Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.     

INTERNAL SOLITARY WAVE IN TWO-LAYER FLUID SYSTEM TOWARDS SHELF

The propagation of an interracial solitary wave in a two-layer fluid system with fixed upper surface to shelf isdiscussed.The numerical results of the Boussincsq model show the fission of the solitary wave,the reflected wavesby the slope and their dependence on the shelf height and slope.It is shown that the amplitude of the first transmit-ted solitary wave fully developed is esscentially independent of the bottom slope.     

NUMERICAL SIMULATION OF SOLITARY WAVE RUN-UP AND OVER-TOPPING USING BOUSSINESQ-TYPE MODEL

In this article,the use of a high-order Boussinesq-type model and sets of laboratory experiments in a large scale flume of breaking solitary waves climbing up slopes with two inclinations are presented to study the shoreline behavior of breaking and non-breaking solitary waves on plane slopes.The scale effect on run-up height is briefly discussed.The model simulation capability is well validated against the available laboratory data and present experiments.Then,serial numerical tests are conducted to study the shoreline motion correlated with the effects of beach slope and wave nonlinearity for breaking and non-breaking waves.The empirical formula proposed by Hsiao et al.for predicting the maximum run-up height of a breaking solitary wave on plane slopes with a wide range of slope inclinations is confirmed to be cautious.Furthermore,solitary waves impacting and overtopping an impermeable sloping seawall at various water depths are investigated.Laboratory data of run-up height,shoreline motion,free surface elevation and overtopping discharge are presented.Comparisons of run-up,run-down,shoreline trajectory and wave overtopping discharge are made.A fairly good agreement is seen between numerical results and experimental data.It elucidates that the present depth-integrated model can be used as an efficient tool for predicting a wide spectrum of coastal problems.     

CHEBYSHEV FINITE SPECTRAL METHOD FOR 2-D EXTENDED BOUSSINESQ EQUATIONS

In this article,an accurate Chebyshev finite spectral method for the 2-D extended Boussinesq equations is proposed.The method combines the advantages of both the finite difference and spectral methods.The Adams-Bashforth predictor and the fourth-order Adams-Moulton corrector are adopted for the numerical solution of the governing differential equations.An efficient wave absorption strategy is also proposed to effectively absorb waves at outgoing wave boundaries and reflected waves from the interior of the computational domain due to barriers and bottom slopes at the incident wave boundary to avoid contamination of the specified incident wave conditions.The proposed method is verified by a case where experimental data are available for comparison for both regular and irregular waves.The case is wave diffraction over a shoal reported by Vincent and Briggs.Numerical results agree very well with the corresponding experimental data.     

NUMERICAL STUDIES OF INTERNAL SOLITARY WAVE GENERATION AND EVOLUTION BY GRAVITY COLLAPSE

In this study, an analysis on the internal wave generation via the gravity collapse mechanism is carried out based on thetheoretical formulation and the numerical simulation. With the linear theoretical model, a rectangle shape wave is generated andpropagates back and forth in the domain, while a two-dimensional non-hydrostatic numerical model could reproduce all the observedphenomena in the laboratory experiments conducted by Chen et al. (2007), and the related process realistically. The model resultsfurther provide more quantitative information in the whole domain, thus allowing an in depth understanding of the correspondinginternal solitary wave generation and propagation. It is shown that the initial type of the internal wave is determined by the relativeheight between the perturbation and the environmental density interface, while the final wave type is related to the relative height ofthe upper and lower layers of the environmental fluid. The shape of the internal wave generated is consistent with that predicted bythe KdV and EKdV theories if its amplitude is small, as the amplitude becomes larger, the performance of the EKdV becomes betterafter the wave adjusts itself to the ambient stratification and reaches an equilibrium state between the nonlinear and dispersion effects.The evolution of the mechanical energy is also analyzed.     

PROPAGATION AND BREAKING OF WAVES ON SLOPING BEACH

In this paper the propagation and breaking of the solitary wave,the sinusoidalwave and the second Stokes wave on a slope of 1/30 are discussed based upon the TUMMACmethod,and the velocity fields of breaking waves on the slope are obtained by using the tracingmethod.The.numerical results for wave deformation are in good agreement with experimentaldata,and the breaker indexes depending on the kinetic criterion agree approximately with previ-ous results.Furthermore,compared with the experimental results measured by Iwagaki and bythe authors,the tendency of velocity distribution of breaking waves computed by this numericalmethod is also satisfactory.     

Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.     

Numerical and experimental study of internal solitary wave loads on tension leg platforms

With the large-scale density stratified tank and the numerical flume proposed,series of numerical cases in line with the experiments are carried out to investigate the interaction between the tension leg platforms(TLPs)and the internal solitary waves(ISWs).The waveforms,and the loads and the torques on the TLP obtained by the experiments and the simulations agree well with each other.Experimental results show that the amplitudes of the dimensionless horizontal force and torque linearly increase with the dimensionless amplitude,while that of the vertical force increases in a parabolic curve.Besides,the numerical results indicate that the horizontal and vertical forces on the TLP due to the ISWs can be divided into three components,namely,the wave pressure-difference forces,the viscous pressure-difference forces,and the frictional force that is negligible.The wave pressure-difference forces are always the major constituents.However the viscous pressure-difference component is unimportant,it is negligible as compared with the vertical forces.     

