水平极限承载力的双重降低效应,为钢管桩预留足够的腐蚀富裕量。     

Probability density functions for non-linear random waves and responses

Non-linear waves have been a research topic for a long time, but have not yet entered common ocean engineering practice. In this article the problem of calculating the probability density function (pdf) for non-linear waves is investigated. The ‘saddle point approximation’ is applied to a second-order wave model to estimate the pdf. The performance of the approximation is compared with the performances of the more commonly used methods for different types of input spectra. In addition, a non-parametric transformation method, with extrapolation of the level crossing intensity, is proposed to estimate the pdf. One simulation and three different data sets are used to investigate the performance of the model.     

Efficient computation method for two-dimensional nonlinear waves

I~IOWNUmerics wave tank is a ~ tOOl by which variouS nonlinear wave - ac interactionpwhleln can be treated in time domain. As the face stage, we f~ our efforts on the devious of an effita saution tee~ of fully nofor waves. aam numtried of water - wavesconnected PwhlemS, es~ in a wave tank, is alwayS comas Of PartS: wave generation, P~ and a~. The effi~ Of a nUm~ wave tankdepends not Only on the qwhty Of the wave abotion tecboaue, which allowS the lOng times~ and keePS finite tank leng…     

Numerical analysis and visualization of fine structures of the fields of two-dimensional attached internal waves

In the linear approximation, we compute the patterns of two-dimensional perturbations formed in a viscous exponentially stratified fluid in the process of motion of a plate at an arbitrary angle to the horizon. The exact solution of the problem obtained in quadratures and satisfying the physically meaningful boundary conditions is numerically analyzed. The properties of the fields are computed and described in broad ranges of all parameters of the problem, including the length and velocity of motion of the plate, the characteristics of stratification and viscosity of the medium, and the slope of the path. In the picture of currents, we distinguish two groups of waves and compact nonwave singularities near the edges of a source of generation. The results of comparison with the available data of independently performed calculations and experiments reveal the existing agreement between the computed and observed pictures of the currents.     

The second order spectrum of two-dimensional random waves

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Spar平台硬舱结构弯曲极限强度有限元分析

Spar是一种新型的深海油气资源开发平台,由于结构比较复杂,平台硬舱结构的弯曲极限强度很难用常规的理论方法进行计算。采用非线性有限元分析方法,分析结构构件、边界及载荷条件对硬舱结构弯曲极限承载能力的影响。结果表明:单舱段和两舱段的极限弯矩计算结果基本一致;当弯矩载荷方向平行中心井对角线方向时,结构的抗弯强度较弱;重力载荷对舱段的极限弯矩影响较小;结构内部的环向框架能显著提高舱段的抗弯强度。