基于光滑质点流体动力学方法数值波浪水槽研究

基于光滑质点流体动力学(smoothed particle hydrodynamics,简称SPH)方法建立二维数值波浪水槽,利用推波板造波生成孤立波和不规则波,模拟结果跟实验值及解析解做了对比分析,结果令人满意.SPH数值水槽中生成的波浪具有明显的非线性,波浪能量沿程有所衰减,与物理水槽结果吻合良好.     

基于Boussinesq数值模型的波浪速度垂向分布模拟研究

在Liu和Fang推导的双层Boussinesq方程基础上,将其简化为一层水波方程,并建立了基于混合4阶Adams-Bashforth-Moulton时间格式的立面二维数值模型;数值模拟了波浪在潜堤上的演化过程,并将数值计算结果与相关实验结果进行了对比,验证了该数值模型的正确性。进而在不同的入射波条件下,将沿着水深分布的水平速度和垂向速度的数值模拟结果与线性、二阶、三阶解析解解析结果进行综合对比。对比结果表明,在不同的无因次水深kh条件下,数值解与解析解的整体吻合程度较好。在不同的波陡H/L条件下,数值解展现了较好的非线性特征。在不同的波高水深比H/h条件下,数值解与解析解之间的整体差异较小。可以看到,该数值模型较好地模拟了波浪垂向速度场分布,体现了其优良的综合性能。     

强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

波浪产生和运动的二阶计算模型

在快速模拟波浪运动的谱方法基础上,引入造波边界,建立了模拟波浪产生和运动的二阶计算模型。采用摄动展开方法简化了带有造波边界的水波运动问题,将速度势分解,得到了满足造波边界和自由面边界的速度势的一般解,运用快速Fourier变换和时间积分,建立了模拟波浪产生和运动的数学模型。基于该模型,采用不同的数值造波条件,模拟了波浪的产生问题;考虑了波浪的初始运动问题;通过把数值结果与物理实验的比较,验证了波浪计算模型的有效性。     

波浪漫滩边界对波生流数值计算的影响

波浪漫滩是近岸波浪的小尺度运动,在实际海域的波生流数值计算中通常被忽略。本文基于Boussinesq方程的FUNWAVE模式,分别采用波浪漫滩边界、固壁边界、海绵边界进行Haller波浪港池物理模型实验的数值模拟,比较三种边界计算结果与实验观测数据的误差,检验波浪漫滩边界对波生流数值计算的影响;然后设计了多种周期、波高的波生流数值模拟试验,分析多种波浪入射条件下波浪漫滩边界对近岸波生流数值计算的影响。结果表明,波浪漫滩对邻近区域波生流有明显影响,漫滩边界下的波生流计算结果更接近实验观测值,在近岸波生流数值模型中引入波浪漫滩边界可以提高波生流计算精度。     

非线性波传播的新型数值模拟模型及其实验验证

以一种新型的Boussinesq型方程为控制方程组,采用五阶Runge-Kutta-England格式离散时间积分,采用七点差分格式离散空间导数,并通过采用恰当的出流边界条件,从而建立了非线性波传播的新型数值模拟模型.通过对均匀水深水域内波浪传播的数值模拟说明,模型能较好地模拟大水深水域和强非线性波的传播.通过设置不同的入射波参数来进行潜堤地形上波浪传播的物理模型实验,并将数值解与物理模型实验结果进行了比较.     

波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

三维完全非线性波浪水槽的数值模拟

用有限元求解拉普拉斯方程,建立了三维完全非线性数值波浪水槽.跟踪流体自由表面的方法为满足完全非线性自由表面条件的半拉格朗日法,对离散单元采用20节点的六面体二次等参数单元.并把数值计算结果与水面初始升高产生箱体内流体运动解析解和二阶斯托克斯波理论解进行了对比,结果表明该模型是稳定的、守恒的,能精确模拟非线性波浪的产生和传播.     

台阶式变深水槽造波的解析研究

利用特征函数展开法对台阶式变深水槽中推板式造波机造波问题进行了研究,建立了相应速度势和波面的解析表达式。与高阶边界元方法(HOBEM)数值结果进行了对比,验证了本解析解的正确性。通过数值试验,研究了台阶对入射波的影响,同时分析了造波板所在位置(上部台阶)水深、水槽工作区(下部台阶)水深、造波板运动周期和造波板水平位置等因素对生成波浪高度的影响。由此选择合适的造波板所在位置及水深来得到所需要的波浪高度,进而根据需要生成波浪的周期和波幅来反演造波板的运动。     

台阶式变深水槽造波的解析研究台阶式变深水槽造波的解析研究

利用特征函数展开法对台阶式变深水槽中推板式造波机造波问题进行了研究,建立了相应速度势和波面的解析表达式。与高阶边界元方法(HOBEM)数值结果进行了对比,验证了本解析解的正确性。通过数值试验,研究了台阶对入射波的影响,同时分析了造波板所在位置（上部台阶）水深、水槽工作区（下部台阶）水深、造波板运动周期和造波板水平位置等因素对生成波浪高度的影响。由此选择合适的造波板所在位置及水深来得到所需要的波浪高度,进而根据需要生成波浪的周期和波幅 来反演造波板的运动。     

多消浪室局部开孔沉箱防波堤反射特性的迭代解析研究

基于势流理论,对多消浪室局部开孔沉箱防波堤的反射特性进行解析研究。研究中采用开孔墙处的二次压力损失边界条件,可以直接考虑波高对于开孔墙处能量损失的影响。利用匹配特征函数展开法和迭代方法得到当前问题的解析解。收敛性验证表明,迭代计算和级数解均具有良好的收敛性。该解析解的计算结果与分区边界元的数值计算结果一致,并且与已有的试验结果符合良好。通过算例分析,研究开孔沉箱防波堤反射系数的主要影响因素。结果表明：与单消浪室开孔沉箱防波堤相比,多消浪室开孔沉箱防波堤可以在更宽的波浪频率范围内保持低反射;增大开孔墙的开孔率,有利于降低多消浪室开孔沉箱防波堤的反射系数;当开孔墙的开孔率沿着入射波方向依次递减时,多消浪室开孔沉箱防波堤的反射系数较小。本文所建立的解析模型简单可靠,可用于工程初步设计中分析开孔沉箱防波堤的水动力性能。     

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.     