SPECTRAL ANALYSIS OF RANDOM WAVE UPLIFT FORCE ON A HORIZONTAL DECK

This article presents a spectral analysis of wave uplift loads on a horizontal deck.The wave uplift force spectrum on the underside of the deck is obtained.It is shown that the wave uplift force spectral density decreases with the increase of the relative clearance1/3Δh /H.The influences of different incident wave parameters,including the relative wave height1/3H /d,the relativedeck width/sB L and the relative clearance1/3Δh /Hon the dimensionless zeroth spectral moment of the uplift forces arediscussed.It is found that the zeroth spectral moment of the uplift forces increases with the increase of the relative wave height1/3H /d,and decreases with the increase of the relative clearance1/3Δh /H.A new dimensionless prediction model for the zerothspectral moment of wave uplift loads on the deck is proposed and the relationship between the wave uplift forces and the zerothspectral moment of the uplift force are obtained.     

NONLINEAR INTERFACIAL CAPILLARY-GRAVITY WAVES IN SHEAR FLOW

In this paper,the capillary-gravity solitary waves in a two-fluid system withshear flow are theoretically investigated.Three cases are considered.For the first case(the nor-mal case),the KdV equation,with the effect of shear flow being taken into account,is derivedand it is found that there may exist single mode travelling solitary waves,slowly travelling soli-tary waves and even more slowly travelling solitary waves at some shear flow conditions.Thesecond case considered is that the fluid system is at the first kind critical condition.The modifiedKdV equation in which the cubic nonlinearity balances the dispersion is obtained and the solutionof mKdV solitary wave in shear flow is put forward.The third case is that the fluid system is atthe second kind critical condition.The generalized KdV equation with the effect of shear flowconsidered is given.It is shown that there exist normal and oscillatory solitary waves and thecondition of existence of oscillatory solitary waves are also presented.     

大型海洋结构物的非线性绕射效应

本文在空间上应用面源法,在时间域上应用步进法,数值处理了三维物体与非线性波浪的相互干扰,研究了结构物的非线性绕射效应。首先,作为比较,求解了正弦波列和孤立波绕射垂直桩柱的情形。接着,进一步求解了大振幅波浪绕射固定在自由面上的大型浮动码头的工程实例。结果表明,非线性波浪绕射力与线性结果,有一定的差别。有时,尽管从总体效应来看,这种差别不十分明显,但从上浪、出水和波的爬高以及局部应力等局部效应来看,这种差别可能很明显。     

浅海人工岛波浪爬高的数值计算和实验验证

本文基于孤立波理论研究了浅海波浪对人工岛的非线性绕射，提出了采用有限差分法和有限远开边界的幅射条件计算人工岛上波浪爬高的数值模型，得到的数值计算结果与整体模型试验的实测结果进行了比较，二者吻合较好，为人工岛工程设计提供了可靠的高度参数。     

Application of artificial neural network to calculation of solitary wave run-up

The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering,but the calculation precision is limited in the existing models.For improving the calculation precision,a solitary wave run-up calculation model was established based on artificial neural networks in this study A back-propagation(BP)network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor.The model was applied to calculation of solitary wave run-up.The correlation coefficients between the neural network model results and the experimental values was 0.9965.By comparison with the correlation coefficient of 0.9635,between the Synolakis formula calculation results and the experimental values,it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave run-up.     

孤立波作用下组合型港池共振响应的数值研究

港池受到孤立波入射时会在港池内激发多种模态的共振响应。为进一步研究不同平面布置形式港池的响应特性和共振规律,建立不同内外港池长度和连接位置的组合型港池,采用基于Boussinesq方程的波浪数值模型MIKE 21-BW模拟了孤立波作用下组合型港池的共振响应,对数值模拟的结果进行频谱分析和波幅分布测定并与现有理论值比较。结果表明,孤立波正向入射组合型港池激发的主要响应模态的频率和与其长度相等的细长港池的理论固有频率接近,各主要共振模态的振幅与内外港池的长度和两港池口门的距离有密切关系;波浪入射方向和港池内边界反射条件的改变对狭长组合型港池中形成的各共振模态的形状影响不大,但是增大港池宽度会使港池内激发明显的横向共振。最后提出了消减港湾共振的平面布置形式,可为实际工程设计提供指导。     

有限深两层流体中内孤立波传播演化理论模型研究

该文对Choi和Camassa给出的一个内孤立波方程模型中的系数进行了修正,并给出了基于方程的内孤立波定态解表达式,将其称为内孤立波me Kd V理论解,进而采用有限体积/有限差分混合方法数值求解内孤立波的三类(Kd V、e Kd V和me Kd V型)非线性传播演化方程,分别以内孤立波的Kd V、e Kd V、MCC和me Kd V定态解作为初始输入波,研究其非线性传播演化特性,并获得其适用性条件。结果表明,三类非线性传播演化方程,只适合于相应内孤立波定态解初始波的定态传播,而对其他定态解初始波将发生波形变形、分裂等非线性现象。在此基础上,定量地给出了三类非线性传播演化方程的适用性条件,为采用何种非线性方程来研究实际海洋中内孤立波的传播演化问题提供了理论依据。     

A 3-D numerical study of solitary wave interaction with vertical cylinders using a parallelised particle-in-cell solver

This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.     

孤立波与潜水台阶相互作用的数值研究

本文用完整二维Navier-Stokes方程和VOF方法研究孤立波与潜水台阶障碍物相互作用问题.本文的计算结果与Seabra-Santos,Penouard and Temperville(1987)的实验结果有较好的一致性,与Germain(1984)基于势流浅水理论的结果较为接近,同时能更好模拟出前传演化波的衰减.只要给出初始孤立波波幅,静水深和潜水台阶障碍物的高度,利用本文方法就能模拟出演化波、分裂波和反射波的波形,并给出每一时刻的自由面形状、流场、涡量和压力的分布.