Wave-induced surge motion of a tension leg structure

An analytical solution for the coupling problem of a two-dimensional tension leg structure interacting with a monochromatic linear wave train in an inviscid and incompressible fluid is presented. The tension legs are considered to be linearly elastic. The flow is further assumed to be irrotational and single-valued velocity potentials can then be defined.The boundary value problem is incorporated into a scattering and a radiation problem. The boundary value problems are then solved separately and combined to resolve all unknowns. The complete solutions of the velocity potentials are represented by the series of eigen-functions, and the surge motion of the structure is described in terms of the incident wave properties.The analytical solution is compared with a computer-coded numerical solution utilizing the boundary element method. The solutions agree very well, and both predict a resonant frequency for a specific structure which is different from the natural frequency of the structure due to the presence of the evanescent waves caused by the structure.     

Transparent boundary condition for simulating nonlinear water waves by a particle method

Open boundaries are important when simulating water waves. In this study, a transparent boundary condition at an open boundary was developed for simulating nonlinear water waves propagating to a distant area using the Moving Particle Semi-implicit method. The novelty of this study is that the technique of wave analysis used in the experiment was introduced into the particle simulation to absorb incident waves; the simulation cost was reduced by employing inflow and outflow regions instead of a long dissipation region. Incident waves in front of the boundary were evaluated using Fourier analysis, and the particles on the transparent boundary were forced to move at the velocity of the analytical solution for Stokes waves in order to absorb the incident waves. The analysis was restricted to periodic waves. Wave propagation was simulated for two wave periods using the developed transparent boundary condition. The results showed that this transparent boundary transmitted the incident waves with small reflection and the simulation cost was lower than that for wave damping by a conventional highly viscous region.     

Wave dispersion study for tsunami propagation in the Sea of Marmara

In this paper the aim is to investigate whether there are differences between the dispersion and non-dispersion solutions on tsunami propagation. For this purpose, two numerical models of tsunami propagation are compared. One of these numerical models is a nondispersive model that uses Saint Venant equations and the other is a dispersive model that uses Boussinesq equations. The tsunamis resulting from a submarine mass failure (SMF) which is settled at the bottom of the north eastern Sea of Marmara are examined. An analytical solution considering wave dispersion is developed for obtaining near-field tsunami amplitudes above the submarine mass failure. Numerical modeling is used at the sea surface from the common boundary called as liquid boundary with incident waves up to the coastal regions to get the tsunami amplitudes. The output of the analytical model is taken as the disturbances for the numerical method. In the numerical solutions TELEMAC-2D software system is used for both dispersive and nondispersive modeling. The results of the dispersive and nondispersive models are compared to each other. Both temporal and spatial differences in the amplitudes and wave shapes are examined. The obtained results demonstrate that there are no noticeable differences between the dispersion and non-dispersion solutions except some special cases and some special landslide velocities.     

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

An active wave generating–absorbing boundary condition for VOF type numerical model

The objective of the present work is to discuss the implementation of an active wave generating–absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces. First an overview of the development of VOF type models with special emphasis in the field of coastal engineering is given. A new type of numerical boundary condition for combined wave generation and absorption in the numerical model VOFbreak² is presented. The numerical boundary condition is based on an active wave absorption system that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The digital filters are derived theoretically and their practical design is discussed. The practical use of this numerical boundary condition is compared to the use of the absorption system in a physical wave flume. The effectiveness of the active wave generating–absorbing boundary condition finally is proved using analytical tests and numerical simulations with VOFbreak².     

Simulation of Fully Nonlinear 3-D Numerical Wave Tank

A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order bouodary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.     

The influence of seaward boundary conditions on swash zone hydrodynamics

The influence of the seaward boundary condition on the internal swash hydrodynamics is investigated. New numerical solutions of the characteristics form of the nonlinear shallow-water equations are presented and applied to describe the swash hydrodynamics forced by breaking wave run-up on a plane beach. The solutions depend on the specification of characteristic variables on the seaward boundary of the swash zone, equivalent to prescribing the flow depth or the flow velocity. It is shown that the analytical solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. J. Fluid Mech. 16, 113–125] is a special case of the many possible solutions that can describe the swash flow, but one that does not appear appropriate for practical application for real waves. The physical significance of the boundary conditions is shown by writing the volume and momentum fluxes in terms of the characteristic variables. Results are presented that illustrate the dependence of internal flow depth and velocity on the boundary condition. This implies that the internal swash hydrodynamics depend on the shape and wavelength of the incident bore, which differs from the hydrodynamic similarity inherent in the analytical solution. A solution appropriate for long bores is compared to laboratory data to illustrate the difference from the analytical solution. The results are important in terms of determining overwash flows, flow forces and sediment dynamics in the run-up zone.     

Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.